help-10

[worn yacht]

.close

[obtuse pebble]

Channel closed

Closed by @worn yacht

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.

[calm ginkgo]

what is this?

[buoyant silo]

the bar means "3 repeating"

so 1.13333333333...

[calm ginkgo]

as a simplified fraction though

its not 1/8

and its not 1/9

[buoyant silo]

here's my trick

we know 1/3=0.333... right

[calm ginkgo]

yea

[buoyant silo]

we can think of 1.1333... as 1.1+0.0333...

and 0.0333... is just 0.333.../10

does this make sense?

[calm ginkgo]

wait what?

oh

hmm

so 1/30?

OH its 34/30

cuz 33/30 is 1.1

and 1/30 is 0.033333...

thanks!

.close

[obtuse pebble]

Channel closed

Closed by @calm ginkgo

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.

[raw lion]

it’s set up as long division

wants me to work it out some long way

my teacher did it with me on a white board but i forgot..

[daring rock]

Long division? or synthetic division?

[raw lion]

long

that’s how it’s wrote out

she did something where she put the zeros

and yea

gives me a headache

[daring rock]

Oh wow okay

That wouldn't be my first choice of method but sure

Yeah, she put the zeros in because you want to have every term represented

so yeah the first thing you want to do is set it up like this

And then we're going to take steps that are (more or less) the same as what you would do with ordinary long division

[raw lion]

above the r6 is going to be r5

[daring rock]

yes

because if you look at the first term of your divisor (r+2), you'd have to muiltiply it by r^5 to get r^6

[raw lion]

mhm

[daring rock]

then think about how you'd do like grade school long division with regular numbers

[raw lion]

this is gonna sound terrible

but i forgot majority of it 💀

[daring rock]

lol no worries

take the last term you wrote on top: r^5

and multiply it by the divisor (r+2)

[raw lion]

2r5

[daring rock]

r^5 (r+2)

is r^6 + 2r^5

so we write that under the corresponding terms, and subtract

then bring down the next term, like this

then repeat until you get to the end

[raw lion]

so on top i got 2r4

if that makes sense

[daring rock]

-2r^4

it should be negative

[raw lion]

you have no idea how many times i’ve screwed up forgetting to put the negative sign

[daring rock]

I am very familiar with that particular mistake lol

[raw lion]

is that what i should have now or?

0+0r^4+0r^3

[daring rock]

when you multiply on the way down, multiply by the entire divisor r+2

so -2r^4 (r+2)

which is -2r^5 - 4r^4

then subtract that and you should get

4r^4

then bring down the next term to get

4r^4 + 0r^3

[raw lion]

i’m confused

apologies im a bit slower at learning things now i had a brain injury few years back that haunts me everyday at school

[daring rock]

all good

one sec

So this part

instead of just doing -2r^4 times r,

do -2r^4 times (r+2)

so instead of just -2r^5, you should get -2r^5 - 4r^4

then subtract and bring down the next term

[raw lion]

4r^3

[daring rock]

for the next term on top

yes

[raw lion]

then on the bottom would it now be 8r^3+0r^2

[daring rock]

close

back up one step

you multiplied to get the new thing at the bottom

then subtracted, right?

in particular, you subtracted 0 - 8

so that should be -8r^3

[raw lion]

so -8r^3 + 0r^2

[daring rock]

yes

do you see why?

[raw lion]

yes

[daring rock]

ok awesome

just keep going like this

[raw lion]

-8r^2 on the top

[daring rock]

yep

be careful on this part, you're going to be subtracting a negative

[raw lion]

16r^2

[daring rock]

after subtracting, right?

[raw lion]

yes

[daring rock]

yep 👍

[raw lion]

then bring the next one down

[daring rock]

yep

[raw lion]

16r on top

then 32r

[daring rock]

be careful with the negatives

you'll be doing 0r - 32r

so after subtracting you'll end up with -32r

[raw lion]

whoops

so then -32 on the top

[daring rock]

yes

but

[raw lion]

-32 x 2

[daring rock]

did you bring down the next term?

[raw lion]

yes

[daring rock]

You should have -32r-64 on the bottom altogether

[raw lion]

i did

[daring rock]

beautiful

[raw lion]

and i am done

[daring rock]

yes, you should end up with a remainder of 0

at the bottom

[raw lion]

I appreciate this so much

i don’t know why but out of all the questions

this one made me hate life the most

[daring rock]

Long division with polynomials can definitely be confusing. Lots of subtraction and places to make mistakes

There are definitely better ways to do this rather than long division

but I guess your teacher really wanted to make sure you know how to do it this way

[raw lion]

she claimed it was the easiest way 💀

[daring rock]

eh

In some cases, it might be your only choice

It's the most reliable way, it works all the time

but in this particular problem, synthetic division or factoring would have been way easier

[raw lion]

ah

welp i gotta get a shower

@daring rock i hope you have a amazing life and a good rest of your day/night

[daring rock]

Same to you 😄

[raw lion]

!close

.close

[obtuse pebble]

Channel closed

Closed by @raw lion

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.

[patent jetty]

,rotate

[patent jetty]

I'm getting the integral of e^tan-1 n stuff somewhere

After lde+byparts

What next

You know... For finding curve

Solution whatevr

[neon eagle]

can you send your working

[patent jetty]

Ohh wait I got it know nvm thanks

.close

[obtuse pebble]

Channel closed

Closed by @patent jetty

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.

[analog coyote]

I'm not sure where to go from here

or whether my approach is right at that

[unreal musk]

Are you sure about that?

[fierce lagoon]

3(1/5)^(2x) -> 3(2y)^2

That ain't right

It'll be $-3(2)^{2x}y$

[analog coyote]

interesting

[fierce lagoon]

Well not even

That

Yeah no

[analog coyote]

i see that i did my basic math wrong there lol
is my approach even right though?

[fierce lagoon]

$\left(\frac{2}{5}\right)^{2x} = 2^{2x}5^{-2x}$

[warm shale]

Umbraleviathan

[analog coyote]

alright wel lthanks

.close

[obtuse pebble]

Channel closed

Closed by @analog coyote

Use .reopen if this was a mistake.

[fierce lagoon]

.reopen

[obtuse pebble]

✅

[fierce lagoon]

Give me a sec to figure this out

[analog coyote]

alright, thanks

[fierce lagoon]

Ngl this just be a graph-and-see kinda problem

,w NSolve[4(5)^x - 3(0.4)^(2 x) == 11, x]

[tardy epoch]

Extra =

[fierce lagoon]

No that's how wolfram works

It's supposed to be ==

Unless they just changed it

Yeah

Wolfram makes it ==

[solemn osprey]

I thought u use logarithms

[fierce lagoon]

Could you?

That 11 makes it kinda annoying

Ugh

[solemn osprey]

Make sure to remember all your logarithm properties

[fierce lagoon]

,w FindRoot[4(5)^x - 3(0.4)^(2 x) - 11, {x, 0}]

[warm shale]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[solemn osprey]

Wait nvm. Maybe log can’t help

[fierce lagoon]

Yeah it won't lol that 11

[fierce lagoon]

Well this is what I got using wolfram lol

Uh

You cannot make a nice substitution

[solemn osprey]

What if u make each term’s base the same? So 11 would be 5^log_5(11)?

[warm shale]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Umbraleviathan#3607

[fierce lagoon]

You could

Try that

Still that

Ehh no

That 11 isn't making it any easier

[unreal musk]

More maddening is that it's 0.4 rather than 0.2

[fierce lagoon]

I could only think of graphing it

[analog coyote]

exactly my thoughts

[fierce lagoon]

Which

I had to use FindRoot

Even wolfram had a moment with NSolve and Solve

So like even it had a meltdown

[unreal musk]

Don't think you get a nice polynomial from it, as then $2 = 5^{\log_{5}(2)}$

[warm shale]

chartbit

[fierce lagoon]

,w FindRoot[4(5)^x - 3(0.4)^(2 x) - 11, {x, 1}]

[warm shale]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[fierce lagoon]

I still get 0.675811

,calc e^(0.675711)

[warm shale]

Result:

1.9654298999634

[fierce lagoon]

,w Log[2]

[warm shale]

Results provided by WolframAlpha

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

Requested by Umbraleviathan#3607

[fierce lagoon]

Hmmm

[unreal musk]

,w 4(5^x) - 3(0.4^(2x)) = 11

[warm shale]

Results provided by WolframAlpha

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

Requested by chartbit#3171

[fierce lagoon]

Yeah I guess

It's just 0.675811

[unreal musk]

Took so much fighting to get Wolfie to recognise what I wanted too

[fierce lagoon]

Yeah ngl @analog coyote it's probably a shit question. You have to graph this or use external resources

I had to resort to FindRoot, which basically finds the zeroes of a function 💀

[analog coyote]

alright well at lesat its better than me just not knowing how to do it (it was on a solving review page xD)

i thought i was tripping

thanks everyone though lol

.close

[obtuse pebble]

Channel closed

Closed by @analog coyote

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.

[worn yacht]

how do I do this?

[proud glacier]

use pythagoras theorem

[obtuse pebble]

@worn yacht Has your question been resolved?

[royal basin]

give names to all relevant points on the diagram. calculate as many side lengths as you can, primarily by identifying right triangles and applying the pythagorean theorem to them.

in case you go into choice-paralysis regarding what names to give to points, here are some.

@worn yacht do you understand what i am telling you to do?

[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.

[high locust]

im not sure why im getting these two wrong? can someone help me?

[tardy epoch]

Show your work for those 2

[high locust]

last one:

f(a+1) =

[tardy epoch]

Your last 3 became a 4

[high locust]

ahhh okok

[timid silo]

woah last time i saw riemann he was green

now he's yellow

👀

anyways

for the 5th one

you just have to replace x with (a+1) as you've done so far

[high locust]

ah yeah, i realized i accidentally put a 4 instead of a 3

now im just stuck on the last problem

[tardy epoch]

You have +25a^2 here

[tardy epoch]

But not here

[high locust]

AHH

ok thank you guys!!

.close

[obtuse pebble]

Channel closed

Closed by @high locust

Use .reopen if this was a mistake.

[timid silo]

ah that's why i was struggling to find what was wrong in the rpocess

[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.

[north scroll]

Question 1, 5th part

[north scroll]

Ping me

[sharp pecan]

where are you stuck there?

there isn't really much to do if you only have to combine

[gleaming ridge]

You only have to expand the brackets and then combine

[north scroll]

The thing

Is

I don't know if we can do like

x^2+3x^2

Because y^3 is multiplying with x^2

[sharp pecan]

you cannot split stuff like x^3y^2

[north scroll]

What do you mean

[sharp pecan]

where is this supposed to come from

[north scroll]

See the question

[sharp pecan]

you will never get a term with only x or only y

the x and y stay together

[north scroll]

Oh okay

Thanks

Bye

.close

[sharp pecan]

you could also rewrite $a=x^3y^3$, $b=x^2y^3$, $c=x^2y^3$

[obtuse pebble]

Channel closed

Closed by @north scroll

Use .reopen if this was a mistake.

[warm shale]

Jigglyproff

[north scroll]

Ohh thanks

Tysm

[sharp pecan]

then replace at the end again

yw

[north scroll]

Yes I get it now

[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.

[young sparrow]

In How many ways 5 physics professors and 3 chemistry professors be seated on a round table if No Professors of chemistry are adjacent?

[young sparrow]

Circular Permutation Problem

i tried but only got confused more

[verbal niche]

wdym not adjacent

[versed turret]

Not next to each other

[young sparrow]

so anyone?

[rain kelp]

5x3x5x3x5x3x5x8?

idk just guessing

[young sparrow]

dont know

[rain kelp]

because its setup to be PP CP PP CP PP CP PP

then ur left with one extra PP who can sit anywhere

actually nvm

idk

[verbal niche]

could it be 5! + 3! ?

[young sparrow]

the answers says 4! x 5 x 4 x 3

[strong atlas]

there are 5 physics proffessors

so the number of ways to arrange them on a round table are 4!

now between the 5 physics proffessors

thr are 5 gaps for the 1st chemistry teacher

4 gaps for the 2nd chemistry teacher

and 3 gaps for 3rd chemistry teacher

so 4! x 5x4x3

[versed turret]

Some of the arrangements of physics profs force the chemistry ones to be adjacent

[strong atlas]

what

the total number of seats are not given

[young sparrow]

but how can there be 5 gaps? there are only 3 seats left now right?

[young sparrow]

oh so if total no, of seats were given than how would answer change?

[versed turret]

Sure, but there are eight total profs

Presumably they don't mean you can space them out by a kilometer or something

[obtuse pebble]

@young sparrow Has your question been resolved?

[obtuse pebble]

@young sparrow Has your question been resolved?

Channel closed

Closed by @young sparrow

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.

[gritty path]

√x+3 = √x + 3

[gritty path]

is there an x?

[timid silo]

are u trying to say

$\sqrt{x +3} = \sqrt{x} + 3$

[warm shale]

♡LexQa♡

[sage geode]

You mean "Is there an x for which $\sqrt{x + 3} = \sqrt{x} + 3$?"?

[warm shale]

A Lonely Bean

[gritty path]

yes

Iike find the x

[timid silo]

$\sqrt{x +3} = \sqrt{x} + 3, \enspace x \in \emptyset$

[gritty path]

i tried everything i know, is it false?

[timid silo]

aka never

[royal basin]

@timid silo \emptyset and \varnothing exist.

[timid silo]

thanks

[warm shale]

♡LexQa♡

[timid silo]

thats better

[gritty path]

does this mean it's false?

[sage geode]

Yeah there's no such x

[gritty path]

tnx

.close to free

[obtuse pebble]

Channel closed

Closed by @gritty path

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.

[toxic hollow]

How is that Taylor series appropriate to use eventhough it’s alternating

[royal basin]

and so what that happens to be an alternating series?

x as summation index is kind of 🤮 tho

[toxic hollow]

I mean how are they equivalent?

The expectation is not an alternating series yet they used the Taylor series of log?

[royal basin]

they rewrote (1-p)^x as (-1)^x * (p-1)^x

...whoever used the letter x for the summation index should be slapped

[robust sleet]

I agree

[trail musk]

What is the law of the unconscious statistician

[obtuse pebble]

@toxic hollow Has your question been resolved?

[kind hawk]

just says that you have E(f(x)) = sum f(x) P(X=x)

or in integral form, E(f(x)) = int f(x) dP(x)

named like that cause you might think this is obvious and forget that in fact you have to prove it

[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.

[mental cloak]

Hello, i m unsure if this relation is correct. Can someone pls verify it? 🙂

[chilly nebula]

Yes it is

[mental cloak]

is there a simple way of imagining it?

[chilly nebula]

It has no effect on displacement multiplication

3 (2×4)=24 4(2×3)=24

2(3×4)=24

[mental cloak]

but this is a vectorproduct

normally you would not be allowed to switch it, but i m unsure since its weird with differentials 😄

so if i could change it, it would kinda also mean. That this is also true.

<@&286206848099549185>

[obtuse pebble]

@mental cloak 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.

[cold summit]

I know this is below basics, but i dont know what convensions are not how do they work, do you write 'a = -b' as 'a - b'

[timid silo]

Well you can represent any subtraction operation as an addition operation

[kind hawk]

wdym. it says it there. instead of a+(-b) you just write it as a-b

[timid silo]

which is the meaning of $a - b = a + (-b)$

[kind hawk]

dont use arrows

use equality signs

[timid silo]

should be valid either way no?

but sure

[kind hawk]

$a-b = a+(-b)$

[warm shale]

Denascite

[kind hawk]

no

arrows are wrong here

[warm shale]

♡Lex♡

[cold summit]

fuck im stupid, sorry i though it was reffering to the -b = -(-a) = a. sorry, and thank you

.close

[obtuse pebble]

Channel closed

Closed by @cold summit

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.

[silver plover]

help plz

with part A

tbh i dont really understand whats going on in the question?

[noble lion]

Id guess it's a binomial distribution with p=2/3

[silver plover]

whats the trials

[noble lion]

Throwing a basketball is hit or miss so a boolean outcome

[civic zealot]

Geometric distribution

X is the number of throws, not the number of hits or misses.

And he stops throwing when he makes one, so only one success at the end

[silver plover]

could u explain whats going on in the question

dont really understand whats happening

[civic zealot]

He’s throwing a ball until he makes a basket. Find the probability it takes 0, 1, 2, and 3 throws

Knowing that he makes a basket 2/3 of the time

[silver plover]

cant really find prob of 0 throws

since the formula doesnt work for it

would the prob just be 0

?

[civic zealot]

Can you make a basket if you don’t throw the ball?

[silver plover]

u cant

so 0

[silver plover]

also in the question

what does it mean by 'free throws'

should it say three throws lol

[civic zealot]

No. It’s a basketball sports term

Just means he’s standing there throwing the ball from the “free throw line” without anyone trying to block him.

[silver plover]

ok

got this

however the probabilites dont add up to 1

[civic zealot]

Correct. There’s an infinite number of options for X. You just have the first 4

[silver plover]

i see

interesting

[civic zealot]

It could take him 1000 throws (it’s very unlikely, but possible)

Or more!

So you need to give a formula for P(x=n)

[silver plover]

when it says find the pmf

is the table not enough?

[civic zealot]

Nope

[silver plover]

ok then

(2/3)(1/3)^x-1

bosh

[civic zealot]

Yep

[silver plover]

for part B i did this

idk how to write the pmf tho

surely is it just (3-y)/3?

[silver plover]

?

[civic zealot]

I’m not sure about B, that question is confusing.

[silver plover]

i just thought youd sub in the range of s into the formula

which is 1 and 2

[civic zealot]

Maybe. Like I said. Not sure.
But I gotta go lol

[obtuse pebble]

@silver plover Has your question been resolved?

Channel closed

Closed by @silver plover

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.

[formal acorn]

I have to find the GCD and the HCF

[formal acorn]

My main problem is to work with a fraction

[drifting loom]

is x a variable

herhe

[formal acorn]

Yeah

It isn't a sign

Uhm i have to go i return from like 30/40min

If do you want to close it it will befine

[nocturne minnow]

It's your channel, you have the power to close it

[drifting loom]

.close

no i cant close

srry

[leaden lion]

Well both are the same thing

[timid yacht]

can you pls upload the whole question with all the info on it?

[leaden lion]

You need to look for the highest common factor

What is the highest power of b which is common ?@formal acorn

[obtuse pebble]

@formal acorn 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.

[final beacon]

If the population of Europe grew at the rate of 0.72% annually, what would be the doubling time?

[lyric ember]

do you know how to start

[final beacon]

nope

[trail cloak]

Lemme give a hint

P = 100 at t = 0

P = 100*(1+0.0072) at t = 1

P = 100* (1 + 0.0072) * (1+0.0072) at t = 2

[lyric ember]

did this help?

[final beacon]

im trying but no, see im dumb
and new to this

exponential function

[trail cloak]

You got the spirit

[lyric ember]

yes thats good

[trail cloak]

But you need a bit of guidance

$A = P(1 + r)^{t}$

[warm shale]

VulcanOne

[trail cloak]

A is the population at any given time

P is the population when the time = 0

r is the rate

And t is the time period

[lyric ember]

ah that's cool I have always used that without exactly knowing the formula

[final beacon]

i see

[lyric ember]

did you have logarithm properties already

[final beacon]

im gonna lose my head

can u do it for me?

[lyric ember]

I will not, but I can help

[final beacon]

fair

[final beacon]

why did he took
P=100?

here

[lyric ember]

Given:
population of Europe, growth rate 0.72% annually

Looking for:
2x population of Europe

correct?

[final beacon]

yes

[lyric ember]

do you know what growth rate annually means

[final beacon]

per year

[lyric ember]

which means
Population at Year 0 = 1 x population of Europe
Population at Year 1 = 1 x1.072 population of Europe

Population at Year 2 = 1 x1.072x1.072 population of Europe

because 0.72 is your given growth rate

[final beacon]

why 1.072?

.072

[trail cloak]

0.72/100

[final beacon]

oh yeah sory

[trail cloak]

Because 0.72% is a percentage

[final beacon]

yesyes mbmb

[trail cloak]

No worries lol

[lyric ember]

yeah we are all learning

[trail cloak]

0.72/100 = 0.0072

[formal acorn]

Uhm i have to response to my question

Can I do it or I have to redo it

I ask here because I did here the question

[trail cloak]

You can open it again on a new channel

[formal acorn]

Okk thx

[lyric ember]

Try to come up with an expression, where for example

x = Years for doubling the growth rate

and the rest are given values

[lyric ember]

with that as a hint

[final beacon]

how do i use this formula

[lyric ember]

You can come up with a formula yourself

[trail cloak]

Can I give another hint?

Let $A = 2P$

[warm shale]

VulcanOne

[final beacon]

why

because

[lyric ember]

Given:
population of Europe, growth rate 0.72% annually

Looking for:
2x population of Europe

[final beacon]

of the doubling rate?

[trail cloak]

Yes

So

$2P = P(1 + r)^t$

[warm shale]

VulcanOne

[trail cloak]

And you know the r

[final beacon]

yes ik
im dumb but not that ;-;

imma do IT

NOW

[trail cloak]

You're smart and it shows

[trail cloak]

[final beacon]

T= 2?

pardon my handwriting

[lyric ember]

You can simplify a bit

divide both sides by P is one thing

[lyric ember]

thats not it, but you will see how to solve for t soon

[final beacon]

okay, p= (1+ 0.0072)^t

p=(1.0072)^t

[lyric ember]

yeah

and what is your p?

[final beacon]

population for 2nd year?

its 1.1499

no

1.1492

[lyric ember]

You already know your P

you dont need to calculate for it

[lyric ember]

if you divide both sides by P

You had:

2P = P(1.0072)^t
=>
2 = 1(1.0072)^t

[final beacon]

now what to do next bro

[lyric ember]

you need to solve for t

[final beacon]

i did a mistake here
thought its p^2 not 2P

[lyric ember]

do you know how to undo an exponential
in other words what the inverse function of the exponential function is

[final beacon]

not at all

[lyric ember]

did you have logarithm already

[final beacon]

i had functions and real numbers

poly, powers

[lyric ember]

ah okay then you should probably try it out with your calculator, until you get the value 2

If you want I can show you how to solve for t tho

[final beacon]

pls

[lyric ember]

okay so did you have the natural exponential function already

e^x

[final beacon]

oh wait, u will take log on both sides?

[lyric ember]

yeah because then you can use logarithm properties

[final beacon]

pls wait

then it will be
log2 = t*log 1(1.0072)

?

[lyric ember]

yeah

log2 = t x log 1(1.0072)

=>

log2 = t x log (1.0072)

[final beacon]

ah so thats what u meant by logarithm properties

[lyric ember]

taking the exponent and making it a factor

that's the logarithm property that you need here

[lyric ember]

ye

[final beacon]

thats the answer?

[trail cloak]

This has a wrong step

[lyric ember]

where is my mistake

[trail cloak]

Line 3

[lyric ember]

I am allowed to do that by exponent rules

[lyric ember]

actually you are right the notation isnt correct

[trail cloak]

$\ln(x^n) \neq \ln(x)^n$

[warm shale]

VulcanOne

[lyric ember]

the bracket is misplaced

[lyric ember]

thats the solution

with the correct way

[lyric ember]

Thanks!

[trail cloak]

[lyric ember]

now just plug it in a calculator for your answer

[final beacon]

i

dont

have it

[trail cloak]

Well you can leave it like that

That's your answer

[lyric ember]

$\ln^n(x) \ne \ln(x)^n$

[warm shale]

tobi

[final beacon]

yeah, i would do that in exams

[trail cloak]

$t = \frac{\ln(2)}{\ln(1.0072)}$

[warm shale]

VulcanOne

[lyric ember]

how to write equals in Latex

[trail cloak]

=

$=$

[final beacon]

anyways thanks guys
u can literally teach anyone if u can teach me

[warm shale]

VulcanOne

[lyric ember]

$\ln^n(x) \ =\ln(x)^n$

[warm shale]

tobi

[lyric ember]

is this correct then

[trail cloak]

[trail cloak]

Yep

Correct notation

[lyric ember]

okay thanks

[trail cloak]

But confusing often

It's preferred to add parentheses if you have the power outside

$\ln^n(x) = (\ln(x))^n$

[lyric ember]

$\ln^n(x) \ = \ (ln(x))^n$

[warm shale]

tobi

VulcanOne

[lyric ember]

?

[trail cloak]

Yeah

[lyric ember]

I should learn Latex this is pretty cool

[final beacon]

years ago, i have a weird habit of learning things without even knowing there name first especially in maths
so i got confused when u said log properties

[trail cloak]

[lyric ember]

that shows your motivation that's great

[final beacon]

it actually shows how ignorant i am

thanks again tho

should i close it now?

[trail cloak]

If you have all your questions answered then you can close it :)

[final beacon]

i was here just for the basics, rest i will do on my own

[lyric ember]

do .close

[final beacon]

.close

[obtuse pebble]

Channel closed

Closed by @final beacon

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.

[sturdy acorn]

how would u write a function that looks like this

[sturdy acorn]

it's the same amount of space inbetween triangles

[timid silo]

A lot of piecewise stuff or just find a trig function that suits the periodicity or something

[sturdy acorn]

I need a function where I can change parameters like height of triangle width and space inbetween

[timid silo]

https://en.wikipedia.org/wiki/Triangle_wave

[sturdy acorn]

is there a way we can make a flat line between triangles ?

[sage geode]

f(x) = c1 for 0 < x <= x1
f(x) = c2 + x1 - |x| for x1 < x <= x2
f(x + x2) = f(x)
I think

Oh wait

Gotta choose the correct value for x2 though

[timid silo]

ig you could multiply it be a raised square wave

[timid silo]

but its much easier to do it piecewise ^

[obtuse pebble]

@sturdy acorn 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

[devout dirge]

.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.

[timid silo]

I don't think calling is possible but I can explain it without that

[knotty crow]

plug values into and check

or you want to solve it algebraically, then follow

[timid silo]

God actually I just don't want to latex right now, sorry

[stable iron]

if you get division by 0 then given root is incorrect

[timid silo]

But just try and join up the terms and fractions

[stable iron]

since this is a test it would be quicker to just plug in the values and check than solve the equation

you missed something

plug 1 into this: $\frac{x}{x-1}$

[warm shale]

ta

[stable iron]

you get $\frac{1}{1-1}=\frac{1}{0}$ which is illegal in maths

[warm shale]

ta

[stable iron]

nope

division by zero is illegal and you need to keep an eye on that when solving equations

so 1 is definitely not a root of this equation, now you only have to check if 3 is

sorry, you also need to check -1 and -3

yes exactly

[solar trellis]

Wrong

Suiiii

1/2 - 2 = -3/2

[rigid lintel]

yes

[solar trellis]

1 - 4 = -3 tho

[stable iron]

https://youtu.be/RunORqzH_90 this should help

although this guy's method is weird

[solar trellis]

1/2 is on the left

So it's 1/2 - 2/1 = 1/2 - 4/2 = (1-4)/2 = -3/2

[stable iron]

generally adding (subtracting) fractions works like this:
$\frac{1}{2}+\frac{2}{3}=\
\frac{1\cdot 3}{2\cdot 3}+\frac{2\cdot 2}{3\cdot 2}=\
\frac{3}{6}+\frac{4}{6}=\
\frac{3+4}{6}=\frac{7}{6}$

[warm shale]

ta

[stable iron]

bro the spacing

but do you understand the logic behind that

so what's the correct way of solving that

oh wait someone already explained it

yes, just like subtracting regular numbers

1 - 4 = -3 right $\$
so $\frac{1}{2} - \frac{4}{2}=\frac{-3}{2}$

[warm shale]

ta

[stable iron]

all you do is add a funny line and a number on the bottom

its ok youre learning

you can picture it like this: $\frac{1}{2} - \frac{4}{2} = \frac{1-4}{2}$

[warm shale]

ta

[stable iron]

its just an example

the easiest way to find common denominator is just multiplying one by another

you see what i did there is basically this

a more advanced example would be this: $\frac{1}{287}+\frac{1}{2}+\frac{3}{10}=\frac{1\cdot 2 \cdot 10 + 1 \cdot 287 \cdot 10 + 3 \cdot 287 \cdot 2}{287 \cdot 2 \cdot 10}$

[warm shale]

ta

[stable iron]

well denominator should be the same in all equations, only then you can add/subtract them

in your case they're different because you've multiplied by 3 instead of 2 here

no problem

[obtuse pebble]

@torpid dagger Has your question been resolved?

Channel closed

Closed by @torpid 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.

[frank hamlet]

if
nCr ≥ nCx
r ∈[?,?]
what will be the range of values of r?

[frank hamlet]

will it be [x,n-x]

assuming x>(n-x)

[rigid lintel]

yeah that looks right

[haughty coyote]

Yes. The binomial coefficients are maximized at n/2 (or the 2 closest integers to it) and are monotonous on each side

[frank hamlet]

Ok so
25C(r+2) ≥ 25C15

I got (r+2) ∈ [10, 15]
but the solution is eliminating r+2=14

I'm assuming it's a mistype then?

[rigid lintel]

could you share that

a picture

[frank hamlet]

,rotate

[rigid lintel]

23 != 25

so your reasoning is correct but not directly applicabvle

[frank hamlet]

huh?

[frank hamlet]

you're supposed to simplify lhs

which comes out to be 25C(r+2)

[rigid lintel]

oh is that that identity

lmao my badf

[frank hamlet]

so 6 should be the right answer?

[rigid lintel]

sorry what is6

[frank hamlet]

number of values of r

for which that inequality is satisfied

[rigid lintel]

i would say so yes

not sure why they eliminate r + 2 = 14

[frank hamlet]

Okay, thanks

.close

[obtuse pebble]

Channel closed

Closed by @frank hamlet

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.

[acoustic pawn]

Is the equality (n+1)!/(2n+1)! = 1/2 n!/(2n)! true?

[acoustic pawn]

R you sure? I tested for some values and it didnt seem to work but i probably made some mistakes

Wait what

Thats something different then what i said

How come you can cancel n! and (2n+1)

I'll rephrase, how are (n+1) and (2n)! the same?

I dont think you can since 2(n+1) =/ 2n+1, right?

[eager pawn]

The equality (n+1)!/(2n+1)! = 1/2 n!/(2n)! is not true.

This can be seen by considering the fact that (n+1)!/(2n+1)! and 1/2 n!/(2n)! are both fractions, but they do not have the same value.

Sorry for that mistake.

[acoustic pawn]

Oh alright, thanks for the help! I'll stick around for a helper just to make sure

[acoustic pawn]

Its fine, good intentions < 3

[eager pawn]

Thanks, I'm genuinely too tired to be doing this, that was the dumbest mistake I've made since the 7th grade.

[acoustic pawn]

i litteraly made the same mistake while deriving the equality tho so i feel you

[obtuse pebble]

@acoustic pawn Has your question been resolved?

Channel closed

Closed by @acoustic pawn

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.

[toxic hollow]

Is the correct derivative the second equation I wrote since it’s with respect to lambda?

[obtuse pebble]

@toxic hollow Has your question been resolved?

[toxic hollow]

This is the ms

But I can’t get that at all

[tardy epoch]

The upper limit should be pi

Once you do that, you just use integration by parts to do the integral

[toxic hollow]

My upper limit is written as pi, apologies for the bad handwriting

But I’ve done the integration and also checked with a calculator but it doesn’t match up with the ms?

[toxic hollow]

I think it might be this one?

Out of the three options I posted which is actually the correct one?

[tardy epoch]

Use that

[tardy epoch]

This looks right

[tardy epoch]

Show your work

[toxic hollow]

Yes this is the correct one I believe, the integration works

[obtuse pebble]

@toxic hollow 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.

[haughty roost]

how can i calculate a primitive with a condition on x

[rigid lintel]

dont calculate the primitive, differentiate the options

much easier

[fierce lagoon]

^

Well ... this one isn't hard to integrate

[knotty crow]

or sub u = x - 2 then you'll get simple integral

[fierce lagoon]

You can let u = x-2 if you need to but

Frankly it would be trivial

[rigid lintel]

true

[fierce lagoon]

Also is your log a natural log by default?

So your log = ln?

[fierce lagoon]

@haughty roost

[haughty roost]

yep

if i solve the integral by substituting

i get -2/(x-2)

[fierce lagoon]

One of them is similar but different by a constant I think

[haughty roost]

ah i forgot that they could the the same just with a constant change

[fierce lagoon]

Note that $\frac{-2}{x-2} = \frac{2}{2-x}$

[warm shale]

Umbraleviathan

[fierce lagoon]

One of the primitives above just differs from them by a constant

[haughty roost]

the right answer is b

so that way the only option is to differentiate the solutions

[fierce lagoon]

It is B

[haughty roost]

since i couldn’t know what constant it is

[fierce lagoon]

But that's because $\frac{x}{2-x} = \frac{x+2-2}{2-x} = -1 +\frac{2}{2-x}$

[warm shale]

Umbraleviathan

[fierce lagoon]

Differs by 1

[obtuse pebble]

@haughty roost 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.

[coral horizon]

Can someone tell me what step did I mess up for this problem? I got -1 but the answer is 1/5

[static beacon]

Which question.

[coral horizon]

#7

[robust sleet]

,w integral of 4sec^2(2x)

[warm shale]

Results provided by WolframAlpha

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

Requested by Gooo#0905

[coral horizon]

it simplifies to -1/-2+3

but if 3 was -3 then it would make sense...

but for some reason the math just isnt mathing out

[robust sleet]

y=1/((-2tan(2x)-c))
,w 1=-2*tan(pi/4)-c solve for c

[elfin burrow]

negative is wrong here

you brought the negative outside

whereas it should only apply to 2tan(2theta)

[coral horizon]

oh wait...

you're ducking right

i should've added parenthesis on the -2tan(2theta) +3

thank you

[elfin burrow]

nw

[obtuse pebble]

@coral horizon Has your question been resolved?

Channel closed

Closed by @coral horizon

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.

[timid silo]

How to do of question number 8 the hexagon?

[obtuse pebble]

@timid silo Has your question been resolved?

[glossy basalt]

hello there! still need help?

[timid silo]

yes please

[ember sedge]

addition of vectors

[timid silo]

How do i express ad vector in terms of a and b?

[ember sedge]

clue : parallel lines (kinda)

divide the hexagon into 6 congruent triangles

you should see that AD is ___ the length of one of the sides

[timid silo]

Thx

[ember sedge]

then i think it's easy to prove the last part 👍

[timid silo]

yes it's pretty easy

thanks

.close

[obtuse pebble]

Channel closed

Closed by @olive elk

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.

[mystic forum]

How is this

[mystic forum]

asymptotic to this

when x = 9?

[obtuse pebble]

@mystic forum Has your question been resolved?

[lost tree]

are these supposed to be functions of alpha?

[mystic forum]

Its basically asking me for which alpha the integral converges

[trail musk]

Taylor series

,w series ln(10-x) at x=9

[warm shale]

Results provided by WolframAlpha

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

Requested by Mr. Gamer#6658

[trail musk]

First order approx is 9-x

[alpine raven]

do it at 0

there is no problem at 9

[mystic forum]

But i am only allowed to use taylor series when i have ln(1+x) and/or ln(1-x)

right...?

[alpine raven]

you never saw taylor expansion formula ?

[trail musk]

You can use taylor series whenever you please

[mystic forum]

Yes i did, but in order to use them i need to have specific cases (at least thats what i thought)

[alpine raven]

huh no

[warm canopy]

Don't drink and derive though

[trail musk]

What else am I supposed to do on the weekends then

[mystic forum]

Okay, but for example isnt the taylor series of log x - 1/2x^2 + 1/3x^3... then why do i see -(x-9) here? There must have been some sort of transformation of what's inside the log before applying taylor's series

i hope you understand what i am asking

[trail musk]

Look up the definition of the Taylor series again

[drifting hinge]

if anyone knows

[trail musk]

Not here

[mystic forum]

Alright i'll do, thank you

[alpine raven]

you never saw taylor expansion formula

[mystic forum]

I believe i did, but i don't know how it could help me

[alpine raven]

$\sum_{k=0}^n \frac{f^{(k)}(a)}{k!}(x-a)^k + o((x-a)^n)$

[warm shale]

Ｈｅｒｅｌｓ

[alpine raven]

did you ever see this ?

[mystic forum]

yes

(without the little o, but i dont think it matters)

[alpine raven]

it does, its not there for nothing

[mystic forum]

Well... my teacher didnt use it :v

[obtuse pebble]

@mystic forum 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.

[wild orbit]

8 just want for 67

*i just want for q.67

[rigid pine]

The z bounds in terms of r and theta are easy. All you need to know how to do is set up a double integral over a semi-circular region for the function which is that single integral where f = 1. The question has given quite a lot to you.

[obtuse pebble]

@wild orbit Has your question been resolved?

[wild orbit]

Z will be 0 to -r sintheta?

R will be 0 to 3 costheta?

[wild orbit]

Theta's upper limit will be 2pi?

What abt the lower limit?

[rigid pine]

We are bounded between the rays theta = 3pi/2 and theta = 2pi.

[wild orbit]

Thnx alot

.close

[obtuse pebble]

Channel closed

Closed by @wild orbit

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.

[dapper wharf]

I tried to solve this integral but Im not entirely sure how to get a first step

[dapper wharf]

The integral is from 1(upper bound) to 0(lower bound): sqrt(x^2+x) dx

[kind hawk]

complete the square inside the sqrt

then use a trig sub

[warm shale]

Modus

[knotty crow]

?

[dapper wharf]

Yes

[kind hawk]

btw usually you would say "from (lower bound) to (upper bound)". so "integral from 0 to 1 of sqrt(x^2+x) dx"

[dapper wharf]

Oh sorry

[cloud berry]

does this really matter

[dapper wharf]

So it’ll be sqrt((x+1/2)^2+3/4)

And then what do i do

[dapper wharf]

Do u mind guiding me pls

[kind hawk]

well it's pretty standard. so if you say "from 0 to 1" but actually mean 0 as the upper bound and 1 as the lower bound then most people will misunderstand you

[dapper wharf]

That why I put it in brackets

[kind hawk]

that does not look like the correct completed square

[cloud berry]

he said what's upper bound and what's lower bound

nvm

[dapper wharf]

Okie

So can someone pls guide me

[cloud berry]

,w integrate sqrt(x^2+x) dx

[warm shale]

Results provided by WolframAlpha

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

Requested by ayushch80#1686

[kind hawk]

so lets first complete the square

what did you do. show your work

[dapper wharf]

Here

Half the coefficient of x

[kind hawk]

the +3/4 is wrong

if you expand (x+1/2)^2 you get +1/4 at the end, so with the +3/4 you get x^2+x+1

[dapper wharf]

Oh yh then it’ll be -1-4

-1/4

[kind hawk]

ok. next sub u=x+1/2

[dapper wharf]

Sorry

[kind hawk]

for convenience

[dapper wharf]

So sqrt((2u)^2 -1/4)

But gotta change du to dx

[kind hawk]

where is the 2u from

du=dx

gotta change the bounds tho

[dapper wharf]

Oh I thought it was the whole thing over two

[dapper wharf]

How do I do that

[kind hawk]

then I would have written (x+1)/2

[dapper wharf]

Sorry

[kind hawk]

if u=x+1/2 and x=0, what is u

if u=x+1/2 and x=1, what is u

[dapper wharf]

1/2

[dapper wharf]

1

So it’ll be between 1 and 1/2

[kind hawk]

.

[dapper wharf]

Yes?

[kind hawk]

1+1/2 = ?

[dapper wharf]

3/2

Omd I keep thinking it’s all over 2

[kind hawk]

if I wanted brackets I would write brackets

[dapper wharf]

Ik sorry

[kind hawk]

ok so now we have the integral $\int_{1/2}^{3/2} \sqrt{u^2-\frac14} du$

[warm shale]

Denascite

[dapper wharf]

Ye

[kind hawk]

there is a very standard trig sub for sqrt(u^2-a^2)

do you know it?

[dapper wharf]

No

[kind hawk]

do you know some trig identity where (trig function)^2 -1 = (another trig function)^2 ?

[dapper wharf]

Sec^2

?

[kind hawk]

yes

so with this in mind, sub u=sec(t)/2

what do you get

[dapper wharf]

Is the whole thing over 2 or just t/2

[kind hawk]

sec(t) is one thing