help-10

[marble hamlet]

hi the problem was graph and find cartesian coords for this: (-1, -pi/6)

my question is why it does not show the negative direction, I thought this should go down -pi/6 for the arc and then move in the opposite direction

My solution came out right just wondering why they drew it this way

to be more specific, my cartesian coords came out in Q 2 - why did they draw this in Q 4 ?

[trail tiger]

Are you sure u did it right ?

If it’s -pi/6 it is in the right place

[marble hamlet]

Hmm the arc for that is the right place but if you travel -1 on the polar plane it goes to Q2

x = r cos(theta) which I got calculated to be x = -1 * sqrt(3) / 2

actually it's showing me Q3 on desmos

<@&286206848099549185>

[obtuse pebble]

@marble hamlet Has your question been resolved?

[obtuse pebble]

@marble hamlet 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.

[autumn spade]

Zaheer Khan has taken 6 five-wicket hauls in his last 15 matches. His match records are selected at random, one by one, and analyzed. If none of the match records is analyzed more than once, then what is the probability that the 8th one analyzed is his last five-wicket haul match?

[autumn spade]

idek where to begin with this one

[next reef]

What distribution do you think it is?

@autumn spade

[autumn spade]

idt they have taught us that

so idk what that means

[next reef]

What is the probability that a match picked at once, is the match that he got a five-wicket haul?

[autumn spade]

6/15?

[next reef]

Yes

We are interested in the case where 8th match analysed is the last five wicket-haul match

${}^7C_{5} \left(\frac{6}{15}\right)^5 \left(\frac{9}{15}\right)^2 \cdot \underbrace{\frac{6}{15}}_{\text{8-th match}}$

[warm shale]

QuantumBee

[autumn spade]

okay ur gonna have to explain to me this

why 7C5?

[next reef]

You can pick select 5 matches from 7 matches in 7C5 ways

It gets multiplied by the probability 6/15 to the power 5 (we select 5 matches in which the player can take five wicket-hauls)

9/15 to the power 2 for the rest of the 7 of the matches

And, the final 6/15 for the 8th one analyzed to be his last five-wicket haul match

[autumn spade]

these are the options tho

[autumn spade]

@next reef someone says that you are choosing with replacement in this answer

which is not the case

[next reef]

Is this the right question?

[autumn spade]

it is

[next reef]

Ok, I'm not sure

[autumn spade]

[next reef]

Wait for someone else to help

[obtuse pebble]

@autumn spade Has your question been resolved?

[autumn spade]

<@&286206848099549185>

[obtuse pebble]

@autumn spade Has your question been resolved?

[autumn spade]

<@&286206848099549185> anybody pls helpppp

[autumn spade]

the answer is B but i need somebody to explain to me how

[obtuse pebble]

@autumn spade Has your question been resolved?

[obtuse pebble]

@autumn spade Has your question been resolved?

[autumn spade]

this is the answer pls explain somebody

[zealous cape]

That's a bad answer.

and all of this can better be handled by not trying to do a /15!.

Okay, a quick explanation of B: we need 5 of the hauls which will be in the first 7 games. That's a 7c5. And we need two others, out of 9 of them. That's the 9c2. We've now picked out our 7 special games. Then we need those in first 7 out of the 15 games. That's the 15c7. And finally, we need to choose the last game to be the haul, 1 out of 8.

I think that's also wrong.

Here's a good attempt at a clean answer:

There are 6 matches that are special, to be distributed among 15 total. We will divide by 15c6. To satisfy the condition, we need to have chosen 6 special matches in the first 8. So 8c6 is the numerator. But we haven't accounted for the possibilty that the last match of those 8 is not special, so we multiply by 3/4 to fix that.
Actual, easy to understand answer is:

8c6/15c6*3/4.

We can then re-write that in lots of ways, starting by breaking out the factorials:

8!/2!/6!* 6!* 9!/15!* 3/4.

Breaking b up into factorials gives:
6! /5!/1!* 9!/2!/7!* 7!* 8!/15! * 1/8

With a little staring, you can see these are the same.

[obtuse pebble]

@autumn spade Has your question been resolved?

Channel closed

Closed by @autumn spade

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]

help me find x

[obtuse pebble]

Please don't occupy multiple help channels.

[tawny fog]

Any angle is given?

Rather than the 90° angle

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

nope

already did it

the answer is 36 probably

[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.

[nova dawn]

Heya, stuck with this relatively simple question on vectors!

[obtuse pebble]

@nova dawn Has your question been resolved?

[obtuse pebble]

@nova dawn Has your question been resolved?

[obtuse pebble]

@nova dawn Has your question been resolved?

[obtuse pebble]

@nova dawn Has your question been resolved?

[noble berry]

I may be off since idk vectors but maybe try proving adb and bde add to 180

[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.

[exotic escarp]

yall know how to do part c

which is this

wait dodamn

godamn

brb

but if

it was power law

how would I solve

[obtuse pebble]

@exotic escarp Has your question been resolved?

[exotic escarp]

<@&286206848099549185>

[obtuse pebble]

@exotic escarp Has your question been resolved?

[exotic escarp]

.clsoe

.close

[obtuse pebble]

Channel closed

Closed by @exotic escarp

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]

Hi I was just wondering how the red colored equation is derived form the blue colored equation?

[drifting wraith]

2x² + (6x+x) + 3 = 0

it's derived by moving around ()

[twin sapphire]

remember + is associative

meaning you can do it in any order

[timid silo]

how do yk where to it around

[patent gyro]

why is it not factorized though?

[twin sapphire]

(a+b)+c=a+b+c = a+(b+c)

[mental plaza]

next step ig

[patent gyro]

ahh i see

[timid silo]

Hold up one second

[timid silo]

Ok this is the notes that he did

Is this similar to what u said

[mental plaza]

?

why is trigo coming here

full qn pls

ah ok

substitution

[mental plaza]

yeye

that’s right

but not complete yet

[timid silo]

Ik it is but like how did we get from point a to point b

This is the notes

[mental plaza]

which is the point a?

[timid silo]

I just dont understand how he got from 2x^2 + 7x + 3 = 0 to (2x^2 +6x) + (x+3) = 0

[mental plaza]

he grp them tgt

cuz for the first bracket

if u factor 2

[timid silo]

Or here how we started from 2x^2 + 7x + 3 =0 to 2x(x+3)+(x+3)=0

[mental plaza]

u get 2x(x +3) +1(x+3)

then from there

factor out x+3

(x+3)(2x+1)

split 7x into 6x + x

[timid silo]

How do yk to split 7x into 6x + x?

[mental plaza]

it’s an dyeing thing

w enough practice

it’ll come naturally

u can do trial and error too

[timid silo]

?

by why did u split 7x into 6x + x

[mental plaza]

so when u factor

ull have common (x+3)

then u can use grouping method

[timid silo]

ok but where does splitting 7x into 6x + x go into play

[mental plaza]

https://youtu.be/t7-JCa7phCQ

[timid silo]

So essentially u split b of the quadratic equation into factors

so that u can group them?

Ok i sorta got the jist of it thx

.close

[obtuse pebble]

Channel closed

Closed by @sturdy dragon

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.

[cloud hull]

Difference between factor theorem and remainder theorem in simple words?

[cloud hull]

and similarities?

[timid silo]

factor theorem you are finding the factors of the given equation

remainder theorem is finder the remainder of that equation

I think similarities is you can use factor theorem to find remainder theorem

[cloud hull]

ohh, I see

Thanks a lot@

.close

[obtuse pebble]

Channel closed

Closed by @cloud hull

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.

[obtuse pebble]

Please don't occupy multiple help channels.

[nimble kindle]

how is the answer not 81/40???

(-40/9)*(-9/40) + 41/40 = 81/40...

[obtuse pebble]

@nimble kindle Has your question been resolved?

[nimble kindle]

<@&286206848099549185>

[opal marlin]

why do u have 40 and not 41

[nimble kindle]

wdym?

[opal marlin]

start by solving for what t is

[nimble kindle]

sin t = 40/41, cos t = -9/41, so tan t = (40/41) / (-9/41) which equals -40/9

or is sin t actually -40/41 since t is in the 3rd quadrant?

[opal marlin]

ye

[nimble kindle]

ohhhhhhhhhhhhhhhhhh

oops 🤦‍♂️

i figured it out

its -1/40

tysm

.close

[obtuse pebble]

Channel closed

Closed by @nimble kindle

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.

[warm shale]

北々な秋

[civic zealot]

Right idea, wrong execution

The conjugate of a complex number switches the sign of the imaginary part of the number.

So when you find $\overline{z+w}$ you need go rewrite z+w in the standard form of a complex number, ie m+ni for some real m and n

[warm shale]

Zybikron

北々な秋

[obtuse pebble]

@woeful berry Has your question been resolved?

[unreal skiff]

$\overline{z-w} = \overline{a+bi-(x+yi)}=\overline{a+bi-x-yi}$

[warm shale]

asuasu

[unreal skiff]

Yes it works for mul and div too

Yes it will change the sign of imaginary part

Anything(real number) attached to i

[obtuse pebble]

Channel closed

Closed by @woeful berry

Use .reopen if this was a mistake.

[unreal skiff]

np

[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.

[abstract sparrow]

Mr T has $2.75 made out of change from 5cent coins, 10cent coins and 20cent coins. If Mr T had 3 times as many 20cent coins then 5 cent coins and he had five more 10cent coins than 5 cent coins. Make an equation to find out how many 5cent, 10cent and 20cent coins he had

[abstract sparrow]

I know the answer

but i dont know the equation

[drifting wraith]

there's one variable

how many 5-cent coins

[abstract sparrow]

we dont know

thats the point

we have to find out

we have to find out how many 5c 10c and 20c coins there are

<@&286206848099549185>

[drifting wraith]

i'm describing what an equation would look like

it has one variable, so like X

(something x) = 2.75

[abstract sparrow]

yeah

you know what nvm

.close

[obtuse pebble]

Channel closed

Closed by @abstract sparrow

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.

[icy cape]

4^y * 9^x * 27 = 4 * 2^x * 3^2y

[icy cape]

please help

[lusty cedar]

Write in terms of exponent of 2 and 3 on both sides

[icy cape]

972^xy = 24^x2y

[lusty cedar]

Wait what?

No no

Like 2^something*3^somethingelse

=in same terms

[icy cape]

oh ight

[icy cape]

2^2y * 3^3y * 3^3 = 2^2 * 2^x * 3^2y

hello

...

.close

[obtuse pebble]

Channel closed

Closed by @icy cape

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.

[loud shell]

if f(a) doesn't exist then f'(a) should also not exist ryt?

[untold flax]

yes

how can a piont that doesn't exist have a gradient

[loud shell]

ty

.close

[obtuse pebble]

Channel closed

Closed by @loud shell

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.

[sage dagger]

So just wanna know if I’m on the right track here

[sage dagger]

,rcw

[sage dagger]

so it would be

x^2 + 2qx - px^2 + q^2?

and make that equal to a^2, b^2?

so is this kinda like in reverse

im confused

its not asking for

a^2 + b^2

but separately?

how do i find those separately

[loud shell]

u know vieta

[obtuse pebble]

@sage dagger Has your question been resolved?

[sage dagger]

ye

[loud shell]

use that then

[sage dagger]

so is 2qx - px^2 one whole term

so 2qx - px^2 is B then?

.close

[obtuse pebble]

Channel closed

Closed by @sage dagger

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.

[signal onyx]

Hi guys, i'm so bad at math and i have a question. I'm trying to figure out how much it would take to upload a file, i did a test on a video long 5:30 hours, and it took 14 hours to upload and now i want to know how much it would take to upload a file long 9:30 hours, so i tried to do an equation but i'm not sure if its right

[signal onyx]

It would be like 5:30 : 14h = 9:30 : x

like does this work with hours?

14*9:30 / 5:30

is this making sense... damn i might be so stupid

[royal basin]

14*9.5/5.5

[signal onyx]

What you did is convert hours into decimal numbers right? would this tool help me? https://www.calculatorsoup.com/calculators/time/time-to-decimal-calculator.php

[royal basin]

you do not need a tool imo

if you know that 60 minutes make an hour then it should not be a stretch to know that 30 minutes = (30/60) hour = 0.5 hour

[signal onyx]

In the future i might upload videos that won't be perfectly 30 minutes, maybe like 48 minutes? all i have to do is 48/60 right?

sorry for these stupid questions i'm not the brightest person

[crisp parcel]

Hey my teacher said i learn math from discord

Idk why

[royal basin]

@crisp parcel if you have a question of your own then please open your own channel, see #❓how-to-get-help for instructions.

[royal basin]

yes.

[signal onyx]

Alright thanks, what about if i want to convert the decimal number back into hours

[royal basin]

well, again, 1 hour = 60 minutes.

so to convert a quantity in hours (no matter if it is a decimal or not) back into minutes, you multiply the number by 60.

[signal onyx]

24,18 what came out from the equation

[royal basin]

,calc 14 * 9.5/5.5

[warm shale]

Result:

24.181818181818

[royal basin]

ok yeah sure

[signal onyx]

Alright this might be another stupid question, so the 24,18 is 24 hours and 18 minutes?

[royal basin]

no

[signal onyx]

damn

[royal basin]

24.18 hours is 24.18 hours.

[signal onyx]

uhhhh

[royal basin]

if you want to convert the 0.18 hours into minutes, i already told you how to do that.

or rather 0.181818... hours - the decimal expansion goes on forever.

[signal onyx]

alright

Thank you and sorry for these things i said...

Now i understand

.close

[obtuse pebble]

Channel closed

Closed by @signal onyx

Use .reopen if this was a mistake.

[royal basin]

(what were you apologizing for?)

[signal onyx]

(for my stupidity)

[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.

[timid silo]

.close

[obtuse pebble]

Channel closed

Closed by @opal shell

Use .reopen if this was a mistake.

[timid silo]

.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.

[dusk island]

Whats the difference between this way of finding the derivative than finding the derivitive with dy/dx?

[stable rain]

just diff way of finding it

think its also how derivatives r defined

[drifting badger]

What do you mean finding it with dy/dx?

[obtuse pebble]

@dusk island 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.

[tropic leaf]

Solve this limit without lhopital

[tropic leaf]

$\lim_{x\to \frac{\pi}{2}} \dfrac{\sin(x) - 1}{x\cos x}$

[warm shale]

sopinha

[tropic leaf]

What i did

$\lim_{x\to \frac{\pi}{2}} \dfrac{\sin(x) - 1}{x\cos x} = \lim_{x\to \frac{\pi}{2}} \dfrac{(\sin(x) - 1) \sin x}{x\sin x \cos x} = \lim_{x\to \frac{\pi}{2}} \dfrac{(\sin(x) - 1) \sin x}{x \cdot \frac{\sin 2x}{2} }$

[warm shale]

sopinha

[tropic leaf]

$\lim_{x\to \frac{\pi}{2}} \dfrac{(\sin(x) - 1) \sin x}{x \cdot \frac{\sin 2x}{2} } = \lim_{x\to \frac{\pi}{2}} \dfrac{(\sin(x) - 1) \sin x}{x^2 \cdot \frac{\sin 2x}{2x}}$

[warm shale]

sopinha

[tropic leaf]

$\lim_{x\to \frac{\pi}{2}} \dfrac{(\sin(x) - 1) \sin x}{x^2 \cdot \frac{\sin 2x}{2x}} = \lim_{x\to \frac{\pi}{2}}\left(\dfrac{\sin(x)}{x} -\dfrac{1}{x}\right)\cdot \frac{\sin(x)}{x} \cdot \dfrac{1}{\frac{\sin(2x)}{2x}}$

[warm shale]

sopinha

[tropic leaf]

That limit is equal to 1-2/pi = (pi-2)/pi
Where is my mistake?

The correct value is 0

[timid silo]

what did u do here

you multiplied the denominator by 1/x?

[tropic leaf]

Multiplied and divided the denominator by x

[tropic leaf]

yes

[tranquil arch]

x is to pi/2, not 0

[tropic leaf]

a

Correct, sinx/x =1 does not apply

thx

.close

[obtuse pebble]

Channel closed

Closed by @tropic leaf

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[naive bolt]

What am i doing wrong?

[cinder cosmos]

did you take
sin +cos as one term while multiplying on numerator and denominator?

[naive bolt]

I took sin + cos + 1

[cinder cosmos]

then numerator becomes

(1+sin)^2- cos^2

the only difference between two terms is cos

because one is sin+1-cos
and other is sin+1+cos

[naive bolt]

Oh

I ignored the - on cos oof

And took abc whole square

.close

[obtuse pebble]

Channel closed

Closed by @naive bolt

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.

[wintry iris]

Find the fraction of the area of a triangle that is occupied by the largest rectangle that can be drawn in the triangle (with one of its sides along a side of the triangle). Show that this fraction does not depend on the dimensions of the given triangle.

[wintry iris]

where did the blue arrow come from?

[old dagger]

Did u draw the diagram?

[wintry iris]

oops forgot to attach the image

[old dagger]

Yes

Then use the similar triangle ratio

And u will get that

[wintry iris]

Can you expound it more

I'm kinda lost. I forgot bout that topic I guess

[old dagger]

Like they have the same angle

[wintry iris]

Ohhhh now I get it

Thanks

.close

[obtuse pebble]

Channel closed

Closed by @wintry iris

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.

[umbral iris]

so i got a question:
for which values of a ∈ R, is ln(x) = o(x^a), x → ∞ ?

[umbral iris]

got trouble to find the solution

[cinder cosmos]

what is that before x^a

[umbral iris]

its not zero i would supose

its an 'o'

[tepid minnow]

yes

[haughty coyote]

ln is negligeable compared to any power of x that's strictly positive

Because any polynomial is negligeable compared to e^x

[umbral iris]

so the answer would be a is greater than 0?

[tepid minnow]

Yes I agree

[umbral iris]

thx ❤️

[tepid minnow]

because you want ln(x) / x^a ---> 0

[umbral iris]

.close

[obtuse pebble]

Channel closed

Closed by @umbral iris

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.

[lusty steppe]

someone please tell me where i messed up because i cant find it

[teal turret]

side note but is that ur handwriting? or did u write and it was converted

[lusty steppe]

its my handwriting but im writing on tablet

[teal turret]

oh wow that looks amazing

[lusty steppe]

tysm

[tepid minnow]

I don't see any mistake

why is it wrong ?

[lusty steppe]

my teacher got it to -2/9

[tepid minnow]

maybe he's wrong

it's possible he's human

[lusty steppe]

yeah thats true :p

[tepid minnow]

Did you try it ?

-2/9 ?

I guess its +- infty

[lusty steppe]

no he got the limit to -2/9, idk what he got the constant A to

thats why i cant try it

[tepid minnow]

Obviously your teacher divided by 2 but he should have divised by 1/2 at the final step

-(4/9) / (1/2)

[lusty steppe]

ohhhh i see

[tepid minnow]

and he thought -(4/9) /2

[lusty steppe]

yeah thats right

simple mistake done by him

[tepid minnow]

Try thinking to things like that, teacher are not robots

And checking his answer is always a good thing to do

[lusty steppe]

yeah thanks!

[obtuse pebble]

@lusty steppe Has your question been resolved?

Channel closed

Closed by @lusty steppe

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.

[blazing spire]

Hey

[blazing spire]

So

I recently learned

Complex number

can anyone explain me this
root under -1 * root under -16

Imaginary numbers*

[lusty steppe]

so basically the square root of 16?

[timid silo]

no

sqrt(a)*sqrt(b)=sqrt(ab) is not true if a<0 and b<0

[timid silo]

sqrt(-1)=i

sqrt(-16)=sqrt(-1) * sqrt(16)

that's a hint I will give

[obtuse pebble]

@blazing spire 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 kernel]

can you translate the question in english pls

sorry i can't french

[slender lagoon]

Prove that with n belongs to N

[brave kernel]

ah ok

thanks

so negative numbers can't be

you can explain to me why?

[slender lagoon]

We have sqrt

[brave kernel]

yes

[unreal skiff]

you can bound the LHS between sqrt(4n+1) and sqrt(4n+2)

[slender lagoon]

What is LHS

[unreal skiff]

sqrt(n)+sqrt(n+1)

[brave kernel]

LHS = Left hand side of an equation

[slender lagoon]

How

[unreal skiff]

take a square and try to simplify the form

oh when i say LHS, it means no floor function

[slender lagoon]

I found

4n+1<sqrt n + sqrt n+1

[unreal skiff]

yeah now compare it with 4*n+2 too

[slender lagoon]

@unreal skiff

[unreal skiff]

cool now you have to prove that 4n+2 cant't be square of integer

[slender lagoon]

How

[unreal skiff]

Hint: ||check modulo 4||

[slender lagoon]

Its 2

[unreal skiff]

well that means it is divided by 2

but not 4

[slender lagoon]

Yea

[unreal skiff]

what do you think? can it be square of number?

[slender lagoon]

It cant

[unreal skiff]

Now i think there is only few observations left to do

[slender lagoon]

So

[unreal skiff]

1. You know that LHS is bounded between 4n+1 and 4n+2

2. 4n+2 can't be squared of integer

is it possible for floor(sqrt(4n+1)) to be different from floor(sqrt(4n+2))

[slender lagoon]

I think no

[unreal skiff]

you are right. but you have to show it

[slender lagoon]

Sqrt 4n+1 can be square of number . Yeah ?

[unreal skiff]

yes

I suggest you draw a line of integer and split it into blocks of [x^2,(x+1)^2]

and see if you can put 4n+1 and 4n+2 on different block

[slender lagoon]

How to draw that ?

[unreal skiff]

now where can i put 4*n+2

[slender lagoon]

I dont have idea to say why it next to it

[unreal skiff]

It should be between 4*n+1 and x^2 right

because 4*n+2 cannot be square

[slender lagoon]

Why it cant be after x'2

[unreal skiff]

because the different between 4n+1 and 4n+2 is only one

so there cannot be integer between that

[slender lagoon]

Yeaah

[unreal skiff]

so the floor function of sqrt of those two will be lower bound

of block

which is ?

[slender lagoon]

X_1

[unreal skiff]

now where can you put sqrt(n)+sqrt(n+1)

[slender lagoon]

Floor of sqrt 4n+1

And sqrtn+sqrt n+1 between them

[unreal skiff]

exactly

[slender lagoon]

Yeeh

Thanku sm

[obtuse pebble]

@slender lagoon 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.

[supple cypress]

How do I find this limit algebraically

[obtuse pebble]

@supple cypress 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.

[exotic sand]

Can I get help in this multiple choice question?
Which pair do not represent allied angle?
1- 90 +- theta
2- 60 +- theta
3- 180 +- theta
4- 270 +- theta
The option selected here is 2nd. But allied angles are the angles which on addition or subtraction, become multiple of 90. Like 150 + 30. So here the value of theta could only be 30 (ignoring negative sign) for the second option to be correct. But value of theta isn't mentioned here. How is it solved then?

[pale sage]

it could also be 120 since it gives 180 which is a multiple of 90, but that's beside the point

if theta isn't given then I'm not sure how you'd answer

[exotic sand]

It is written on the same page that allied angles are ones in which theta is being added to multiple of 90. In this case 60+theta won't be allied angle as 60 is not a multiple of 90 and 2nd option would be correct but it is not the actual definition of allied angle right?

[pale sage]

2 angles are allied if their sum is equal to 0, 90 or a multiple of 90

given angles 60 and theta they can be allied if theta is 30, 120, 210 etc..

it depends on what theta is

[exotic sand]

okay thanks

.close

[obtuse pebble]

Channel closed

Closed by @exotic sand

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.

[unborn sky]

.close

[obtuse pebble]

Channel closed

Closed by @unborn sky

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.

[last kelp]

Need help

[twin sapphire]

ask your question directly

[last kelp]

I don’t know if I got the second one right

And I’m not sure how to do the last two

[twin sapphire]

what did you try for the first two?

[last kelp]

That’s the second

That’s the first

[twin sapphire]

first is right

second why did you change B={2} U[3,4) to B=[2,4)

?

[last kelp]

I thought you had to convert it to a set notation

[twin sapphire]

you cant do better than this

two disjoint intervals is not equal to a single interval

like for example 2.5 isnt in B right?

given this

but 2.5 is in [2,4)

[last kelp]

No

I realised that

It didn’t make sens e

But I still did it

[twin sapphire]

to me B is already in "interval" notation

because you cant simplify it more

and B is expressed through a union of disjoint intervals

so it seems you understand what are intersection and unions

maybe try to work out what is AnB

without doing something that doesnt make sense

[last kelp]

Should I exclude the 2

[twin sapphire]

no

[last kelp]

Okay

[twin sapphire]

you should keep B as it is

[last kelp]

Ill try again

Okay give me 5 mins

[twin sapphire]

sure

[last kelp]

Do I just say that they are disjoint?

Or would I use this symbol

[twin sapphire]

if you thinkk they are disjoint yeah its that

this means empty set

like there are no elements in it

[last kelp]

Oh

So would that be my answer

[twin sapphire]

almost right

AnB = {2}

(i use "n" for intersection symbol)

[last kelp]

What howww

[twin sapphire]

2 is in A

and 2 is in B

so its in AnB

[last kelp]

Ohhhh okay okay I was think of the whole notation including the C intersection

I think I’ve got it from there with question two

[twin sapphire]

oh

[last kelp]

The last two

[twin sapphire]

i was just talking about AnB

but its a union with C

not an intersection

[last kelp]

My bad I meant union

[twin sapphire]

so you got empty set for the union?

[last kelp]

Give me a sec

And no

I didn’t

Wouldn’t it only be an empty set if it was an intersection with c

In the case of a union

I’m not sure what to do

Actually

Would it be (1,3)

[twin sapphire]

for union it is indeed (1,3)

[last kelp]

I’m wrong

For intersection

[twin sapphire]

for intersection it would be {2}

[last kelp]

U said it

For the last 2

[twin sapphire]

i said earlier that AnB={2}

what im saying now is that

AnBnC={2}

[last kelp]

For the last two was a separate comment

I just forgot to Type the rest

For the last two I’m unsure

For three it got [3,4)

[twin sapphire]

oh ok

[last kelp]

I

[twin sapphire]

thats rtight

but also i'm not sure how you get those because sometimes your answers are right and sometimes theyee wrong but i dont get how you do it

did you understand why you got it wrong in the 2nd case?

[last kelp]

For number 2

?

For number two I went wrong because I tried to combine disjointed values instead of treating them as what they are… disjointed values

Since two was disjointed

[twin sapphire]

yeah but you said you got empty set

also

[last kelp]

It meant that there is a gap between the two sets in which x can not be

That’s why it wouldn’t make sense for me to combine it

The two sets

The symbol?

[twin sapphire]

its not clear

what are you trying to say

?

[last kelp]

Are U saying that I was claiming there was an empty set because of the symbol

[twin sapphire]

oooh i get it

[last kelp]

I thought this symbol mean they are disjointed. But even then the answer still wouldn’t be right.

[twin sapphire]

you werent saying AnB=empty

[last kelp]

I can’t put disjointed as an answer

[twin sapphire]

this symbol is for the empty set

and A and B are disjoint

if and only if

AnB =empty set

[last kelp]

U helped me realise that

[twin sapphire]

but in our case A and B are not disjoint right?

[last kelp]

No no

B is the only disjointed set

[twin sapphire]

a set alone cant be disjointed

[last kelp]

Class

[twin sapphire]

its just that B can be defined as a union of two disjoint intervals

[last kelp]

??/

[twin sapphire]

disjoint is a relation between two sets

[last kelp]

Okayyyyyy

That’s how u describe it

Disjoint describes the existence of two sets that don’t coincide

[twin sapphire]

yeah

not the existence

but a property

of those two sets

together

[last kelp]

Thank you

[twin sapphire]

so now lets try 4?

[last kelp]

For the last question. I know that the value of the compliment of b would be any real number that is not contained within b. Only issue is that I’m not sure how to format the interval.

This is what I got

[twin sapphire]

why is it a closed interval for 2,3?

and also you should use union

since thats what it is

[last kelp]

Idk why I did that. It can’t be closed intervals for two or three since those are already values in B

I think I just made a mistake

[twin sapphire]

yeah so its just open

on both

but appart from that its good if you add the union

s

B^c = (-inf,2) U (2,3) U[4,+inf)

[last kelp]

Yeah that’s what I did after you corrected me

I think I’ll be good from here. Tysm

[twin sapphire]

good luck

[obtuse pebble]

@last kelp 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.

[valid aspen]

i can't do this one, i keep getting 0 when the answer is 2

[haughty coyote]

Linear approximation of sqrt(1+x) for small x makes it very simple

[viral blade]

Take the limit as r->0

or r^2->0

substituting r²=x²+y²

[thick fog]

The easiest way imo is to just multiply by the conjugate. You can do the entire limit in your head.

When you multiply by the conjugate the +1 and the -1 cancel (in the denominator), which lets you cancel the x^2 + y^2 in the numerator and in the denominator. Then you immediately see the sqrt(1) + 1 = 2 remaining.

[valid aspen]

Ohhh

it worked, thanks guys

[obtuse pebble]

@valid aspen Has your question been resolved?

Channel closed

Closed by @valid aspen

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.

[next yoke]

How am I supposed to solve for problem 1? This problem is confusing to me

[next yoke]

I subtracted the 90-55 and got 35 and subtracted 1000-500 and got 500, so 35/500 does not make sense. How does that work

[hexed agate]

For b? They want you two ordered pairs

Ordered pair is like (x,y)

[next yoke]

Alright yeah they just want the ordered pair. Did I get it right?

[hexed agate]

No

They are given in the question

They want two ordered pairs that are clearly written on the question

[obtuse pebble]

@next yoke 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.

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.

[sour jungle]

Given:
--> Initial positional vector "P" using XYZ coordinates, will always be on the sphere.
--> Initial velocity direction "V" using XYZ coordinates, this is the direction "P" will travel across the sphere.

Find:
If "V" has a constant velocity value, using the direction of "V" and current position of "P"..... find an integral equation that will integrate "P" 's X,Y,Z position over time

[royal shard]

what exactly are we looking for?

[sour jungle]

I am looking for P's position overtime as it follows the velocity vector direction

[royal shard]

ah ok

since P and V are given, can you give them?

[sour jungle]

"V" can have any direction as long as it is tangent to sphere and stems from P

[royal shard]

or are they arbitrary

ah ok

[sour jungle]

arbitrary

[royal shard]

sad

[sour jungle]

Everything is given in XYZ coordinates, I'd like to integrate "P"'s position so I can have it's components (X,Y,Z) in a graph over time

[royal shard]

i would say P(t)=P+V(t)*t

but then we need V(t)

which is dependent on P(t)

[sour jungle]

Yeah, which is the harder part to do together 😦

[obtuse pebble]

@sour jungle Has your question been resolved?

[sour jungle]

<@&286206848099549185>

[obtuse pebble]

@sour jungle Has your question been resolved?

[sour jungle]

Did you have any advice or any direction I could try?

[royal shard]

if there is nothing else given, then i dont know

[obtuse pebble]

@sour jungle Has your question been resolved?

[obtuse pebble]

@sour jungle Has your question been resolved?

[obtuse pebble]

Channel closed

Closed by @sour jungle

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.

[abstract galleon]

I know its not cubic is it cubed root?

[abstract galleon]

this is the only thing I need help with

i remember every other graph

except this one

its not exponential

its not square root

its not cubic (i think)

most def not quadratic

[obtuse pebble]

@abstract galleon Has your question been resolved?

[obtuse pebble]

@abstract galleon 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.

[sacred birch]

hey i have to find the derivative of this equation. how can i do this?

[sacred birch]

so you could get 3/(5x^4) + 2/(4x^3) +6*(x^1/3)

but thats where im stuck

[obtuse pebble]

@sacred birch Has your question been resolved?

[inner vault]

Term by term:

d/dx(3/(x^5))
=((x^5)(0) - (3)(5x^4))/((x^5)^2) (Quotient rule)
=(-15x^4)/(5x^10) (Simplify)
=-3/(x^6) (Simplify)

d/dx(2/(x^4))
=((x^4)(0) - (2)(4x^3))/((x^4)^2) (Quotient Rule)
=(-8x^3)/(x^8) (Simplify)
=-8/(x^5)

d/dx(6(x^(1/3))) (Cube root of x = x^(1/3)
=6(1/3)x^(-2/3) (Power rule)
=2/(x^(2/3)) (Simplify)(Could also be written as the cube root of x squared)

All terms:

-3/(x^6) + -8/(x^5) + 2/(x^(2/3))
= ((-3) + (-8x) + (2x^9))/(x^6) (LCD)
=(2x^9 - 8x - 3)/(x^6) (Reorder)

You might wanna check my work I did this on phone

[sacred birch]

you are a god.

[inner vault]

Lol thx

[sacred birch]

thank you! ill check over it but i appreciate the help cuz i was very lost on this

.close

[obtuse pebble]

Channel closed

Closed by @sacred birch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[obtuse pebble]

@lavish zinc 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 shard]

my teacher gave me a problem to solve for tan5theta in terms of tantheta

i used de moivres theorem to compare real and imaginary parts to get sin5theta and cos5theta

but im kinda stuck

any hints?

i tried factoring the fraction at the bottom but no luck

if the image is too small to read let me know and ill send zoomed in parts of it

nvm i got it

it was this simple

.close

[obtuse pebble]

Channel closed

Closed by @late shard

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.

[scenic sable]

can someone explain the steps my teacher did lol

[obtuse pebble]

Please don't occupy multiple help channels.

[storm tapir]

You're learning about inverse functions right?

In the equation, you get the inverse by just switching all the x with y and all the y with x

So he replaced g(x) AKA y with a, and replaced x in the log2(x+3) with y

Then he added 5 to both sides

So he skipped a step

Should've been x+5 = log2(x+3)

[scenic sable]

ooh

[storm tapir]

And then he did 2 exponent of the entire equation

[scenic sable]

ok

how did he graph it tho?

[zenith raft]

it might not be about inverse functions?

[storm tapir]

You just switched the x values with the y values

If originally when x is 1 y was 2 then in the inverse y is 1 and x is 2

[scenic sable]

yea but how did he find the first set of values

[storm tapir]

He must've plugged them into the original equation

[scenic sable]

?

[storm tapir]

Like, solved for y depending on x

[scenic sable]

lol yea but how did he know how to use those numbers?

[zenith raft]

from your other post I thought it was just to get nice numbers to use for the table

[scenic sable]

for example can i plug in any number

[storm tapir]

The table seems like he plugged in when x is -7 up to -2 and he must've done the calculation

[scenic sable]

oh?

[scenic sable]

wdym

[storm tapir]

For example g(-7) = log2(-7+3) -5

[scenic sable]

yea i got that part down but im confused on how he decided to use -7

[storm tapir]

Hold up what the fuk

Oh

[zenith raft]

if you just try like x = -2.5, x = -2, x = -1, x = 0 and such, g evaluated at that those points won't be integers

[storm tapir]

He did it for the other one

[scenic sable]

ohh

so he calculated the points that would be integers?

[scenic sable]

which?

[storm tapir]

Mb he plugged in x as -7 up to -2 for the inverse

Like the 2^x+5 -3 = y

[zenith raft]

yea pretty much

[storm tapir]

So like 2^(-7+5) -3 = y

And then in the bottom table he switched the values

[scenic sable]

but how would i know which numbers would be make an integer

[scenic sable]

oh

im still stuck on why he chose -7

up to 2

[zenith raft]

it was kinda arbitrary

could have been -9 or -10 or -15

[scenic sable]

oh rlly

cuz thats what i was thinking

so if i plugged in a random number it would still work?

[zenith raft]

yea unless there are some weird strict rules for what points to plot lol

[scenic sable]

ok so i can plug in -3, -2, -1 0, and 1?

[storm tapir]

Yeah it is probably, but the general trend for this function 2^x+5 -3 seems to be that when x is more negative, the 2^x+5 is getting smaller and smaller so I think the numbers from -2 to -5 were relevant and it makes sense that he went over a little bit

If you look at the plot he did of the original function, the log one, you see the points he collected are all pretty relevant to the shape of the graph. He probably predicted this by thinking about how the function will behave and chose points accordingly

[scenic sable]

ohhh

idk how to choose points accordingly tho

😔

[storm tapir]

Yeah but you can kinda tell by experimenting in your head and like just doing critical thinking

Analyzing the behavior of some functions would give you insight

For example all exponential functions like 2^x or 5^x or anything similar all tend to get smaller and smaller if you go towards negative infinity but larger and larger if you go towards positive infinity

Also, 2^0 = 1, so when x was -5, 2^(-5+5) was 2^0

[scenic sable]

ohh

thats kinda confusing ngl😭

[storm tapir]

Yeah sorry, but you kinda get a feel for it after doing many problems

Usually you want to plot points where things are happening. Like I would say f(-999) isnt so different from f(-1000), but f(-5) is very different from f(-4) In the function you sent so you would want to look for points there

[scenic sable]

okk

thx for the help

.close

[obtuse pebble]

Channel closed

Closed by @scenic sable

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.

[agile whale]

hi

[agile whale]

is this correct

<@&286206848099549185>

[violet sentinel]

!15m

[obtuse pebble]

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

[agile whale]

my fault

is it right tho

!doone

!exist

!exit

!finish

!close

!end

im donw

done

Close this

[analog jetty]

Do .close

[obtuse pebble]

@agile whale Has your question been resolved?

Channel closed

Closed by @agile whale

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.

[broken matrix]

I need help solving #9. I'm so lost

[timid silo]

you probably would find better help in the physics server

[obtuse pebble]

@broken matrix 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.

[bleak scaffold]

Hello can anyone help me which is true and wich is false?

[zenith raft]

for a, intersect two circles

[bleak scaffold]

so its true?

[zenith raft]

wait shoot sorry I totally misread

yea, it's true

[bleak scaffold]

and how to prove it?

@zenith raft

[zenith raft]

what's the definition of convex?

[bleak scaffold]

A subset C of R
n is called convex if
λx + (1 − λ)y ∈ C, ∀ x, y ∈ C, ∀λ ∈ [0, 1].

like that?

[zenith raft]

yea sure

kinda follows right from the definition now

let x and y be points in A int B

and λ be in [0,1]

A is convex, B is convex

so... λx + (1 − λ)y is in A and in B

and that's kinda all there is to it lol

[bleak scaffold]

thank you so much

[zenith raft]

yep ^-^

[bleak scaffold]

in b its also true right?

from the convex definition?

λx + (1 − λ)y ∈ C, ∀ x, y ∈ C, ∀λ ∈ [0, 1]

[zenith raft]

I think so

[bleak scaffold]

I don't understand c

what to do there?

[zenith raft]

not sure, never heard of polar cone :c

sounds tasty though

[bleak scaffold]

okey and d or e?

[zenith raft]

e might be true

[bleak scaffold]

1 A set C c lRn is a cone if AX E C for all A � 0 and
all x E C.

[zenith raft]

I have no idea about c and d, sorry

I think e is true but it seems annoying to prove

[bleak scaffold]

@zenith raft

[zenith raft]

I'm sorry I don't know 😭

[bleak scaffold]

.close

[obtuse pebble]

Channel closed

Closed by @bleak scaffold

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.

[gleaming coral]

can someone please help me to find where i went wrong

[gleaming coral]

question:

solve the equation sin2x=2sin^2 x for 0<x<2pi

so i expanded the question

becomes

2sinxcosx=2sinxsinx

therefore

cosx=sinx

and if you divide both sides by cosx

it becomes

tanx=1

and if you graph that and solve it

x=45,225

but the answer has 3 more points of intersection that i didnt get

[royal basin]

you forgor the solutions which satisfy sin(x)=0

you lost them when you divided out by sin(x)

[gleaming coral]

oh

is there another/better method to do this question?

[gleaming coral]

this is hard to see at first

[royal basin]

well you could subtract rhs from both sides then factor

2sin(x)(sin(x)-cos(x)) = 0

[gleaming coral]

ahh

i see

thanks

.close

[obtuse pebble]

Channel closed

Closed by @gleaming coral

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.

[royal basin]

tfw the watermark is more visible than the text itself

[untold flax]

lol

[untold flax]

which part you stuck on

[proper raptor]

i mean i just dont really get the question

[untold flax]

q 6?

[proper raptor]

yea

[untold flax]

what's the formula for working out gradient

[proper raptor]

y2-y1/x2-x1

[untold flax]

ok

so change in y / change in x

we're given that this = 3.5

what else are we given

[proper raptor]

height is 7

[untold flax]

so what's change in y?

[proper raptor]

wdym

[untold flax]

what's y2 - y1

[proper raptor]

7?

[untold flax]

ye

now solve for the horizontal distance

so the x distance

[proper raptor]

2?

[untold flax]

yes

[proper raptor]

o

ok tysm

[untold flax]

well you're not done

do you see how to solve now?

[proper raptor]

yea

y2-y1 = height x2-x1 = horizontal distance

just didnt realise that

[untold flax]

ye

how would you work out length of ladder now

[proper raptor]

pythagoras?

[untold flax]

👍

smae type of thing for q7

[proper raptor]

ok

ty for your help

[untold flax]

np

[proper raptor]

.close

[obtuse pebble]

Channel closed

Closed by @proper raptor

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.

[bold siren]

is it correct?

[obtuse pebble]

@bold siren Has your question been resolved?

[obtuse pebble]

@bold siren 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.

[static patio]

L are languages, R is reverse and h^1 preimage

are those languages equal?

[royal basin]

try $L = {ab}$ and $h : {a,b,c}^* \to {a,b}^*$ defined by $h(a) = a, h(b) = b, h(c) = ab$

[warm shale]

Ann

[obtuse pebble]

@static patio Has your question been resolved?

[static patio]

ah

so difficult

[static patio]

so both inclusions do not hold ?

[royal basin]

i wouldn't have come to this conclusion just by analyzing the example i presented