help-10

[heavy depot]

$\pi$

[warm shale]

CrEpasPmkinPie

[raven portal]

no its 3 i just forgot to change it

[royal shard]

so like this?

$log_{y}x=1/3$

[warm shale]

~Martin

[raven portal]

yea

[royal shard]

alright

and we want:
$\log_x x\sqrt{x}$

is that a "y" ?

[raven portal]

yeah

and its xsqrt(x)

no no

[warm shale]

~Martin

[raven portal]

let me send another one

[heavy depot]

$\log_{x\sqrt{x}}(y)$

[warm shale]

CrEpasPmkinPie

[royal shard]

ah ok

$\log_y x=\frac{1}{3} \ \text{then what is }\log_{x\sqrt{x}} y$

eugh

[raven portal]

wait

[warm shale]

~Martin

[heavy depot]

do we have it?

[raven portal]

yeah

xsqrt(x)^y

[royal shard]

$\log_y x=\frac{1}{3}\Leftrightarrow y^{1/3}=x\Leftrightarrow y=x^3$

[warm shale]

~Martin

[raven portal]

i dont think this is the answer

[royal shard]

it is not

but it leads us to it

[raven portal]

ok

[royal shard]

we can now substitute that into what we want

if we substitute it in we get

$\log_{x\sqrt{x}}y=\log_{x\sqrt{x}}x^3$

[warm shale]

~Martin

[royal shard]

do you know how to go from here on?

[raven portal]

yeah

anser is two

huh

it was easier than what i though

[royal shard]

👍

[raven portal]

can i ask another question

[drifting badger]

No. Only 1 question per life time. Come again when you're reincarnated

[raven portal]

What about this one

@ruby fulcrum

[obtuse pebble]

Channel closed

Closed by @raven portal

Use .reopen if this was a mistake.

[raven portal]

.Reopen

[obtuse pebble]

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.

[royal basin]

assuming we're meant to look at the yellow bit, yes

[obtuse pebble]

Channel closed

Closed by @timid moss

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.

[static fulcrum]

Is my solution correct?

[timid silo]

,w 6/(x-3) < 5

[warm shale]

Results provided by WolframAlpha

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

Requested by hibyehibye#9497

[timid silo]

yes

[static fulcrum]

Thanks @timid silo

,w x^2+2x+3=0

.close

[obtuse pebble]

Channel closed

Closed by @static fulcrum

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.

Channel closed

Closed due to the original message being deleted

[crisp quail]

.close

[obtuse pebble]

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.

[bright python]

Is there any way to simplify A'b + cb'
Boolean algebra

[timid silo]

no

[obtuse pebble]

@bright python Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[meager zealot]

I need help using a simple decomposition theorem to integrate a polynomial fraction

[meager zealot]

Where I get lost is the 1 = (A+B+C)*x^3 + (3A + 4B + C + D)x^2 and so on because I have no clue how to determine what expressions to use as coefficients for the powers of x

As in, I have no idea where 3A+4B+C+D came from

[kind hawk]

multiply out the previous expression

and collect the x^2, the x and the constant terms

[meager zealot]

Can you elaborate a bit?

@kind hawk

[kind hawk]

not sure what else to say

you multiply out (x-1)(x+^2)A+x(x+2)^2B+....

and then collect the terms

[meager zealot]

Oh shit

That was much simpler than I anticipated lol

Thanks @kind hawk

.close

[obtuse pebble]

Channel closed

Closed by @meager zealot

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.

[silver plover]

i need some help rn with this question

first of all how does my graph look?, and my working

secondly, the points of (-2,b) and (a,1) dont plot on my curve, so idk if ive done this correctly

i have a MS but i dont wanna see it rn otherwise im gonna see the answer straight away from the graph, wanna seek assistance first

[obtuse pebble]

@silver plover Has your question been resolved?

[silver plover]

<@&286206848099549185>

[noble dust]

I think that your graph looks fine and the working looks good

The intersection point of the red lines is (-2,1)

So (-2, a) are the points above and below the crossed intersection lines

And there are no points to the right and left parts on the graph so there are no points where y=1

@silver plover

The label -2 and 1-sqrt(2) are in the wrong places in your diagram

[silver plover]

how come

[noble dust]

This tells you about where -2 should go

[silver plover]

how is it the intersection point of the red lines?

[noble dust]

Plug it into the equation and see if it works

So if x=-2, for both lines you get y=1

[silver plover]

ye

works

ok so

why is 1 - sqrt2 in wrong place?

[noble dust]

The point (-2, 1-sqrt2) should lie on the hyperbola

It's the turning point of the bottom branch of the curve

[silver plover]

but than it would go above the intersection of the oblique asymptote with the y axis

which wouldnt make sense

the red line

[noble dust]

So your turning point needs to be higher than that point

[silver plover]

but how would i know that tho

without looking at desmos

[noble dust]

You compare the values

1-sqrt(2)

And the intersection of the line with the y axis

That helps to see if the turning point is above or below

[noble dust]

Which is 1-2sqrt(2/3)

[silver plover]

also how do u know the -2 point is the turning point?

[noble dust]

It's going to be the point nearest to the intersection of the asymptotes

As the curve comes up then goes down

Since it's symmetric

We know it must be at -2

[silver plover]

yh i mean

i dont think ive done this accurately at all

icl

but what do u think

[noble dust]

The branches need to look less rounded

[silver plover]

i see

also

[noble dust]

You want to come up closer to the asymptotes

[silver plover]

ive messed up this point there, 3-2sqrt6 / 3 is larger than 1-sqrt2

[noble dust]

You can draw you asymptotes first so that they have more distance in the y axis

With a sharper looking gradient

[noble dust]

It still works as long as the turning point is between zero and that value

[silver plover]

ight kl yh

these r hard to sketch man

main thing is

ive pretty much sketched it to a decent level

just less rounded

[noble dust]

Yeah exactly and you can also draw it closer to the asymptotes for this particular question

[silver plover]

heres the MS btw

[noble dust]

They haven't thought about the turning point as deeply as you have done

[silver plover]

ye i noticed

[noble dust]

One other thing

Your line starts to go off the asymptotes at the ends

[silver plover]

ye, as u said

not rounded

well i was too rounded

would my sketch have been good enough

in an exam

u reckon?

par the roundness

[noble dust]

Yeah I think so, just add the intersection point of the lines as a coordinate just incase it's worth a mark

[silver plover]

perfect

cheers mate

.close

[obtuse pebble]

Channel closed

Closed by @silver plover

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[vast locust]

hi im working through differential equations. Why do we multiply by P-knot at the last line?

[kind hawk]

We replace the C

Which we calculated to be P_0

Btw pretty sure it's nought

[vast locust]

lol -- i cant read thanks

.close

[obtuse pebble]

Channel closed

Closed by @vast locust

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[graceful quail]

I am confused on this. Am I supposed to calculate the answer with just 9.8 and pi/3 or am I somehow supposed to keep the m/s^2 and use degrees? I am confused on what to use as the variables.

[graceful quail]

If anyone can tell me what to google I would extremely appreciate it a lot.

[obtuse pebble]

@graceful quail Has your question been resolved?

[graceful quail]

Hopefully this is how you would solve it unless I put in the wrong variables which is what I am worried about.

[obtuse pebble]

@graceful quail Has your question been resolved?

[obtuse pebble]

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.

[rancid wagon]

When writing a proof would replacing "so" with the implies arrow be a valid use of it? "a < b, so b - a > 0"

[rancid wagon]

Would replacing "so" with an equal sign be valid?

as in they're equal statements

what's the nicest way to write this type of thing in a proof?

[brisk matrix]

"so" is best

equal sign is inappropriate

you can use "so", "then", "thus", "hence", "therefore", ...

[rancid wagon]

ok and when is the implies arrow used?

[brisk matrix]

in formal proofs not very often

it's a shorthand

[rancid wagon]

as in in a formal proof you would literally write "implies"?

[brisk matrix]

or "so", "then", "thus", "hence", "therefore", ...

there's no 1 word

[rancid wagon]

oh so they are synonymous

how about the use of the arrow inside of a predicate statement?

https://www.geeksforgeeks.org/types-of-proofs-predicate-logic-discrete-mathematics/

is the arrow there still interchangeable with words?

[brisk matrix]

sure

[rancid wagon]

oh I mean same thing I guess

[brisk matrix]

but it's more common to use arrows

because you're working with some sort of symbolic system

when discussing predicate logic you'll typically keep it as arrows and logical operators'

like you'd write $P \land Q \implies R$

[warm shale]

maximo

[brisk matrix]

but if you're writing a proof it is probably best to use words

[rancid wagon]

gotcha

ok cool ty

.close

[obtuse pebble]

Channel closed

Closed by @rancid wagon

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.

[west bone]

i don't get how this happened

[brisk matrix]

how what happened

[west bone]

why did they add +1

and how did it change rs/st and rv/uv - > rt/st and ru/uv

[brisk matrix]

st/st = 1

and uv/uv = 1

[west bone]

i get that

[brisk matrix]

they added one to both sides

that's allowed

[west bone]

how did it change the side's letters?

i don't get that

[brisk matrix]

they did so to write it as st/st and uv/uv

rs + st = rt

the line segment from r to s + the line segment from s to t = the line segment from r to t

[west bone]

so the S's cancel out?

[brisk matrix]

look at the image

identify RS, ST, and RT

and notice how RS + ST = RT

[west bone]

yes true

[west bone]

so what does that mean? i know that's what makes up RT but how did the letters change

[brisk matrix]

which letters changed

can you circle it

[west bone]

.

[brisk matrix]

they showed you the steps

i don't quite understand what you don't see

[west bone]

okay so in this do the S's cancel out or something? i'm not sure how the letters change

[brisk matrix]

sure, but only if they are in a straight line

again

notice how they are equal

RS + ST = (S-R) + (T-S) = T - R = RT

[obtuse pebble]

@west bone Has your question been resolved?

[west bone]

back, so how were the two S's taken if there's a different letter taking from it?

[brisk matrix]

im confused by your question

work out the subtraction

[west bone]

S-R = -SR

They can't cross out each other

[brisk matrix]

S-R = RS

[west bone]

how

im so confused lmao

where did the subtraction come from?

okay so to keep it in simple terms, when this happens, the same letters cancel out?

[obtuse pebble]

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.

[timid silo]

How do you find the size of ADC?

[high lily]

hint: ABCD is a cyclic quadrilateral

[timid silo]

Okie

Wait before that

I don’t get this question

[high lily]

what have you tried for that

[timid silo]

Nothing cause I don’t how what it wants me to do

Is it like

Finding x?

[high lily]

yes

find the values of x

[timid silo]

Oh

Values

[high lily]

another way to put it would be to solve the equation

[timid silo]

Y’know I don’t wanna say this

But

I

don’t have a clue

Okay

So solve the equation is like

Uh

There are 2 xs?

So

[high lily]

first try rid yourself of fractions and variables in the denominator (using the appropriate multiplication)

[timid silo]

So

Make the denominator the same number?

[high lily]

that's one way to do it

[timid silo]

I’m not good at thinking

Okay

But

would -x do ;-;

Not really

Okay

Help

oh wait

I might have done something

I still don’t know though

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Somebodydyydydydydyydydydyydd

Cause

It’s not getting the correct answers

Honestly man I don’t even know why this is so hard

I got the aswerR

[timid silo]

Now back to this thing

.close

[obtuse pebble]

Channel closed

Closed by @inner torrent

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[blissful marlin]

I need help with the problem of the week for waterloo's cemc

I was wondering if I was correct?

Here's my solution:



We know that, before the removal of the dot, the chance of picking a card that is even/odd would be 3:6.

Afterwards, some guy comes, and then removes a dot, we then gain two probabilities which are:

4:6 (if the dot is removed from an even card)

2:6 (if the dot is removed from an odd card)



We can then combine these two statistics;

(3/6)(4/6) + (3/6)(2/6) = 1/2



Therefore, there's a 50-50% chance of that person getting an odd card.

[obtuse pebble]

@blissful marlin Has your question been resolved?

[drifting wraith]

what's 3/6

how does it stay a part of your calculation

[blissful marlin]

it's the total probability of getting an odd card

[frosty spoke]

I don't think it's 50/50

[drifting wraith]

why

[frosty spoke]

maybe it is

but seems wrong

there are more dots on the odd cards

odd cards are more likely to lose a dot

[blissful marlin]

well we don't know what card loses a dot actually

[drifting wraith]

3/6 is true if there's no removal of the dot

[blissful marlin]

yeah

3/6 is the probability of chosing an even card to remove one of the dots

[drifting wraith]

whichever dot is removed, it's not longer 3/6

[blissful marlin]

then that even card becomes odd

[drifting wraith]

ok but that's also false

[frosty spoke]

P(drawing odd) = P(drawing odd | odd card loses a dot, becomes even) P(odd card loses a dot) + P(drawing odd | even card loses a dot, becomes odd) P(even card loses a dot)

[drifting wraith]

out of 27 dots 12 are on even cards

so 12/27 is probability of even card becoming odd

there's just nothing 3/6 about it nowhere

[blissful marlin]

the 3/6 comes from how 27 dots are equally likely to be removed

it's a 50% chance of a 50% that one card becomes even or odd

[drifting wraith]

that's just coming out of nowhere

this is the mistake, case closed

[blissful marlin]

I've asked others, I also got another solution as well if you are willing to check that

"So there are 27 dots with 12(2,4,6) dots belonging to even cards and 15(3,5,7) belonging to odd cards. So 12/27*4/6 + 15/27*3/6 which is some number thats not 0.5"

ohhh fcck wrong number its 2/6 still not 0.5

dot, we then gain two probabilities which are:

4:6 (if the dot is removed from an even card)

i think ur wrong cuz ur not treating the uniform choice from 27 dots properly

Here's the convo

[drifting wraith]

sure

that's my opinion too

an even card becomes odd 12/27, otherwise an odd card becomes even

[blissful marlin]

so, 27 dots, that's like 12/27 are even, and 15/27 belong to odd - so then we multiply them by the ratios?

[drifting wraith]

you're just asking multiple people, weighting their responses by the amount of math they say, and using that to come to the answer

it's not interesting

[blissful marlin]

I've asked the tutor and they came up with a different answer...

Which is what I came up as well.

[drifting wraith]

yeah

i understand that

you've asked multiple people

[blissful marlin]

ugh why doesn't waterloo just put the answers after posting the question

If you'd like, I can DM you the answer when it comes out

[drifting wraith]

no, i'm confident

[blissful marlin]

alright, thanks for the help!

[obtuse pebble]

@blissful marlin Has your question been resolved?

Channel closed

Closed by @blissful marlin

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.

[timid silo]

How do I do part b?

[neon eagle]

use part a

[timid silo]

How?

[timid silo]

I tried

Look at my answer

[neon eagle]

where?

[kindred jay]

your work is really small maybe enlargen it?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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.

[hot dawn]

How do I interpret the vertical bar notation?

9 | 6 • x

[royal basin]

divides

[hot dawn]

"9 is divisible by 6 • x"?

[royal basin]

other way around

6x is divisible by 9

[hot dawn]

How does he get to 3 | x

[sage geode]

For a number to be divisible, it has to have two (or more) factors of 3, right?

[hot dawn]

yeah

wait

to confirm, 9 \vert 6 • x is equivalent to saying $$\frac{6 • x} {9}$$?

[sage geode]

No

9 | 6x is a statement
6x/9 is a fraction

\vert has to be in $$ as well

[hot dawn]

so, there's only a semantic difference?

[sage geode]

I guess you can say so

[obtuse pebble]

@hot dawn Has your question been resolved?

[obtuse pebble]

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.

[slender venture]

Hello! I am Syed (Panzer).

For the sake of this question, I want you to think of me as a person who doesn't know any mathematics at all. (This is not true but will help me get the answer i want here.)

I want to learn mathematics from the absolute beginning, where i learn something and use what i have learnt to learn something else. Kind of like building on top of knowledge and expanding it.

What i need is a "roadmap" to accomplish this task.

While i don't think its possible to have a roadmap that covers all of mathematics, i just want enough math that i can turn it into a hobby and understand basic and advanced formal, natural and social science concepts.

[misty gate]

which grade

?

[royal basin]

http://khanacademy.org/ perhaps?

[obtuse pebble]

@slender venture Has your question been resolved?

[slender venture]

.close

[obtuse pebble]

Channel closed

Closed by @slender venture

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.

[faint ore]

hello

[faint ore]

.close

[obtuse pebble]

Channel closed

Closed by @faint ore

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[strong aspen]

I need to with tangent properties

how do I know which angle does ECB = ?

[obtuse pebble]

@strong aspen Has your question been resolved?

[obtuse pebble]

@strong aspen Has your question been resolved?

[obtuse pebble]

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.

[late flare]

both have the same answer

[late flare]

right?

[wise talon]

,w lim x to infinity cos(3x)

[warm shale]

Results provided by WolframAlpha

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

Requested by DerpZ#9141

[late flare]

then the same

[wise talon]

no

the first manipulation you made is invalid

first image

[late flare]

the other equation has cos too

[wise talon]

if the limit does not exist algebra of limits is not allowed

so you cannot split it up like that

[late flare]

why they dont have same answer

dne

both have cos

and cos inf = dne

[warm canopy]

Because multiplication can make limits exist

Lim as x goes to 0 of 1/x does not exist, but lim as x goes to x of x*1/x = 1 is 1

[late flare]

i dont understand

[warm canopy]

$\lim_{x\to 0} \frac{1}{x}$ DNE

[warm shale]

ΣAC

[late flare]

what

nvm

[warm canopy]

But $\lim_{x \to 0}\left(x\cdot \frac{1}{x}\right) = \lim_{x \to 0} 1 = 1$

[warm shale]

ΣAC

[late flare]

yes

how is this related to our problem

[late flare]

this isnt my problem

[late flare]

this is

shouldnt both be undefined

cuz cos ~( inf ) = dne

[knotty crow]

it is, you splitted 1st one into two limits while condition I've just send doesn't hold

[late flare]

so i cant split?

this isnt my problem anyways

my problem is with evalating

evaluating

the limit

[knotty crow]

1st one is DNE, 2nd is 0, why do you think result should be same?

[late flare]

cuz both have cos

why 2nd is 0

[knotty crow]

can be solved by squeeze theorem

[late flare]

and what about the first

cant the first be solved by squeezze theorm

[warm shale]

Modus

[knotty crow]

1st one is like 0 + DNE -> DNE

[obtuse pebble]

@late flare Has your question been resolved?

[obtuse pebble]

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.

[stark hollow]

I don't know where to start(((

[obtuse pebble]

@stark hollow Has your question been resolved?

[stark hollow]

<@&286206848099549185>

[timid silo]

Do you have any context to where this question was given?

Like any properties or topic you did beforehand before this topic

[balmy mortar]

I would approach by considering constraints (which is 'cheating' since it relies on the fact the question should have 1 answer)
However, this can still hint you towards the intended solution

[stark hollow]

this question is from the book called zambak 7 geometry

[stark hollow]

hmm i think it does not have a property for this

[stark hollow]

how can i do it?

[unreal musk]

options for them btw

[balmy mortar]

Think about whether this question needs CE to be some fixed value

Like does it actually constrain CE?

(and BD)

This at least hacks an answer out

[obtuse pebble]

@stark hollow Has your question been resolved?

[balmy mortar]

Did you understand my hint?

[stark hollow]

can you please clarify it?

[balmy mortar]

The question should only have 1 solution

Since it is multiple choice

[stark hollow]

i did this but i can't really prove it

[balmy mortar]

I'm claiming that diagram isn't actually fixed.

Ah ok, that's one choice

There's an easier choice for BD = CE = ? though

[balmy mortar]

If you want to carry on with this approach, extend a perpendicular from D to line AC

I also advise drawing your own diagrams for geometry in general

[thick gyro]

for this

i get an equation of

12 for y and 6 for x is an answer

but there are others depending on what x is

[unreal musk]

You could find x in terms of y of course

[supple granite]

i doubt you have to go as far as cosine rule for this

WAIT I GOT IT

there

SAS congruency

therefore AD=DF=6sqrt3

[balmy mortar]

ah very nice

[supple granite]

[thick gyro]

@stark hollow this just confirms jays answer

green line in question

[balmy mortar]

Im stealing this question.

[supple granite]

same

well i already did

[balmy mortar]

So what I was hinting at before was that you could set these lengths to be 0 and get an answer

[supple granite]

i spread it to another server

[thick gyro]

like a virus

[stark hollow]

WOOOW OMGGG

[supple granite]

lmao the geometry virus

[stark hollow]

THANK YOU SO MUCH GUYS!!!

[thick gyro]

it takes a bit of time before you realise that AB and BD have no set length

[supple granite]

[thick gyro]

so @balmy mortars method would be the quickest

[balmy mortar]

hack

[thick gyro]

since setting BD to 0 will make the ? side, the same as the equalateral triangle of 6sqrt(3)

[balmy mortar]

At least it makes you realise ADE is probably isosceles

and that might hint you the right construction

[thick gyro]

how would you see that

beforehand

[balmy mortar]

Before realising the answer is 6sqrt3 ?

I mean...

Under some manipulations you probably would have guessed it is isos already

I think jay guessed that before

[supple granite]

yeah i just tried to prove that it was isos

[thick gyro]

@stark hollowi think you forgot to .close

[stark hollow]

.close

[obtuse pebble]

Channel closed

Closed by @stark hollow

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.

[knotty crow]

sin(A+B)

formula

[warm shale]

Modus

[obtuse pebble]

Channel closed

Closed by @pine oxide

Use .reopen if this was a mistake.

[obtuse pebble]

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.

Channel closed

Closed due to the original message being deleted

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.

[lean ember]

I need help

How am I supposed to find those numbers?

[gleaming ridge]

when (2n+3) divides (5n^2 - 9)

[lean ember]

Yeah... I tried alot

But how am I supposed to do that

I tried factoring the numerator

But still didn't got much

[gleaming ridge]

show what you did, I might be able to help

[lean ember]

Okay

It's quite messy

So I am writing again

1 min plz

This is one of the ways I tried to approach

[gleaming ridge]

I was thinking the same

[lean ember]

But realized it didn't work

[gleaming ridge]

I wrote a small code and seems like 2n+3 divides n^2 only when n=3

[lean ember]

This is my other approach

Oh..

[lean ember]

Then what to do....

I don't think this is a mathematical proof

[gleaming ridge]

what we can do is assume that n^2/(2n+3) = k then simplify

[lean ember]

hm...

[gleaming ridge]

we should get a quadratic in n

[lean ember]

hm....

I didn't get it

[lean ember]

what are we gonna do with this ratio again?

[gleaming ridge]

n^2 = k(2n + 3), simplify and get a quadratic equation in n

[lean ember]

Fine

Here

But why are we doing this?

[gleaming ridge]

to find out n lol

[lean ember]

Oh....

[gleaming ridge]

use quadratic formula

[lean ember]

Fine....

Let me

See

Here

Oops

A minor mistake

I forgot k

Now its better

K is already a variable

What now

[gleaming ridge]

yeah, so now k should be such that (k^2 + 3k) > 0

and (k^2 + 3k) must be a perfect square

[lean ember]

hm....

[lean ember]

In other words root of this value should be natural

How are we going to determine that?

[lean ember]

That this is a perfect square?

I think we are making this complicated

But I trust u

[rare sedge]

Do you know the divide sign?

[lean ember]

U mean?

[rare sedge]

I mean like 2|4

[lean ember]

oh....ya

[rare sedge]

Means 2 fully divides 4

[lean ember]

2 divides 4

[rare sedge]

Yup

[lean ember]

Yes

Similarly

[rare sedge]

Using the divide sign this question is quite not that hard in fact

[lean ember]

2n+3 divides the numerator

[rare sedge]

You want 2n+3| 5n^2-9 right

[lean ember]

Oh

Yes

[rare sedge]

Then you recall, if a|b then a|b+ka

[gleaming ridge]

I think so too but I can't think of any other way to do this

[lean ember]

But the result must always be natural

[rare sedge]

for k being a integer, can you see why?

[lean ember]

Wow😮

[rare sedge]

The trick here is that you want something to cancel out the n^2, because its hard to deal with so you do the following

[lean ember]

I have a doubt

[lean ember]

About this

[rare sedge]

since 2n+3| 5n^2-9

[rare sedge]

Hmm?

[lean ember]

Nah...

Got it

Sorry continue

[rare sedge]

Okok

[rare sedge]

Since this is true

This is also true

2n+3|(5n^2-9)x2

You multiply it by 2, ill explain later why

[lean ember]

Let me be clear, our objective is to find all values of n such that f(n) is natural

[rare sedge]

Yup

So we have 2n+3| 10n^2-18

[lean ember]

Is that "x" a multiplication sign?

[rare sedge]

Yes

[lean ember]

Okay

[rare sedge]

its obvious that if a|b this means a|kb for k integer

[lean ember]

Oh okay

[rare sedge]

And now , to get rid of the n^2 we do the following trick

[lean ember]

I am bad with notations

Okay

....

[rare sedge]

We would have

2n+3|10n^2-18-5n(2n+3)

[rare sedge]

From this

[lean ember]

But...

Oh got it

[rare sedge]

Great

Simplifying we get

2n+3| -18-15n

[lean ember]

Hm...

[rare sedge]

Btw this just means -18-15n after dividing 2n+3 is an integer ( could be negative),

[lean ember]

But we need positive Right?

[rare sedge]

Yup I will get to that later

[lean ember]

Fine...

[rare sedge]

Just know that this is true

[lean ember]

Well it looks so fR

*far

[rare sedge]

Then heres the thing, we know managed to get rid of the n^2 here right

[lean ember]

It should be i guess

[rare sedge]

We can actually apply the same trick to get rid of our -15n

[lean ember]

Yeah...

Okay....

[rare sedge]

How? First we multiply by 2
We see 2n+3| (-18-15n)x2 right

Which means 2n+3| -36-30n

[lean ember]

Yes

Yes

[rare sedge]

Then we use the same trick , we have
2n+3|-36-30n+15(2n+3)

[lean ember]

hm...

[gleaming ridge]

I think we should be able to prove that k^2 + 3k = k(k + 3) is a perfect square only when k=3. Then we're done

[rare sedge]

Which then we would have 2n+3 | 9

[lean ember]

oh...

This mean....

3 is the only number?

[rare sedge]

And then its simple from there, it means 2n+3 must be a factor of 9

[lean ember]

Other?

[rare sedge]

But 9 only has factors 1 3 9

[lean ember]

No other number?

Oh....

[gleaming ridge]

yep

[rare sedge]

Yup so 3 is the only number

[lean ember]

hm...

[rare sedge]

This is basic number theory, wait a second I can send a document

[lean ember]

Thank you very much🥹

[rare sedge]

http://www.its.caltech.edu/~kpilch/olympiad/NumberTheory-Complete.pdf

This is basic olympiad number theory, which covers these kind of divisibility questions

[lean ember]

You sure I won't be able to find any other natural number no matter what I do right?

[rare sedge]

Yup

[lean ember]

wow...then good

I am still not completely able to digest this but got the intuition i guess

[rare sedge]

Nice, the way using equations is also doable, but its much complicated than this once you get the hang of divisibility rules

[lean ember]

We can get worse questions than these right?

[rare sedge]

Urm, depends,

[lean ember]

I will try writing this in notes.

[rare sedge]

For example in the notes I sent

One of the question was like

[lean ember]

I feel like question is easier when the degree is less

[rare sedge]

As you can see the general idea to solve these kind of problems is to reduce the power on the RHS

[rare sedge]

Yup, so thats why we use

if a|b then a|b+ka

[lean ember]

okay.......

I have another one now...

Let n be a natural number

n+5 is a perfect square

And n-11 is also a perfect square

Then how many possible values of n are there?

Considering n is natural

[rare sedge]

Urm for this you can just try values of n, and then to prove there arent other cases, just note the gaps between squares get bigger as the numbers get large

[lean ember]

hm....

[rare sedge]

Obviously n>11, trying n=12,15,20… you notice for n=20 this works

Also we picked n=12,15,20 because this guarantees n-11 is a square

Then to prove there arent any other possible n

You notice the gaps between consecutive squares

Ie

[lean ember]

Wait wait....

How is 20-11 a perfect square?

n should obey both equations simultaneously

[rare sedge]

Urm its 9?

[lean ember]

Oh....

Hehe😅

[rare sedge]

Oh lol

[lean ember]

Sorry my bad

[rare sedge]

Also 20+5 is 25

[lean ember]

I can't argue this

[rare sedge]

So to prove there arent any other n, you notice the difference between squares,
(k+1)^2-k^2 = 2k+1
But then you notice to for k being like >=14
n+5 and n-11 cannot be both perfect squares,

Why? Because the gaps between squares are like at least 29 numbers apart

But n+5 and n-11 reaches a gap less than that,

[lean ember]

Hm...

[rare sedge]

Thus by just checking for those squares, you can just brute force the rest

[lean ember]

So what you basically mean is....

Just find some numbers by hit and trail first

And you will probably not be needing to go more than 14-15

[rare sedge]

Actually for k>=8 this is already enough

[lean ember]

Then, prove that the numbers you got are the only possible values

[rare sedge]

Yup

By noticing the gaps between squares grow too large for any n to even exist there

Do you understand this? Or should I give an easier example

[lean ember]

Please do

[rare sedge]

Urm a simpler question would be like

Find all naturals n, such that n-1 and n+2 are both perfect squares

You can immediately see that n=2 works

[lean ember]

Okay i will

hh..m

[rare sedge]

But how do you prove that other n do not work?

You notice likes the gaps between squares

Like 1 and 4, the gap is 3

4 and 9 the gap is 5

9 and 16 the gap is 7

Right

[lean ember]

Ya....

[rare sedge]

The gap keeps growing

[lean ember]

Yup....

By 2k+1

[rare sedge]

But n-1 and n+2 only has like a gap of 3

[lean ember]

Convectively

I mean consecutively

[rare sedge]

Therefore it cannot be other squares because their gap is too large

[lean ember]

Oh

For some reason I feel like i got enlightenment

Just wow.....

[rare sedge]

lol

[lean ember]

Okay...let me try

[rare sedge]

Alrighty

[lean ember]

lets say....

n+5 and n-4 are perfect squares

Then...

I have to do hit and trail

Since 4 and 5 are small numbers I have to look around small numbers

So I found that the only number is 20

Then I have to prove that there is no other number other that 20

[rare sedge]

Yup

[lean ember]

Here....

Oh!!

I got something

Here, I can see that the gap between those two perfect squares should be 9

And it is impossible to have a gap lesser than 9 once the numbers start going above 25

So this means 5 is the only way

Thank you

I think I am done

U helped alot

[rare sedge]

Alright no problem

.close

[obtuse pebble]

@lean ember Has your question been resolved?

[lean ember]

Yes

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[plucky patio]

pretty straight forward but isn't this right?

[plucky patio]

I did
x/360 * 2pi(4.5)=1
And solve for x

[kindred jay]

find the circumfrence

find what percent of the circumfrence 1 m is

[zenith vale]

iam using arc length formula

i am getting 1/4.5

[kindred jay]

2/9?

[zenith vale]

yes

[plucky patio]

but that's in radians

it asks for degrees

which would be 12.7, no?

[zenith vale]

well

you need to convert it

in degree

lemme tyin

[kindred jay]

huh thats rly strange

[zenith vale]

well

dk

[obtuse pebble]

@plucky patio Has your question been resolved?

Channel closed

Closed by @plucky patio

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.

[timid silo]

How do you do this

[tranquil sonnet]

Power of a point

[timid silo]

Aah

What is that

In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle. It was introduced by Jakob Steiner in 1826.

ALR

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

DOING IT

I feel sucky idk elementary shet

[tranquil sonnet]

lol

[high lily]

PB is currently unknown you can keep that as PB

[timber island]

I don't understand..why is he multiplying?

[tranquil sonnet]

Wait are you doing it or are you stuck, cause I don’t mean lol if you’re stuck

[timid silo]

IDK

[timid silo]

I’m

Stuck

[tranquil sonnet]

What you have written is correct, you just need to substitute

[tranquil sonnet]

^

[timid silo]

Ah okay

Now what

Num

I got it

[timid silo]

.close

[obtuse pebble]

Channel closed

Closed by @inner torrent

Use .reopen if this was a mistake.

[tranquil sonnet]

No

That’s not right

160/10=16 @timid silo

[timid silo]

Oh

[timid silo]

AAH

OKAY

Thanks bro

[tranquil sonnet]

[timid silo]

Ahwe

[obtuse pebble]

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.

[fresh bay]

The degree is all the x together roght
So it would be 4?

[daring glacier]

degree is max power of x

so in this case its x2xx

=4

yea

[obtuse pebble]

@fresh bay Has your question been resolved?

[obtuse pebble]

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.

[brave oxide]

How’s this wrong?

[forest sinew]

bad algebra

here

[brave oxide]

Sorry I don’t want any answers from someone who cares about pronouns

[forest sinew]

haha

ell

well

it should be **+**x²

[brave oxide]

It should be infinity but yeah I guess I just plug in values that get closer and closer to 3 and see that the number is getting bigger. Problem is that I can’t use a calculator so I need to train my instinct to see when the number will end up tending to +/- inf

[cyan kite]

...

[forest sinew]

you just recognize denominator goes to 0

thats a probler

small denominator is big number

[cyan kite]

yeah

as the denominator of a fraction approaches 0, the fraction approaches infinity

[brave oxide]

Clear

Much love

[cyan kite]

👍

[brave oxide]

/close

[cyan kite]

use a dot

@brave oxide

[brave oxide]

.close

[obtuse pebble]

Channel closed

Closed by @brave oxide

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.

[pseudo ledge]

The rest of the options are "made an error on line 2..3..4" etc

[obtuse pebble]

@pseudo ledge Has your question been resolved?

Channel closed

Closed by @pseudo ledge

Use .reopen if this was a mistake.

[elfin belfry]

Error at 3) I believe

[obtuse pebble]

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.

[ocean jay]

Hello, I am confusion. Can someone help explain? 🥲

[pseudo ledge]

Thanks!

[pseudo ledge]

Make a tree diagram

[ocean jay]

Eyy wait :0 after that I understood that I'd just be needing to add 1/2 and 2/5? Or am I high?

[pseudo ledge]

I’d still recommend drawing a tree diagram 😭

[ocean jay]

Okay done😭

[pseudo ledge]

Actually think about it
To get AT LEAST one batter out,
You can’t get both batters out, right?

[ocean jay]

Yep

[pseudo ledge]

And assuming you know all probability adds up to 1

[ocean jay]

I don't get it sorry

[pseudo ledge]

Does this help?

[ocean jay]

yo I'm really sorry but I don't get it. Where did the 10 come from? And idk why I understodo that 2/5 was the answer. I'm so confused.

[pseudo ledge]

do you know how probability tree diagrams work?

or how probability of events occurring works?

You times them

So
3/5 x 1/2 = 3/10

The answer is 7/10 but if you want me to explain you can DM me 😭

[ocean jay]

Where did 3/5 came aAaA. I feel so stupid. 😭

[pseudo ledge]

If the probability he strikes the first batter is 2/5

Then the probability he DOESN’T STRIKE (D.S) the first batter is 3/5
Cuz all probability add up to 1 and
1 - 2/5 = 3/5

[ocean jay]

Ahh I get where that's found. 😭
I'll also try researching more to understand it, but really thank you. 😭

.close

[obtuse pebble]

Channel closed

Closed by @ocean jay

Use .reopen if this was a mistake.

[obtuse pebble]

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.

[versed marten]

hi

[versed marten]

what be the method to find c

[knotty crow]

rather numerical methods

[versed marten]

numerical methods

whats that

[forest sinew]

cosx = e^x

looks like its lambert

its cosxe^(-x)=1

[forest sinew]

youll have to use w function

solves ye^y=x

[versed marten]

idk what that is

lambert?

w function

?

[forest sinew]

it basically means

the solution comes using a made-up function

there is no way to write it cleanly without using a made-up function

so you approximate it

this is what numerical methods mean

you can look at newtons method

or bisection

those are two common 'easy' ones

youll want to implement them on cos(x) - e^x = 0 as a root-finding problem

[versed marten]

im jsut tryingh to find the area

[forest sinew]

https://calcworkshop.com/derivatives/newtons-method/

[forest sinew]

there's no good way to express what c is without using the made-up function

youll need to approximate it

for which you could use desmos

or make your own algorithm

there is no 'exact' way without using W

[versed marten]

hmmm

i see

very well

ty

[forest sinew]

you could just say

"c uses the lambert w function"

and just leave it as "c"

an option

[versed marten]

.close

[obtuse pebble]

Channel closed

Closed by @versed marten

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.

[timid silo]

hello

[teal turret]

Raijinmaru

What’s ur question

[timid silo]

So it needs to be expressed as a singe log

I do not understand why they do x^1/2 - 3 at the top

[teal turret]

$\log_3{\sqrt{x}} - \log_3{x^3}$ right?

Breh bot down

[timid silo]

lol yes the first one in orange

[teal turret]

Ok so do u know that the square root of x is = x^(1/2)

[timid silo]

that would be 1

[teal turret]

What would be 1

[timid silo]

oh your telling me. Yes it is rasied to (1/2) because it is taking the square root

[teal turret]

Yep

[timid silo]

And since they are being subtracted they need to be changed to division

[teal turret]

Yes

[timid silo]

So in the start it is log3 (x^1/2 / x^3)

[teal turret]

(Changed to division after the log terms are combined)

[teal turret]

Yes

[timid silo]

So here is where I am stuck

[teal turret]

How to do x^(1/2) / x^3 ?

[timid silo]

In to a single log yes

[teal turret]

Well that’s just exponent laws

For example

x^6 / x^2 = x^(6-2) = x^4

Similarly

x^(1/2) / x^3 = x^[(1/2) -3] = x^ (-2.5)

[timid silo]

Oh ok because exponent is the inverse of log

[teal turret]

Yes that’s true, but I’m not sure how that applies to this

[timid silo]

so when u have a exponet you takes the 2 power and subtract them

[teal turret]

Take a look at quotient rule

a^m / a^n = a^(m-n)

[timid silo]

ohhhh

ok

ok

[teal turret]

U get it now?

[timid silo]

So in the example video the just subtracted 3 and got like denominators ?

[teal turret]

Yes

[timid silo]

Ok think I got it

[teal turret]

Cool

Good luck Raijinmaru