help-13

[cedar kiln]

Channel closed

Closed by @old fjord

Use .reopen if this was a mistake.

[cedar kiln]

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.

[pseudo merlin]

Hi my classmate wants to ask

[cedar kiln]

Please don't occupy multiple help channels.

[pseudo merlin]

For this question is it right

[fluid pulsar]

,rotate

[pseudo merlin]

?

[grizzled plank]

rotating pic

[pseudo merlin]

do u know if its right

[grizzled plank]

trying to see

could u rotate this

[pseudo merlin]

,rotate

[rose olive]

looks good to me

[pseudo merlin]

wait can u pls walk me through what he did

i dont get what he did

[grizzled plank]

i can see cross multiplication

[pseudo merlin]

if u prove it like that?

dont u need to work in reverse

[grizzled plank]

hm

[pseudo merlin]

because u cant prove a statement by assuming the statement is true

[grizzled plank]

im also confused lol

[pseudo merlin]

i hate this logic ass math

y cant i go back to pythagoras theorem

[grizzled plank]

math

[pseudo merlin]

me i got 100% on that test 😎

[stiff vigil]

its quite easy, just look from (a-b)^2>=0

then a^2-2ab+b^2>=0

a^2+b^2>=2ab

a^2+2ab+b^2>=4ab

(a+b)^2>=4ab

[grizzled plank]

where is >= 0

[pseudo merlin]

so he has to work in reverse

to avoid working in reverse

[stiff vigil]

oh its basically that any square of a real number is greater than or equal to 0

[pseudo merlin]

cant i just be like

say a+b/2 - 2ab/a+b

and then at the end be like

since it is >0 then a+b/2 is greater than 2ab/a+b

[stiff vigil]

then how is (a+b)/2 greater than 2ab/(a+b)?

[pseudo merlin]

because when we subtract it

it is >0 than 0

therefore a+b/2 is greater than 2ab/(a+b)

[stiff vigil]

but how do u know that its >0

it could be <0

[pseudo merlin]

ok let me do it

[grizzled plank]

is there a way to make them common denominators

[stiff vigil]

wdym?

[pseudo merlin]

for a and b are 2 positive real numbers

can i just do that instead

or no

oh wait

i can further simplify it

nvm i cant

[stiff vigil]

wait, did u just rearrange the equation in the question?

and show how the expression on the left is >=0

[pseudo merlin]

uh

i think idk

is that wrong

[stiff vigil]

no its not wrong

[pseudo merlin]

i feel like in this way i dont need to work backwards like how my friend did it

so it saves me more time

[stiff vigil]

yeah u dont need to work backwards

just use (a-b)^2>=0

[pseudo merlin]

how about the denominator?

nvm

i am stupid

[stiff vigil]

lets say you started with (a-b)^2>=0

how would u expand it?

[pseudo merlin]

a^2 -2ba + b^2

[stiff vigil]

yes

then what happens if you add 2ab on both sides

[pseudo merlin]

ya i get it dwdwdwdwdw

[stiff vigil]

ok

[pseudo merlin]

i just wanted to help my friend

hahahaha

hes struggling very bad in the course

rip

[stiff vigil]

is it spesh math?

[grizzled plank]

i got the difference is (a+b)^2 - 4ab / 2(a+b)

[pseudo merlin]

tes

are u WA?

[stiff vigil]

no, im from VIC

[pseudo merlin]

y u still awake

go to sleep

[stiff vigil]

haha

[pseudo merlin]

yeh he might drop it

its too hard for him

and its really hard cuz our spesh teacher has a really really really

big chinese accent

[stiff vigil]

bruh

[pseudo merlin]

LOL

he used to be a calculus professor in china

[stiff vigil]

wow

he must be rlly smart then

[pseudo merlin]

yeh he just doesnt make sense

i had to get 3 days extra tutor after school

cuz hes so bad

ya ok thanks :P

[stiff vigil]

maybe just give your teacher another chance

idk

[pseudo merlin]

no i wont im getting sunday tutoring too

hes so bad

[stiff vigil]

oh no

[pseudo merlin]

30k school fees for what

[stiff vigil]

huh private school?

[pseudo merlin]

yea

[stiff vigil]

how hard does your friend find spesh math btw?

[pseudo merlin]

he doesnt understand a thing

bc he has no tutoring

every class he comes out mind boggled

and our periods are 1 hr long

[stiff vigil]

same

[pseudo merlin]

in yr 10 he was averaging 95%

hes a scholarship kid

[pseudo merlin]

oh

did u pass

we had a sign a contract

we have to get at least 55% in the course or they'll force us to drop

it

they review it in week 8 and end of sem 1

[stiff vigil]

i did really well

[pseudo merlin]

bruh

U SAID U GOT MIND BOGGLED

[stiff vigil]

nooo

what i meant was that our periods are also 1 hour long

lol

[grizzled plank]

i just found out how

[pseudo merlin]

ohh

[grizzled plank]

thats a interesting problem

[pseudo merlin]

what?

[stiff vigil]

is that your teacher?

[pseudo merlin]

yes

[stiff vigil]

he is alright

[pseudo merlin]

ok i need to go now

its my bed time

[stiff vigil]

sure

[pseudo merlin]

WAIT FIRST

[pseudo merlin]

tell me how

that is an EASY problem 😭

[grizzled plank]

i didnt think of cross multiplying

[pseudo merlin]

oh

[grizzled plank]

am dumb

[stiff vigil]

bruh it is easy though

[pseudo merlin]

noo ur not

theres a lot of ways to solvei t

the answer in my textbook is

answers will vary

[stiff vigil]

yeah there are probably many ways

[pseudo merlin]

ok anyways bye

[pseudo merlin]

also can i dm u for spesh help or nah

[stiff vigil]

cya

[stiff vigil]

sure, no prob!

[pseudo merlin]

ight thanks :D

.close

[cedar kiln]

Channel closed

Closed by @pseudo merlin

Use .reopen if this was a mistake.

[cedar kiln]

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.

[livid peak]

Hello could I get some help on 4a please Just need help on how to start it

[lean berry]

ln(a/b) = lna - lnb

Tag me if you need more hints or the full solution

[cedar kiln]

@livid peak Has your question been resolved?

[livid peak]

I’m guessing it would be pq^2 - root r

[lean berry]

Yes but there are more rules, like ln(a*b) = lna + lnb, and ln(x^n) = nlnx

When I struggle a bit I always write up all the rules I'm going to use. Makes me remember them better, and easier to reason with myself.

[livid peak]

Ah ok ty

[livid peak]

So would q1 just be what I said

Or is there more to it

[lean berry]

Well, if you want to express it in terms of lnp, lnq, and lnr, you'd want to get them all "alone"

There's more to it sadly 😄

[cedar kiln]

@livid peak Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[dusk goblet]

if the limit as n goes to infinity of a sequence isn’t zero this would mean the series diverges but does this always hold even if we have an alternating series

[flint plinth]

yes it does

[dusk goblet]

why does this say it converges

[flint plinth]

if the terms don't go to zero, the series doesn't converge, period

[dusk goblet]

the limit is 5/4

no?

using alternating series test

limit has to be zero

[flint plinth]

yep, they're completely wrong

[dusk goblet]

ok thanks i figured that was the case

.close

[cedar kiln]

Channel closed

Closed by @dusk goblet

Use .reopen if this was a mistake.

[cedar kiln]

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.

[maiden venture]

A body suspended at the point Q = (0, −2, −1) [m] weighs
with force F = (0, 0, −900)T
[N] on the three bear lines QP1,2,3, there
the support points have coordinates (ON coordinate system in [m]):
P1 = (1, −3, 2), P2 = (0, −1, 2) and P3 = (−1, −2, 2).
In the three ropes, tension forces f1,2,3 arise, directed along respectively
line. Determine these forces and state their magnitude in [N]. Finally,
which of the ropes is most loaded?

[maiden venture]

could anybody help me solve this?

[cedar kiln]

@maiden venture Has your question been resolved?

[maiden venture]

<@&286206848099549185>

[maiden venture]

.close

[cedar kiln]

Channel closed

Closed by @maiden venture

Use .reopen if this was a mistake.

[cedar kiln]

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 sedge]

can someone teach me about inequalities and how to solve them?

[crimson sedge]

$5x > 8x + 27$

[wraith dagger]

∑🪡﹐m!nj!　⟢

[crimson sedge]

so like

the algebra is the exact same stuff as if there was an equality sign instead

with a few extra if's

for example, if you multiply/divide both sides by a negative then you flip the > to be a < and vice versa

[crimson sedge]

ohh

okk

try like

isolating the x's

,align
5x &> 8x + 27 \{???} &>27

[crimson sedge]

what is ???

since we have to make it balance do you have to - 27 and 8

with 5

nope

what number makes 8x be 0 you think?

ok thats badly worded

i mean, what do you subtract with 8x to make it 0?

using 8?

wdym by that

8 - 8 is 0

ok but why are u removing the x

😭

but ok cool

8x - 8x = 0

so, subtract 8x from both sides of the inequality

what do you get

8x - 5x = -3x
8x - 27= -19x

please please dont remove the x's

like seriously

it is not unimportant

😭

sorry

but like

a lot of things went wrong here 😅

so like

you are subtracting 8x, but why did you put -5x instead?

8x - 5x = -3x
8x - 27= -19x

no but like

you cant do what u did in the second equation

you cant subtract non-like terms

like

2 + 2 = 4 (this is right)
2 + 2x = 4x (this is wrong)
2x + 2x = 4x (this is right)

oh so what do i do with 27?

just leave it chilling there for now

also

8x-5x is not -3x

so lets backtrack a bit

you have[
5x > 8x+ 27
]

[crimson sedge]

i want you to just subtract 8x from both sides

dont do anything else

wouldnt i use the non term to substrate both sides

which is 27

no

you dont

so how do you know which one you use...

well like

try and think of what you are trying to achieve

you have two terms with x

you want to turn them into one term with x

so you move 8x to the left to subtract it with 5x and turn it into one term

so you only use the side that has the same term?

wouldnt that be 3x

like

lemme make it a whole lot simpler for you:

you can add/subtract WHATEVER you want as long as you do it to both sides

but you said im not able to substract 27 cause its a non termmm

,texSo for example:
\env{align*}{
18x &= 2 + 3x \
18x \c b{-2} &= 2 + 3x \c b{-2}\
18x -2 &= 3x
}
but you can also could have done
\env{align*}{
18x &= 2 + 3x \
18x \c b{-3x} &= 2 + 3x \c b{-3x}\
18x -3x &= 2
}
Or even you could have added something completely different
\env{align*}{
18x &= 2 + 3x \
18x \c b{[phone]} &= 2 + 3x \c b{[phone]}\
18x [phone] &= 2 + 3x + 28828282
}

[crimson sedge]

The point is, you can add/subtract whatever the hell you want from both sides as long as you do it to both sides

alright

now, would be that meaningful always? No. For example, that 28828282 is making everything worse, but like, there is nothing wrong with what we did

anyways

just needed to clarify this

i gtg thank you tho

.close

[cedar kiln]

Channel closed

Closed by @raw kindle

Use .reopen if this was a mistake.

[crimson sedge]

with this, you can apply the same concept.

Our goal: we want to make the two terms with the two x's become one term

How to do that: we can subtact 8x from both sides because 8x - 8x = 0

[crimson sedge]

oh okay

[cedar kiln]

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 sedge Has your question been resolved?

[cedar kiln]

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.

[upbeat lagoon]

calc 2

[upbeat lagoon]

how did they get that for the sub? can someone explain that pls

[livid hound]

which part are you referring?

[upbeat lagoon]

integral of u^2 / u^2 +1

why did they substutte the integral like that

sub*

[livid hound]

results in something simpler than what they started with

substitution of a complex component may be helpful when integrating

[upbeat lagoon]

shouldnt it be the integral of u/x ?

[livid hound]

after choosing the sub, it's just going through the usual steps of getting the relationship between dx and du, and algebraic manipulation

[upbeat lagoon]

how did they get u^2

[livid hound]

well you'd want the entire thing in terms of a single variable

how are you getting Integral of u/x

[upbeat lagoon]

u = square root (x^2 +1 )

subsitute square root (x^2 +1 ) with u

[livid hound]

that'll result in
$$\int \frac {\blue{u}}{\red x} \dd{\red{x}}$$
when doing integration by sub, you'd want to express everything in terms of your new variable.

[upbeat lagoon]

so I have to express x as u as well?

[wraith dagger]

ℝαμΩℕωⅤ

[livid hound]

yes, everything

after substitution ,you shouldn't have any more x in your integral

[upbeat lagoon]

ok so how would I approach that for this problem? do I algebraically manipulate u = squareroot (x^2 -1) to get x alone?

[livid hound]

yes

well actually that's not quite needed here

[upbeat lagoon]

what do you mean

[livid hound]

applying the relationship between dx and du here will result in you having x^2

so you don't actually need to isolate x, just x^2

[upbeat lagoon]

this is what I wrote down to isolate the x^2

[livid hound]

where's the dx in your original integral

[upbeat lagoon]

I forgot but yes It should be there

I just wrote it next to it rn

[livid hound]

where is your dx in the stuff in the top right?

[upbeat lagoon]

its next to it hold on

ur gonna have to flip it

square rooting it would make it u + 1 for x

which would be u/ u+1 but in the answer key that got u^2/u^2 +1

why are they squared?

[livid hound]

how are you getting u+1 for x

[upbeat lagoon]

sorry

that waas wrong

u + 1 was wrong

so we get x^2 = u^2 + 1

we have to square the numerator as well?

[livid hound]

no, did you apply the relationship between du and dx?

[upbeat lagoon]

du = x/squareroot(x^2-1) dx

do you mean solve for dx?

[upbeat lagoon]

kinda confused by what you mean by this

[livid hound]

yeh,

[upbeat lagoon]

ok ok

[livid hound]

after substitution ,you shouldn't have any more x in your integral

(anywhere)

that's what you should be currently aiming to do, do whatever is needed to achieve that

[upbeat lagoon]

do you think you draw this out for me on microsoft paint? applying the relationship between du and dx?

[livid hound]

dx = ?

[upbeat lagoon]

du =x/squareroot(x^2-1) dx

idk what dx equals

how do I get dx alone

[livid hound]

more or less the same way you'd solve for a variable in other equations

[upbeat lagoon]

ok

.close

[cedar kiln]

Channel closed

Closed by @upbeat lagoon

Use .reopen if this was a mistake.

[cedar kiln]

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.

[warm niche]

cos(x)=-24/25
what is cos(x/2)

[warm niche]

kindly ping me whenever a helper is here

<@&286206848099549185>

[undone cliff]

you can isolate the x in the top equation by doing arccos and then plug it into the 2nd equation

[warm niche]

that-
lemme try wait

[warm niche]

I have to find answer as a fraction

while that will give me the answer
it'll be an exact value

[undone cliff]

ohh

uh let me think for a second

[warm niche]

take ur time
I've been at it all day too 😭

[undone cliff]

there's definitely a way to do it

I just forget cuz the last time I did this was a long time ago

[warm niche]

well yes
and I'm sure it has something to do with the double angle formula but I can't wrap my head around how to do it

best bet is if I plug it in like so

would like a second opinion on this tho

[undone cliff]

didn't even know an equation existed for this

[warm niche]

it does

BUT

if I have a (x) outside instead of a (x/2)

the value inside is doubled

so the inside is gonna be a cos2x

but the answer I'm getting like this is also not very reliable so yes

[undone cliff]

im confused what you mean

isn't it just

$\sqrt{\frac{1+\frac{-24}{25}}{2}}$

[wraith dagger]

Panda

[undone cliff]

• or -

[undone cliff]

why sin

[warm niche]

it's sin and 3rd quadrant so it'll be a -

[warm niche]

just showing u an example of how the change will work

[undone cliff]

don't you just simplify this and get an answer?

[warm niche]

nope

wait

AAAA

lemme see

I'll test it out

nope
that's not it 😭

[undone cliff]

wdym

i got + or - 1/5sqrt(2)

$\pm \frac{1}{5\sqrt{2}}$

[wraith dagger]

Panda

[warm niche]

can we cross compare using this?

considering that it's in 3rd quadrant

[undone cliff]

yeah it's the same answer

[warm niche]

could you show me your working rq
I'm still a bit confused

[undone cliff]

sure

hold one on second

[warm niche]

sorry I wasn't very clear but I meant by this method

[warm niche]

thank you thank you

[cedar kiln]

@warm niche Has your question been resolved?

Channel closed

Closed by @warm niche

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.

[worldly walrus]

I'm not sure where to begin

[livid hound]

long division to decompose the fraction

[worldly walrus]

Ok

[drifting marlin]

!help

[cedar kiln]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[worldly walrus]

Sorry... are you able to help a little bit more? I'm not that great at math so I just need a bit more help

If u cant no worries

[cedar kiln]

@worldly walrus Has your question been resolved?

[raw gulch]

I wrote a very similar example for you, read it and do yours the same way

[cedar kiln]

@worldly walrus Has your question been resolved?

[worldly walrus]

Thanks! I got 2+5/x-1

.close

[cedar kiln]

Channel closed

Closed by @worldly walrus

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.

[soft copper]

Hey can someone help?

[wicked dune]

Did you try squaring?

[frigid wadi]

How would I do 1200 is deposited into an account that earns 7% compounded monthly. How long would it take to reach 1398.23

[wicked dune]

?

[frigid wadi]

oops

[soft copper]

Yes

[wicked dune]

So what did you get?

[cedar kiln]

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

[soft copper]

9/16 but it showed the answer was wrong

[plucky owl]

Can you show your work?

[wicked dune]

And what happens when you try to plug it back into the original equation?

[soft copper]

They had different answers they were -1.25 and 1.25 but the site doesn’t have an option for specifically plus or minus for x

[wicked dune]

Ok well -1.25 doesn't equal 1.25, does it?

So there are no solutions

Because we have checked that 9/16 is extraneous

[soft copper]

Well yes that’s what I thought as well but It was wrong

[wicked dune]

wdym?

[soft copper]

The site has an option for no solution but that wasn’t one of the options

[wicked dune]

Well the site is wrong idk what to say

https://www.wolframalpha.com/input?i=sqrt(x)+-2+%3D+sqrt(x%2B1)

[soft copper]

Yeah sucks I guess

[dire geode]

x = 9/16 is not a solution

Plug it into the original equation to see

[cedar kiln]

@soft copper Has your question been resolved?

[cedar kiln]

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.

[crimson sedge]

can someone please help

[crimson sedge]

im lost

[crimson sedge]

o

.close

[cedar kiln]

Channel closed

Closed by @high marten

Use .reopen if this was a mistake.

[cedar kiln]

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.

[fading knot]

i’m struggling hard and got 20mins left on my homework

<@&286206848099549185>

@wraith dagger

[cedar kiln]

@fading knot Has your question been resolved?

[cedar kiln]

@fading knot Has your question been resolved?

[cedar kiln]

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.

[slow jewel]

Is it 8% of total volume or of volume after each day?

Did you do part a?

So you took 8% of 5000m³ for every time it decreased is it?

Oh ok

Ya ik

[slow jewel]

I just had to get this clarified

So the volume that decreases after each day is 0.08*5000

What'll be the total volume decreased after say, x days?

But you said it was 8% decrease of 5000m³ each day

[cedar kiln]

Channel closed

Closed by @hearty bloom

Use .reopen if this was a mistake.

✅

[slow jewel]

Ohh

But for part b it's better to find the volume of water lost

Coz they have mentioned how much of it is lost, i.e, 3000m³

Right so

After day 1, volume of water lost is 0.08(5000)
After day 2, total volume lost it 0.08(5000)(2)
After day 3 it's 0.08(5000)(3) and so on..

Do you see why?

??

It loses 0.08(5000) each day
So after 2 days, it should be 0.08(5000)+0.08(5000)= 0.08(5000)(2), no?

Is that why you've taken 4 as the power here?

[cedar kiln]

@hearty bloom Has your question been resolved?

[cedar kiln]

@hearty bloom Has your question been resolved?

[cedar kiln]

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.

[dense cargo]

i know the answer intuitively but idk how to prove it

can someone guide me to find how the distribution for the joint pmf of nx might look like

[cedar kiln]

@dense cargo Has your question been resolved?

[dense cargo]

.close

[cedar kiln]

Channel closed

Closed by @dense cargo

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.

[dreamy falcon]

Would anybody like to help? Before I mess up the whole thing lol

[crimson sedge]

Have you learned the fundamental theorem of calculus

,,f(x)=∫ag(x)​h(t)dt

[wraith dagger]

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

[crimson sedge]

rip

[dreamy falcon]

oh yes

ftc

AHHH I FORGOT ABOUT FTC

a to b f(x)dx = F(x) int = F(b) - F(a)

right

something like that

thats what im doing right now but, im struggling with the part i last left off

it doesnt feel right

[crimson sedge]

yeah, im trying to find an image of the equation you need

[dreamy falcon]

for context, answer is F'(x) = 96x^11 + 12x^2

[crimson sedge]

yes it is

[dreamy falcon]

oh i have it in notes

[crimson sedge]

So what was the question lol?

[dreamy falcon]

yeah but im trying to find the steps to that answer

[crimson sedge]

ohh ok

[dreamy falcon]

If F(x) = integral (4) to (2x^3)... (2t^3 + 2) dt, Find F'(x)

is the question

(2t^3 + 2) is f(x) to be clearer

[crimson sedge]

@dreamy falcon does this help?

[dreamy falcon]

uh no not really lol

umm

referencing back to my imag

[dreamy falcon]

sorry for the verticality!!!

but the bottom part is hwere i left off

and i felt my steps so far are a bit off

[crimson sedge]

You aren't actually supposed to integrate at all

so back all the way up 😅

@dreamy falcon

[dreamy falcon]

oh crapppp//

lol sorry

[crimson sedge]

np

[dreamy falcon]

just pure FTC?

[crimson sedge]

this

[dreamy falcon]

i see

ashh thats why u put that there

i was so confused

i was trying to plug in integrated version into it lol

[crimson sedge]

plug things in to the bottom one

you are trying to find the derivative

[dreamy falcon]

thats right

[cedar kiln]

@dreamy falcon Has your question been resolved?

Channel closed

Closed by @dreamy falcon

Use .reopen if this was a mistake.

[cedar kiln]

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.

[wraith trellis]

cah someone help

proove this

[cedar kiln]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[wraith trellis]

.close

.close

[cedar kiln]

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.

[rustic verge]

Umm the question is kinda from programming, but I was just doing the math for it so ig ill ask.
If i have a system of things like a rotating screw and a rod attached to it. the rod's end point(p) is at p = p1 + l*(cos(a),sin(a)) where p1 is the position of the screw, l the length of the rod, and a the angle of rod/screw.
I want to change the angle so that p gets closer and closer to a desired position t.
ig it has something to do with gradients, like dp/da = (-l*sin(a), l*cos(a) but idk how to get the change needed in the angle from thereon
pls help

Edit1: and yeah i cant simply use cos-1(p.x/l) as i would have screws attached to rods which are attached to screws and so so......

[safe vessel]

Hi guys I need help

[rustic verge]

see #❓how-to-get-help

[safe vessel]

I see it

[rustic verge]

and yeah i cant simply use cos-1(p.x/l) as i would have screws attached to rods which are attached to screws and so so......

[sweet thicket]

.close

[rustic verge]

🗿

hi KProck22, I am KKrock07

[cedar kiln]

@rustic verge Has your question been resolved?

[cedar kiln]

@rustic verge Has your question been resolved?

[cedar kiln]

@rustic verge Has your question been resolved?

[cedar kiln]

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.

[swift saffron]

f(n) states the number of positive factors of n that have a value < 10 for example f(30) = 5 because 1,2,3,5,6 are factors of 30
Determine the value of f(1)+f(2)+...+f(2020)

[cedar kiln]

@swift saffron Has your question been resolved?

[swift saffron]

<@&286206848099549185> help

[cedar kiln]

@swift saffron Has your question been resolved?

[swift saffron]

<@&286206848099549185>

[queen ice]

That seems far off. 1 is a factor < 10 for all those numbers. So the answer must be at least 2020

[queen ice]

What have you tried

[valid adder]

I figured it out

It is 3685

[queen ice]

Im still getting a higher number

Im getting 3702 by only considering the factors 1, 2 and 3. it’s a lot higher when considering the other factors as well

[livid hound]

how are you getting that...?

[wheat ocean]

@swift saffron think about how many numbers from 1 to 2020 are divisible by 1, how many by 2, ..., how many by 9

[stiff vigil]

Is the answer 15694?

[stiff vigil]

Using this method, I performed the summand from n=1 to 2020 floor(2020/n)

[wheat ocean]

summation is by 9, we consider only factors <= 9

[stiff vigil]

Ohhh ok

I accidentally thought u had to count all the factors

Yeah

The summand is from 1-9

I am getting 5712 now

[queen ice]

That’s what I got as well I believe

[stiff vigil]

The answer is basically floor(2020/1) + floor(2020/2) + … + floor(2020/9) = 5712 I think

[queen ice]

That’s my intuition as well. I haven’t proved it to the degree that I can say I’m certain, but it seems to be the case

[livid hound]

think op completely abandoned this

[queen ice]

Seems so

[cedar kiln]

@swift saffron Has your question been resolved?

[cedar kiln]

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.

[deft mountain]

Can anyone explain how to graph log function

[small dust]

on what

like software or by hand

[deft mountain]

by hand

[rocky harness]

One easy way is if you know that inverses are reflections about the line y=x, and that the logarithm is the inverse of the exponential function. so knowing the graph of the exponential function is enough

[deft mountain]

I don't know the graph of the exponential function

[torn oriole]

then learn it

[rocky harness]

Thats tough

[small dust]

[deft mountain]

Uhhm? like this?

[rocky harness]

The blue is an exponential function, yes

[torn oriole]

bruh

[hot crag]

firstly, when we say $\log x$, we usually mean $\log_{10} (x)$

[deft mountain]

teach me

[wraith dagger]

ren

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

[hot crag]

what are you trying to do

[torn oriole]

logarithms have bases

[hot crag]

^^

$\log_{10} x$ refers to the amount that 10 must be raised to to get x as a result

[wraith dagger]

ren

[hot crag]

in other words, $10^{\log_{10} x}=x$

[wraith dagger]

ren

[torn oriole]

Whenever $a > 0$ is a positive real number such that $a \neq 1$ and $x > 0$ is a positive real number , we define $log_a(x) = L$ such that $a^L = x$

[wraith dagger]

Bishop

[hot crag]

and a more generalized result would be $a^{log_{a} (x)}=a$

[wraith dagger]

ren

[deft mountain]

lets say there is a function f(x) = $\log_{z} x$ = y

[wraith dagger]

Captain Random

[deft mountain]

So how to graph it

I'm asking that

[hot crag]

$z^{y}=x$

[wraith dagger]

ren

[deft mountain]

ok, how to plot it?

[hot crag]

well, it's the inverse of z^x

[deft mountain]

Shall I have to take samll values each for x, y and z?

[hot crag]

don't try that--won't work usually

[deft mountain]

so how does that work?

[hot crag]

it's $z^x$ reflected across the line x = y

[wraith dagger]

ren

[deft mountain]

What's the meaning of that?

[hot crag]

it's sorta like the mirror image of z^x, where the mirror is the line x = y

[hot crag]

an example

[deft mountain]

Oooh, like that?

[hot crag]

yep

[deft mountain]

so is z^x is plotted the same way as x^2 or there is another method?

[hot crag]

no...

10^x is not plotted the same way as x^2...

(i took z = 10 as an example)

[deft mountain]

ok, let me try

[hot crag]

okay

@deft mountain one thing

[deft mountain]

wait a bit

I'm switching devices

[hot crag]

keep in mind that $10^{n+0.5}$ is roughly equal to $3 \cdot 10^{n}$, so it increases differently--exponentially

[wraith dagger]

ren

[deft mountain]

Yes

[deft mountain]

Wait.... @hot crag do we need to differentiate the expression?

[hot crag]

what?

no ofc not

how would you incorporate derivatives when graphing by hand

[deft mountain]

Well that's a point

Ok, so I'm taking $\log_{10} x$ to plot the graph

[wraith dagger]

Captain Random

[hot crag]

okay

[deft mountain]

@hot crag

[hot crag]

ummm

one second

seems good ig

[deft mountain]

Thanks

.close

[cedar kiln]

Channel closed

Closed by @deft mountain

Use .reopen if this was a mistake.

[cedar kiln]

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.

[errant loom]

Hi, I’m using u substitution to find arc length and I got to the final part before plugging in my boundaries but I’m not sure how to get the answer that’s in the box. Did I mess up somewhere?

[runic garnet]

howd u go from $\frac 32 x^{\frac 12}$ to $\sqrt {\frac 32 x}$

[wraith dagger]

Stephen

[runic garnet]

the ^ 1/2 doesnt extend to the 3/2

but u squared it properly anyways so it doesnt really matter

[errant loom]

Oh yeah I meant to delete that part lol sorry

[runic garnet]

also, once you complete the integration, you should remove the integral symbol

when u went from u^ 1/2 to 2/3 u^ 3/2

[errant loom]

Ah okay got it will do that

[runic garnet]

also, whyd u sub u back in if u changed the bounds lol

thats prolly why its wrong

if u change the bounds, you dont need to plug u back in

[errant loom]

Oh really

What do I do with the final part I got after then?

[runic garnet]

yea, because the new bounds are only for the u

not for the x

just keep it as 8/27 u ^3/2

[errant loom]

Ohhh I see

That makes sense

[runic garnet]

then keep the bounds as 10 and 13/4

that should get you the correct answer

[errant loom]

I think I’m having trouble understanding how the algebra works after plugging that in to get the answer with the square roots and pulling the 1/27 out

[runic garnet]

so we have $\frac 8{27} u^{\frac 32} \eval_{\frac {13}{4}}^{10}$

[errant loom]

I think it was u^3/2 but right

[runic garnet]

yea mb

[wraith dagger]

Stephen

[runic garnet]

so now we get

$\frac 8{27} (10^ {\frac 32} - (\frac {13}{4})^{\frac 32})$

[wraith dagger]

Stephen

[errant loom]

Right

[runic garnet]

and theres ur answer

[errant loom]

Oh can I just leave it in that form?

[runic garnet]

i mean if ur teacher is ok with that

that seems fine to me

[errant loom]

Got it lol but there is a way to manipulate it further to get that boxed answer right

[runic garnet]

the boxed answer is correct?

[errant loom]

Yeah that’s what was on the answer sheet

[runic garnet]

ok if u distribute the 3/2 exponent to the 13 and the 4

u get 13^1.5 /8

$\frac 8{27} \cdot 10^{\frac 32} - \frac {13^{\frac 32}}{27}$

[wraith dagger]

Stephen

[errant loom]

Then the 8’s cancel to get 1/27 I’m guessing?

[runic garnet]

yea

[runic garnet]

thats how we got this

[errant loom]

Ah okay got it

[runic garnet]

yea i mean its the same numerical value when u put it in a calculator

that answer and the boxed answer

[errant loom]

Okay cool that should be fine then haha

Thank you for the help it was very informative!

.close

[cedar kiln]

Channel closed

Closed by @errant loom

Use .reopen if this was a mistake.

[cedar kiln]

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.

[lilac cobalt]

I don’t understand how to solve

[mighty shuttle]

multiply both sides by x-2 to begin

[lilac cobalt]

Ok

What next?

[livid hound]

multiply both sides by 5

[lilac cobalt]

Ok next?

[dusty hazel]

Subtract 30

[livid hound]

you should recognise you have a quadratic equation (with no fractions)

from here rearrange to general form and use common methods like
factorisation or quadratic formula to solve

[lilac cobalt]

5, -8 right?

[livid hound]

yes

[lilac cobalt]

Site says I’m wrong???

[livid hound]

ss, the site and what you're entering

[lilac cobalt]

It’s like a Google classroom forum sorta

Teacher says he makes em

Do u think he made a mistake or sum?

[livid hound]

maybe don't bother writing the x and/or list your values in ascending order

[lilac cobalt]

Nah both are wrong still

With or without X and ascending don’t matter

He probably just made a mistake

[livid hound]

or that bolded 3 is part of the question

[lilac cobalt]

No he like screen shots problems from the paper that other teachers print out for their students

[livid hound]

oh

ic

they want you to give one solution here

and the other below it in q6

[lilac cobalt]

I’m blind

Ight wtf

And swapped does not work.

[livid hound]

try with x=

[lilac cobalt]

It worked

Thx

.close

[cedar kiln]

Channel closed

Closed by @lilac cobalt

Use .reopen if this was a mistake.

[cedar kiln]

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.

[native viper]

We consider only such settings that person p1 will stand first in line for his checkout.
How many such settings are there?```

I probably find solution but I'm not sure its correct:

[fair geyser]

it's not clear if they mean no line is empty

it would make sense

180 is right if it's not implied that no line is empty

[native viper]

lines can be empty

[fair geyser]

yes 3×5c2 to choose how many people is in each line, times 3! = 180

hm

now i'm also not sure

[native viper]

yeh, weird task ;/

[mortal grove]

the way i would personally do it is by placing p1 in c1 first, then consider 3 cases: 1 other person is in c1, 2 other people are in c1, 3 other people are in c1

then tripling whatever result that gives you to account for p1 being in c2 or c3

it's very algorithmic and not as straightforward, but it makes more sense to me

[fair geyser]

if you can do it without giving up it's a good solution

[fair geyser]

anyway, i think you got it right

[native viper]

ok, thanks for help 🙂

.close

[cedar kiln]

Channel closed

Closed by @native viper

Use .reopen if this was a mistake.

[cedar kiln]

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.

[errant loom]

hey could someone explain how it became 25x^8? specifically the x^8 part. I understand they multiplied to get the lcd

[dire geode]

4 = 8-4

[errant loom]

oh i got it now lol we just multiply by 5x^4 right

.close

[cedar kiln]

Channel closed

Closed by @errant loom

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.

[hardy pike]

Can someone help me to show that this function h is injective on the interval [0,2pi) ?

[cedar kiln]

@hardy pike Has your question been resolved?

[hardy pike]

<@&286206848099549185>

I tried classical way: starting from h(t1) = h(t2) to find t1 = t2, but I didn't find anything convincing

<@&286206848099549185>

[viscid heron]

This is not my type of math

I had a stroke looking at this

[hardy pike]

:/

[mortal grove]

uhhh well it's definitely not injective on [0,2pi)

is that an okay answer?

[hardy pike]

mm not for me

actually for me she’s injective

[mortal grove]

dump her

you deserve better

[hardy pike]

😅

graph of x,y and z
x(t) in blue, y(t) in orange, z(t) in purple

can’t find two t where x(t1)=x(t2) AND y(t1)=y(t2) AND z(t1)=z(t2), then I guess h is injective but I don’t find a way to prove it

black axis on the right is t=2pi (not in the interval we work on)

<@&286206848099549185> anyone else ?

[viscid heron]

Not me

[cedar kiln]

@hardy pike Has your question been resolved?

[cedar kiln]

@hardy pike Has your question been resolved?

[hardy pike]

😢

[cedar kiln]

@hardy pike Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[wispy talon]

hello

i have a question

so

i understand everything about the image

except!

this line

a<0 so reflect

what do they mean by a?

[dreamy sleet]

Not sure

Maybe you could ask the person who wrote it

[wispy talon]

hmm

yeah..

i could on monday

but im just so curious why they used the word reflect

im assuming they meant that something is repeating?

[dreamy sleet]

Is this a picture of your teacher's notes from a lesson you didn't attend?

[wispy talon]

kind of

yes

[idle tusk]

i think they mean a=-3

and because a is negative we need to reflect around the x axis

instead of just stretching

[wispy talon]

!!!

that is totally reasonable

yeah i agree with that

thank you

you are my hero

.close

[cedar kiln]

Channel closed

Closed by @wispy talon

Use .reopen if this was a mistake.

[cedar kiln]

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.

[magic dew]

prove that the product of 10 consecutive positive intergers is not square

[dreamy sleet]

By googling, I found this result: https://math.stackexchange.com/questions/2361670/product-of-10-consecutive-integers-can-never-be-a-perfect-square

[magic dew]

i know it, but i want a better solution

[dreamy sleet]

Oh, you could've said that

[magic dew]

it was the solution for n consecutive intergers

[cedar kiln]

@magic dew Has your question been resolved?

[magic dew]

.close

[cedar kiln]

Channel closed

Closed by @magic dew

Use .reopen if this was a mistake.

[cedar kiln]

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.

[worthy tree]

why can we tell that e^x * e^-x is a constant for this result? i dont get how this follows from the result equalling zero

[sour horizon]

which functions have 0 derivative?

[worthy tree]

😮

.close

[cedar kiln]

Channel closed

Closed by @worthy tree

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.

[swift saffron]

find the maximum value K so that on an 8x8 chess board K pawn can be placed and the distance between any two pawn is greater than 2

[sour horizon]

what have you tried?

[swift saffron]

I dont know where to start

I just try to put the pawn on the chessboard

[sour horizon]

yea you could probably get a good guess for the answer like that

after that you could try showing it’s impossible to place K+1 pawns down

[sour horizon]

by thinking about how many squares are “used” by a pawn

[swift saffron]

I also wondering is it allow to place like this

[sour horizon]

if anything there is invalid i think it would be the bottom 3

[swift saffron]

So it is only allowed if vertical and horizontal?

[sour horizon]

it’s not 100% clear what distance means but i’d guess the bottom 3 are invalid

[swift saffron]

Can you explain more about this

[sour horizon]

so is your guess for the answer 8?

[swift saffron]

4

[sour horizon]

that’s too low

8 is also too low

[swift saffron]

I think diagonal isnt allowed

[sour horizon]

yea i would think so as well, but i can still place more than 8

[swift saffron]

How?

[sour horizon]

put 3 in the top row, 3 in a middle row, 3 in a bottom row

[swift saffron]

The distance of each pawn is >2

[sour horizon]

yea

you can fit 3 in a single row

[swift saffron]

This is what you mean?

[sour horizon]

yea

[swift saffron]

This isnt allowed

Every pawn distance is 3 or more

[sour horizon]

and they are…?

[swift saffron]

This

Or (b8, f8), (c8, g8), etc

[sour horizon]

i gtg but think about how many ineligible tiles are made when you put pawns in certain places

and how there are only 64 tiles

[cedar kiln]

@swift saffron Has your question been resolved?

Channel closed

Closed by @swift saffron

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.

[old fjord]

what is a parameter? and how do I use it in this question

[marsh lake]

i think its like a variable that can be anything

in this question you could let x = t, t ∈ R (free parameter)

y would be 6-t

[old fjord]

im confused

explain this as if I am a toddler

because that is how much I know about this

genuinely

[crimson sedge]

Do you see that if x=t and y=6-t both equations are satisfied?

[old fjord]

i see

[crimson sedge]

Now t is just a random (real) number

So there are infinitely many solutions

For example t=1 gives the solution x=1 and y=5 and t=-2.5 gives the solution x=-2.5 and y=8.5

[marsh lake]

adding these up give 6 (for (1))

[old fjord]

okay doki

[crimson sedge]

And thats basically what a parameter is

[old fjord]

ok nice thank you

[marsh lake]

or if you want, you can let y = t, t∈R

[old fjord]

whats that weird e you are using

[deep pivot]

x and y are interchangeable

[deep pivot]

sign for denoting a value

[crimson sedge]

Element of

[deep pivot]

^

[old fjord]

oo okay

[crimson sedge]

Like t is in the set of real numbers

[old fjord]

okay thanks!!

have good days!

.close

[cedar kiln]

Channel closed

Closed by @old fjord

Use .reopen if this was a mistake.

[cedar kiln]

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.

[real tree]

howd u get r = 2x+1

that isnt true for term 2/ term 1

1*2x+1

isnt x

it should be true for all

[feral coyote]

x^2 = 2x^2+x?

[real tree]

let me get a hand on it wait

finding my book

[feral coyote]

Geometric progression from 1 to x, meaning multiplied by x each time

3rd term has to be x^2

[real tree]

is that even a true gp

[feral coyote]

That's why I make them equal

[feral coyote]

It is

[real tree]

is the answer -1

yeah

I got it

howd u want me to explain it

ok so listen

I used

t2/t1 = t3/t2

find out x

got 2 values x= 0 or x = (-1)

0 dosent make up a gp

so its x= (-1)

now u know the rest

I hope

[cedar kiln]

@hearty bloom Has your question been resolved?

Channel closed

Closed by @hearty bloom

Use .reopen if this was a mistake.

[cedar kiln]

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.

[hollow storm]

help please

[hollow storm]

Consider a typical deck of 52 cards (4 suits and values ​​2,...,10,J,Q,K,A). A set of 5 cards makes a straight if those cards can be placed in consecutive order. For example, the set containing the 3 and 6 of hearts, the 4 of spades and the 5 and 7 of clubs creates the straight (3,4,5,6,7).
The set containing the ace of hearts, the 5 of spades, the 2 of clubs and the 3 and 4 of diamonds creates the straight (A,2,3,4,5) - which is the minimum straight. The set containing the Jack of spades and the 10, Q, K, A of diamonds makes the straight (10,J,Q,K,A) - which is the highest straight. (Note that A can take on either the value "1'' or "14'' in a straight, considering J=11, Q=12, K=13. Also note that all cards in a straight could be of the same suit).
Now suppose that two aces and a jack are removed from the deck. How many sets of 5 cards in the remaining deck make a straight?

there exist 10 straights 1/2/3/4/5, 2/3/4/5/6, 3/4/5/6/7, etc

and we multiply the straights by 4^5 because the suits dont matter

10 x 4^5 is the total number of straights (?) and from this we have to subtract the repeating cards to get the total number of straights if there are 52 cards in the deck

i dont know if this is right

[cedar kiln]

@hollow storm Has your question been resolved?

[cedar kiln]

@hollow storm Has your question been resolved?

[cedar kiln]

@hollow storm Has your question been resolved?

[hollow storm]

.close

[cedar kiln]

Channel closed

Closed by @hollow storm

Use .reopen if this was a mistake.

[cedar kiln]

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.