help-39

[toxic lichen]

i thought i was clear enough.

[crude crown]

can u help with another 2 qutions if okay with u '

[crude crown]

u were

[toxic lichen]

well, okay, let's consider the first one done.

send pictures of your new questions, if possible.

[crude crown]

ok

[toxic lichen]

,rccw

[crude crown]

nah this server is cool

so

[toxic lichen]

okay, so which of these questions would you like to do first?

[crude crown]

the world problem pls

[toxic lichen]

uh huh.

any progress on that one?

[crude crown]

24 divided by 4

equals 12

but x = total numbers

[toxic lichen]

24 divided by 4 does not equal 12.

and the relevance of this arithmetic to the problem is questionable

[crude crown]

6

[crude crown]

HUH

SIMPLE ENGLIS

PLS

WHO IS ARTHUMUCS'

lets just focus on rthe quetion

[toxic lichen]

arithmetic means basic calculations with numbers, usually limited to not much more than the four operations of addition, subtraction, multiplication and division

[crude crown]

oh

[toxic lichen]

you calculated one-fourth of 24, and you got the correct value of 6 after i corrected you,
but this calculation is irrelevant to your problem,

[crude crown]

cool

[toxic lichen]

and you did not do what was asked of you

[crude crown]

i see

[crude crown]

true

so how do i do it?

i have absulopelfy no idea

[toxic lichen]

well

the problem tells you to use the letter x to denote the total number of miles' marbles

can you write down an expression in terms of x for "one-fourth of the number of miles' marbles"?

[crude crown]

so

x = 1/4 multiplied of 24

[toxic lichen]

no

this is not what i asked for,

and forget about the 24 for a moment

[crude crown]

so

x = 1/4

of miles marble

[toxic lichen]

no

miles' marble count = x
one-quarter of miles' marble count = ?

[crude crown]

omg

6

[toxic lichen]

no!!!

[crude crown]

OMG

[toxic lichen]

forget about the goddamn 24 for a second!

read what i am asking you, and do not read between the lines!

and don't overthink it!

miles' marble count = x
one-quarter of miles' marble count = ?

[crude crown]

wait

is ti 24 x 4

[toxic lichen]

no!!!

i want you to give me an expression that has the letter x in it.

miles' marble count = x

one-quarter of miles' marble count = ?

[crude crown]

TOTAL NUMBER

[toxic lichen]

one-quarter of x = ?

[crude crown]

idk

[toxic lichen]

how do you find one quarter of something

[crude crown]

u divide

[toxic lichen]

divide by what

[crude crown]

4

[toxic lichen]

right

and what happens when you divide the variable x by 4?

what expression do you get when doing that

[crude crown]

x/4

[toxic lichen]

that's right.

that's what i've been wanting from you.

so, one-quarter of miles' marble count is x/4.

we are told by the problem that one-quarter of miles' marble count is 24 marbles.

can you write this info down as an equation?

(do NOT solve the equation UNTIL i tell you to. ONLY write down the equation itself)

[crude crown]

x/4 = 24

[toxic lichen]

that's right.

[crude crown]

yay

[toxic lichen]

and now,
are you able to solve this equation?

[crude crown]

x = 24 / 4

= 6

[toxic lichen]

incorrect.

i want you to describe in words what you did to get from x/4 = 24 to x = 24/4.

[crude crown]

i though to get x u make sure nothuing is with x

i made a mistake'

my sincere apology

[toxic lichen]

i don't want or need your apologies.

[crude crown]

cool

[toxic lichen]

i want a description of what you did.

that, or you now admitted you made a mistake and don't want me to see it.

[crude crown]

i moved 4 into rhs

[toxic lichen]

okay, see?

now i can tell you that there is no such thing as "moving" anything anywhere in algebra.

certainly not "moving" stuff from LHS to RHS or vice versa.

[crude crown]

i will reply to this later

[crude crown]

'i see

[toxic lichen]

what you should've done here was multiply both sides by 4.

[crude crown]

so 4x = 96

[toxic lichen]

incorrect.

(x/4) * 4 is not 4x.

[crude crown]

x divided by 4 is what

[toxic lichen]

sorry, i don't understand your question.

[crude crown]

what is the corrct way

[toxic lichen]

well,

when you divide a number by 4 and then multiply the result back by 4,

what do you get

[crude crown]

4

hold up

1

its 1

1

[toxic lichen]

so,

you say that if you take any number,
divide your number by 4,
then multiply the result by 4,
the final result will always be 1?

[crude crown]

yes

[toxic lichen]

how odd.

let's forget about our problem for a moment.

because i want to pay some attention to this previously unknown mathematical discovery.

[crude crown]

mh

[toxic lichen]

ok, here's what i want you to do:

let's start with the number 60.

i want you to divide this number by 4, and tell me what you get.

[crude crown]

15

[toxic lichen]

now, i want you to multiply this by 4.

and tell me what you get.

[crude crown]

60

[toxic lichen]

oh, but weren't you supposed to get 1?

[crude crown]

what is the picture suppose to do?

[crude crown]

we were usaing number 60

[toxic lichen]

the picture is a screenshot of me asking to confirm what you said, and you confirming it.

YOU YOURSELF said that starting with ANY NUMBER, dividing it by 4, then multiplying it by 4, will ALWAYS give the number 1, NO MATTER which number we started with.

i was hoping to make it obvious how wrong your claim was with this little exercise.

[crude crown]

k

congrats

now can we

solve the qution

pls

[toxic lichen]

when you divide a number by 4 and then multiply the result back by 4,

you get the number you started with

you know

[crude crown]

ok

[toxic lichen]

multiplication and division undo each other

[crude crown]

which is x

[toxic lichen]

yes

exactly

so when you take the equation x/4 = 24

and multiply both sides by 4

the left-hand side is just x

and the right-hand side is of course 24*4

[crude crown]

so x = 96

[toxic lichen]

yes

[crude crown]

thats the answe?

[toxic lichen]

yes

we were asked to find the value of x

do you have any questions about the word problem or the solution thereof?

[glacial sequoia]

thereof

[toxic lichen]

did i say something funny?

[pearl pond]

@crude crown Has your question been resolved?

[pearl pond]

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[pearl pond]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[stuck seal]

1

[glacial sequoia]

something fancy ✨

[pearl pond]

@stuck seal Has your question been resolved?

[autumn fossil]

Can you find coordinates of point S?

[stuck seal]

nope

[autumn fossil]

It's simetrycal about the origin

[stuck seal]

hmm

[autumn fossil]

Well nvm. Can you find what will sin(A) and cos(A) be?

small hint:

[stuck seal]

i assume a =0.6

im not sure

o = 0.8?

[cunning condor]

hello friend

[limber comet]

hello friend

[cunning condor]

hello!

[stuck seal]

hello friends

LOL

[cunning condor]

lmao

[stuck seal]

hey you both

haha

[autumn fossil]

Have you heard about sine and cosine before btw?

[stuck seal]

i do

idk what's the adjacent /hypo

[limber comet]

is it

phasor diagram

??

[limber comet]

this one

[stuck seal]

dunno

[stuck seal]

IM RIGHT

but the negative confused me

-0.8

now i know how to do

i will just have to minus the angle i found right?

180 -

[autumn fossil]

Once you find A, you will just do 180-A

Which will be x

[stuck seal]

let's goooo

wait

can i use tan?

since i don't have h

[autumn fossil]

You could, but notice that the radius of circle is 1

And h is the radius

[stuck seal]

alr

the -0.8 change it to positive?

[limber comet]

well using tan is easy here

[pearl pond]

@stuck seal Has your question been resolved?

[pearl pond]

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[pearl pond]

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[harsh dragon]

The question is asking for angle a. I know that minor arc AE is 30, but I don't know where to go from there.

[pearl pond]

@harsh dragon Has your question been resolved?

[harsh dragon]

<@&286206848099549185>

[harsh dragon]

.close

[pearl pond]

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[paper mural]

how is this wrong?

[paper mural]

i first completed the square

then used the formula

integral dx/ sqrt(x^2 - a^2) = ln abs(x+sqrt(x^2-a^2))

.close

[pearl pond]

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[late moon]

<@&268886789983436800>

[pearl pond]

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[midnight haven]

Could someone explain the 2nd part of the proof where you substitute t= pi/2-theta?

[midnight haven]

<@&286206848099549185>

[plush bramble]

follows from cofunction identity

[midnight haven]

yeah I see that, but is there something wrong with the proof? I don’t get why they inversed the integral

[plush bramble]

what do you think is the correction

• int 0 to pi/2 instead?

[midnight haven]

Okay I understand that, but using the 2nd part can you truly equat sin theta to cosine theta?

[plush bramble]

type out exactly what you don't understand

[midnight haven]

I don’t understand if t= pi/2-theta then how does sin t take the place of cos theta?

In the last expression

[plush bramble]

.

[plush bramble]

when you say "i see that", did you mean something else?

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

Yeah

I don’t know if it’s my lack of conceptual knowledge about integrals but the main thing I’m stuck on is how the cos^2 theta gets replaced by sin^2 theta?

If the cos(pi/2-theta)= sin theta

[plush bramble]

Compare the two integrals f(cos) and f(sin) on the two lines.

Then plug f(sin) into the definition of f

[midnight haven]

Alright

[midnight haven]

The definition of the integral?

[midnight haven]

They both equal 0?

[plush bramble]

no. define the integrand to be f(cos). now write down f(sin)

then eqn (1) is the top left and the very last integral is in the bottom right (with some 4a factor somewhere)

[midnight haven]

Could you simplify what you’re tryna say, I’ve been trying to follow along, but I’m kinda getting overwhelmed I apologize.

[plush bramble]

simplify how?

integrand = function being integrated

$f(\cos(\theta)) = \sqrt{1-k^2 \cos^2(\theta)}$

[jolly parrot]

riemann

[plush bramble]

now write down the identity with $f(\sin(\theta))$ as the integrand

[jolly parrot]

riemann

[pearl pond]

@midnight haven Has your question been resolved?

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[midnight haven]

.reipen

.reopen

[pearl pond]

✅

[midnight haven]

Alright I’ll try it thank you

.close

[pearl pond]

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[raw summit]

Hello I was wondering how this was reached from the integral of cos^2xsin^2xdx

[raw summit]

Im aware the half angle identity is

so how do they still have another 1+cos2x

after taken out the 1/2

[finite crown]

wym?

we have a 1-cos(2x), because sin^2(x) is 0.5(1-cos(2x))

[raw summit]

I just mean from the beginning question

if we had cos^2 (x) sin^2(x) dx

[broken ivy]

sand+coal=silicon sorry wrong

[raw summit]

cos^2(x) identity is as follow

im just lost how the had a 1+cos2x

with a 1/2 out of it

[raw summit]

when like algebraically if I took a 1/2 out of this I wouldnt be able to get another 1

[finite crown]

???

[raw summit]

or maybe im dumb

[finite crown]

https://gyazo.com/c1da815344c3b08c189dcc46e867f142

Should be 2 halfs

and 2 cos's

[raw summit]

is 1/2(1+cos(x) the same as 1+co2x/2

[finite crown]

$\frac{1}{2}(1+\cos(x)) = \frac{1+\cos(x)}{2}$

[jolly parrot]

Mortta

[raw summit]

oh im just dumb at algebra

[finite crown]

mhm

[raw summit]

just so Im not tripping could you explain

[finite crown]

just puts the half underneath

[raw summit]

how if I took a 1/2 out of the resulting equation

how theres still a 1 there

idk why its hard for me to grasp that

[finite crown]

lets pretend we have an equation

[raw summit]

sorry Im leaving this here for later

[finite crown]

$y = \frac{1}{2}(1+\cos(x))$

[jolly parrot]

Mortta

[raw summit]

I guess its the same as 1+cos(x)/1

ohhh

I get it I guess

[finite crown]

$2y = (1 + \cos(x))$

[jolly parrot]

Mortta

[finite crown]

See how we took the 2 out

and it didnt effect the one

or the cos

[raw summit]

yep I get what u mean there

[finite crown]

basically what we did

[raw summit]

thank you

[raw summit]

for this

how did they implement

the identity again?

I was unaware you could do cos^2(2x)

or would u just let 2x be like u in this situation or something like that

[finite crown]

basically yea

u = 2x

do it for cos(u)

than sub in

AKA u just times the bracket by 2 again

[raw summit]

how did they get an extra 1/2?

ohh

they just factor

nvm

if I wanted to get familiar with this

[finite crown]

They distribute the 1/2

[raw summit]

Id just practice half angle?

or what unit would u suggest

[finite crown]

honestly just practice like whole of trig identities as a whole

wait

,texit factod trig

[jolly parrot]

Mortta

[finite crown]

wtf

[raw summit]

I think what I'm confused about is what the general identity is for cos^2x

[finite crown]

,tex \factoid trig

[raw summit]

is it just 1-cos(2(x)

[jolly parrot]

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

[finite crown]

,tex \factoid trig

[jolly parrot]

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

[raw summit]

OHHH I FIGURED OUT WHAT WAS STUMPING ME

[finite crown]

its trolling

but learn all these

[finite crown]

You'll be the best at trig

[raw summit]

IN THIS

where does that extra 1 come from

in the 1-1/2

[finite crown]

nothing

it just stayed there from the top

[raw summit]

oh I guess

you dont need the 1 to do the identity thing

you just need cos^2(x)

ahh

so when they make 2x the u are they integrating in that step or did they not integrate yet

[finite crown]

I mean i wouldve just changed that the sin^2(2x)

[finite crown]

They integrated last step here

[raw summit]

changed which to sin^2(2x)

they change it to sin(4x) after they integrate

[finite crown]

No its fine just stick wit hthe way they did it

[raw summit]

when they integrate 1/2cos(4x)

does that 4 come out?

and then multiply with the 1/2 to make 1/8

[finite crown]

Yea

[raw summit]

why does that even happen

[finite crown]

reverse chain

[raw summit]

oh

im just gonna spend like an hour doing trig identities i guess

trig identity problems should include half angle right

@finite crown hey question

for a problem like

integrating

sin^3(x)cos^6(x)

would I still need to do trig identities

or would it be more so u sub

with a little bit of trig

[finite crown]

yep you will always use trig identities

but ofc you will have to spot them

U could use both u sub and trig

99% of times its both

[raw summit]

question

it says for a problem like this I should make cos^6 the u

because its even and the other is odd what does that mean

it says to make cos(x) not even cos^6(x)*

Oh I guess it should be the even ne because you cant do a half angle one on a odd power right

[finite crown]

Hm

i wouldnt do that first tho

But u could

[raw summit]

what would u do first?

[finite crown]

sin^2 = 1 - cos^2

So than your only left with one sin

and than get Derivitive

cancles out

[raw summit]

wait wait wait

how did their u become sin

if they said their u was cos

[finite crown]

du

becamse sine

derivitve of cos

[raw summit]

even though du is that isnt u still cosx

even symbolab says

symbolab says it should still be cos i think

[finite crown]

??

u will always be cos

we said du is -sin

which is true

[raw summit]

but like for their final answer

somehow its sin^9x

[finite crown]

Yea

they did it wrong

symbolab is right

[pearl pond]

@raw summit Has your question been resolved?

[raw summit]

question

is cos(2x)

the same as 1/2sin(2x)?

this doesnt seem right

the question is integral of

x^2cos2x

[finite crown]

No

The the derivitve of 0.5sin(2x) is cos (2x)

[pearl pond]

@raw summit Has your question been resolved?

[pearl pond]

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[valid raptor]

how would I go about researching this, also if yk the answer lmk

[valid raptor]

wut

ok why is this right?

[pearl pond]

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[midnight haven]

https://media.discordapp.net/attachments/908078493655502919/1072308546663874600/image.png?width=1472&height=917

[midnight haven]

is this wrong

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[pearl pond]

Please don't occupy multiple help channels.

[midnight haven]

.close

[pearl pond]

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[modest zealot]

where's the maximal error formula from

[pearl pond]

@modest zealot Has your question been resolved?

[pearl pond]

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[crystal isle]

can someone help me with some basic algebra?

[crystal isle]

Trying to study for my GED very dumb person here

[midnight haven]

yo whats GED

[crystal isle]

when I take a number

that is not a fraction

and make it into one

does it become a negative

with teh number

I'm subtracting it with

[wanton scroll]

r=5

[crystal isle]

I'm trying to understand

not get the answer

GED is the highschool diploma equivalent

fgor homeschooled kids

[wanton scroll]

Bro do you know transposition?

[crystal isle]

no

how do I take a whole number

and turn it into a fraction

is it always over 1?

so like

if I took "12"

and then wanted to turn it into a fraction

it would be "12/1"

right?

[wanton scroll]

So when a fraction is on one side of the equation, you can shift it to the other side with opposite operator

[crystal isle]

that's mainly my question

nice

thanks

[wanton scroll]

yeah you can do this

[crystal isle]

yeah sorry

thanks for the help guys

alright

sounds good

I like it

thanks guys

.close

[pearl pond]

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[pearl pond]

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[zinc kelp]

Just did this question I got Gradient at (1,1) = 1/2 but I'm unsure, could anyone verify this?

[pearl pond]

@zinc kelp Has your question been resolved?

[zinc kelp]

<@&286206848099549185>

[granite sundial]

,w gradient y^2+2xlog(y)=x^2

[jolly parrot]

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Requested by Jukelyn#9848

[granite sundial]

what the fu-

,w derive y^2+2xlog(y)=x^2

[jolly parrot]

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[granite sundial]

yeah 1/2

[zinc kelp]

Thank you!!!

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[pearl pond]

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[tough token]

it is just solving for when $ba^t=0.78b$

[jolly parrot]

Duh Hello

[tough token]

dont worry i understand that. but you have that after $t$ years the amount of carbon-14 in the tree is 78% of the amount of carbon-14 it contained when it died. since you have the model that says that after $t$ years the amount of carbon-14 left in the tree is given by $f(t)=ba^t$ then you can simply solve for when this amount is equal to 78% of the starting amount, mathematically you have $$ba^t=0.78b$$

[jolly parrot]

Duh Hello

[tough token]

so from here you can solve for the time $t$ when this is true, and that is the estimated age of the tree

[jolly parrot]

Duh Hello

???42

[tough token]

what do you think you could do?

[jolly parrot]

???42

[tough token]

no

b is the starting amount

b is not equal to 0.78

you have that after a certain amount of years, the amount has become 78% of the start amount, which is just 0.78 times b

aka $0.78b$

[jolly parrot]

Duh Hello

[tough token]

which is correct

[jolly parrot]

???42

[tough token]

yep

(you can cancel the b's)

well is there 0.78 carbon-14 left in the tree?

since that is what it would mean if you say that

it is 78% of the start amount

and what is the start amount?

[jolly parrot]

???42

???42

[tough token]

you cannot

do you know what b is in this case?

like what does b represent?

correct

78% of what?

is it 78% of the carbon which is left?

its 78% of the initial amount

not the amount left

ok

so how would you write 78% of the initial amount mathematically if the initial amount is given by the variable b?

yes 78% is 0.78

but what is it 78% of?

like lets say i have 12 donuts, and i give you 50% of my donuts, how many donuts did i give you?

mathematically how did you get to that?

so if i had b donuts, and i give you 50% of them, how many donuts did i give you?

does that make sense?

let me choose b=12 now and get the same problem i had before. then by your logic i would have given you 12^2 donuts which is 144 donuts

the correct answer is $0.5b$ because i gave you 50% of my $b$ donuts, and since $50%=0.5$ we multiply this amount by $b$ to get the amount of donuts i gave you

[jolly parrot]

Duh Hello

[tough token]

does this make sense to you?

but many times you wont

like in this problem

what is b in this problem?

hint: you will not need it

yeah me neither

it is not given

and we will not use it

because many times we dont know what this variable is

this donut example is me trying to understand what you know

because you were lacking an understanding in it and its something that is important to know

im not entirely sure how to get you to understand it properly tho. do you see how this donut problem i created relates to what we were doing before it?

well i was trying to use a simpler example to show you why we have 0.78*b and not 0.78 carbon-14 left

just like in our example i didnt give you 0.5 donuts, i gave you 0.5*b donuts

quite far off

but thats because you are going at roughly 66% instead of 78% which are quite far apart

for 66% the amount of years would be 3435 years

but no you are not supposed to eyeball it

you are supposed to calculate it

[tough token]

which you are pretty close to doing here

no worries, maybe some rest will help. sometimes its best to sleep on problems and suddenly you might just get it

[tough token]

if you cancel the b's on both sides here and solve for t you will get an exact answer

not quite square root

you need to take the log

let me just show you. i think it might be best. im just gonna keep $a$ in as a variable that gets plugged in at the end. we have $$ba^t=0.78b$$ $$a^t=0.78$$ $$\log_a a^t=\log_a 0.78$$ $$t=\log_a 0.78$$ $$t=\frac{\ln 0.78}{\ln a}$$

[jolly parrot]

Duh Hello

[tough token]

unfortunately i dont think i can give any more than this without it being me just giving you the answer

[tough token]

do you understand what happened here? and do you understand what the last line says?

$\ln=\log_e$

[jolly parrot]

Duh Hello

[tough token]

its not basically the same, its literally the same

this is the definition of ln

neither of those mean anything

$\log_{10}^2$

$\ln^2$

[jolly parrot]

Duh Hello

Duh Hello

[tough token]

you need an argument

$\log_{10}2^2$

this means something

[jolly parrot]

Duh Hello

[tough token]

you put it into a calculator

this isnt something you can do with regular calculations

is it because its giving a negative value?

since your problem is using a slightly wrong model

it should be $ba^{-t}$

[jolly parrot]

Duh Hello

[tough token]

i dont think i did

thats pretty common

its nice to be able to visualize the thing you are working on

btw just wanna ask, are you sure the problem doesnt state that $f(t)=ba^{-t}$?

[jolly parrot]

Duh Hello

[tough token]

correct

even if a figure is given it doesnt mean that the answer is on it

its nice to have since you can confirm that your answer makes sense

what if you instead got 6000 years

you could look at the picture and see that its not correct

im not sure what you are saying here

at start we have 100%

and after 2000 or so years we have 78%

just like the picture predicts

i did the problem

did you get an answer in the end?

if so what is this exact answer that you got

[tough token]

so you are stuck at this then?

so how do you get to the exact answer without doing all the log shit?

i havent said the exact answer yet

huh?

[pearl pond]

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[tough token]

.reopen

[pearl pond]

✅

[tough token]

do you not want to understand this? you need to tell me what it is that you are struggling with

[pearl pond]

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[old geyser]

Man I love it when OPs do not understand no matter what

[pearl pond]

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[warm mountain]

I have a discrete math problem...

[warm mountain]

The problem: if you have 10 people to choose from, who could sit on a committee of 4 positions (president, vp, etc, etc) and 3 of those 10 people are physicians, how many permutations where there is exactly 1 physician in the committee

I know P(10, 4) will give all permutations

but I think I need to use division in some way

like 10!/(10-4)!3! maybe

but I don't think that's right

[pearl pond]

@warm mountain Has your question been resolved?

[pearl pond]

@warm mountain Has your question been resolved?

[pearl pond]

@warm mountain Has your question been resolved?

[warm mountain]

Yes

[pearl pond]

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[midnight haven]

[old geyser]

Gonna ask you first what f(3) would be

And what's your process for evaluating f(3) would be

[flat bolt]

Wow

[old geyser]

The process you use to find f(3) is gonna be the same as finding f(x+3)

[wary bane]

f(y) = -2y, find f(x+3)

Can you do the question now?

[midnight haven]

I'm dumb

[flat bolt]

No u r not

[midnight haven]

So, how should I start?

[flat bolt]

First f(3)=-2(3)

Right?

[midnight haven]

why did you put f(3)?

[coarse dawn]

Example

[old geyser]

As an example

[old geyser]

_ _

[midnight haven]

oh

[flat bolt]

Lol

Now f(x+3)=-2(...)

Think of x+3 as a whole as x

(x+3)=x

[midnight haven]

I mean this is supposed to be a problem of transformation of linear equations

[flat bolt]

Oh

Really dude

[midnight haven]

bruh

[flat bolt]

Alr then

x+3 is what kind of transformation

[midnight haven]

yea

[flat bolt]

Horizontal or vertical

[midnight haven]

h

[flat bolt]

Alr left or right

[midnight haven]

left

[flat bolt]

Wait

Wait

Wait

[old geyser]

It is left

[flat bolt]

He is suppose to plug x+3 as x

[old geyser]

I mean yeah

[flat bolt]

Unless he is going to graph it then huh

[midnight haven]

i wont

I mean I don't have to

[flat bolt]

Do it anyways

[midnight haven]

ok

[flat bolt]

graph the original

Graph the new one

[flat bolt]

Alr

Now find the slope intercept form of the new line

[midnight haven]

ok

I think I'm supposed to do it in point-slope form

[flat bolt]

Bruhhhhhhhhhh

[midnight haven]

[old geyser]

Are you sure you need to do it in point slope form

Like

What directions

Post the directions

AND

You do realize slope-intercept form is a specialized case of point-slope form right

[midnight haven]

nvm I'll do it in slope intercept form

[flat bolt]

Alr what is it

[flat bolt]

😂😅😂😂😂😂

[midnight haven]

y = -2x-3

[flat bolt]

Huh

Check yo math

[flat bolt]

I think u got the wrong y intercept

[midnight haven]

the y intercept is - 6

y = -2x-6

[flat bolt]

Yes

I mean you couldve have done
f(x+3)=-2(x+3)
f(x+3)=-2x-6

But still fine

[midnight haven]

So could I have done this without having to graphic the functions?

[flat bolt]

I mean u said transformation

[midnight haven]

ye

[flat bolt]

I like pics more than explaining don't u think?

[midnight haven]

yes

[flat bolt]

Is that it?

[midnight haven]

so what you did here was a composition of functions?

[flat bolt]

That is step by step solving

[midnight haven]

a

thank you

[flat bolt]

Anything else or that's it

[midnight haven]

thats it

.close

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[merry forum]

need help with finding volume by slicing for semi-circles (part d).

[merry forum]

the graph is basically 1/4th of a circle but idk how to find the volume with the formula

[old geyser]

,w graph y=4, sec(x)^2

[merry forum]

the formula being: (pir^2)/2 but i keep getting 9.99

[jolly parrot]

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Perhaps try rephrasing your question?
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Requested by Umbraleviathan#3607

[old geyser]

Epiccc

Hold on

Also no it's not a quarter circle or ellipse

It's close but not quite

You'd have to do integration

[merry forum]

according from an answer sheet the answer is supposed to be (around) 2.4999 but i don’t know how people got that

[old geyser]

,w Pi/2 NIntegrate[((4 - Sec[x]^2)/2)^2, {x, 0, Pi/3}]

Hm

Oh I see

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[old geyser]

@merry forum (4-sec^2(x)) is the diameter

[merry forum]

omg

[old geyser]

If you change the pi/2 to pi/8 you should get the right answer

[merry forum]

im an idiot

thank yo uso much

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[lament ingot]

Factorize x^5 y + 256xy^5

[lone belfry]

Is that a negative

In the front

[lament ingot]

no

[lone belfry]

OK well what do both terms have in common

Let's start with that

[lament ingot]

xy

[lone belfry]

Mk

So can you factor that out

[lament ingot]

so I take xy common

[lone belfry]

Yep

[lament ingot]

then 256=16^2

=4^4

Now after that im stuck

idk what to do

[wooden ice]

You can factorize the a²-b²

[lament ingot]

oh

[lone belfry]

$xy(x^4+256y^4)$

Yeah

[wooden ice]

That is 256y⁴-x⁴

[lone belfry]

Difference of swuares

[jolly parrot]

ℕαv

[lament ingot]

yup

[wooden ice]

-x⁴

[lament ingot]

no its +

[lone belfry]

Oh hold on

[wooden ice]

How

O

[lament ingot]

k got it

I use asquare b square property

(a+b)(a-b)

= a^2-b^2

A rectangular piece of paper 22 cm × 8 cm is folded without overlapping to make a cylinder of height 8 cm. Find the volume of the cylinder.

In this question, I remember my answer was like 301 or 308 something

but other people were getting like some crazy answer 707/349 something

can someone pls check once

[last summit]

I think you would solve that by relating the surface area of the paper and the cylinder

and then you could solve for its radius since you already have its height

[lament ingot]

so

will 22 cm be the perimeter of base

or csa

@last summit

sry for ping

<@&286206848099549185> sry for pings

[midnight haven]

22cm would be the circumference, you have to find the radius using the circumference

[lament ingot]

yes exactly

ty

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[boreal crescent]

we have k an integer $k>= 1$ and a serie $Un = (k+1)^2$ and for all $n>=1 , Un+1 = (Un-1)^2$ prove that $Un >= 3$

[jolly parrot]

phoestaclies

[boreal crescent]

I found that Un >= 4 but not 3

[tropic saddle]

I mean U_n >= 4 is stronger

and immediately implies >= 3

[boreal crescent]

but in the proof we can say that Un can be equal to 3 but in mine it's superior or equal at 4 and impossible to be 3

[earnest stratus]

If I say x >= 3 it doesn't necessarily mean x is or has to be 3 too.
4 >= 3 is a true statement for instance.

=
Greater than OR equal to.

Not AND.

[boreal crescent]

i don't understand, like in my proof Un can't be 3 but we need to prove that it can be 3 or more

[tropic saddle]

well then you might have made a mistake somewhere

show your work

[boreal crescent]

in the correction they said also that Un >= 4

ok wait a sec

ok no i understand now

Un+1 >= 4 >= 3 ok and it's true

i had in my mind Un+1 >= 3 >= 4

ok sorry thanks

👍

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[earnest stratus]

If you want help with multiplication, and from others, then might as well use calculator.

No?

Interesting.

[timid spindle]

<@&268886789983436800>

[ember cloak]

Thanks

[earnest stratus]

Good.

[lilac jackal]

.close

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[raven hull]

Hi

[raven hull]

I have got one question about financial mathematics

In 2019 and 2020, we invested 400 euros in the bank at the beginning of each month. We will withdraw the saved funds in the following way: with equal withdrawals of b euros at the beginning of each month in 2022, 2023 and 2024 and with another withdrawal of c = 3,000 euros at the end of 2024. Calculate b if interest is paid in a conformal manner with monthly capitalization and if the annual depreciating interest rate is 3% all the time.

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[valid raptor]

How is 0.18... wrong?

[tropic niche]

you have 12 instead of 24 when you did the calculation

[valid raptor]

yup my bad, screen shotted the wrong formula

[tropic niche]

does it ask you to round at a specific number?

[valid raptor]

that was the final number

"Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.)"

[tropic niche]

sorry, but where does b-a come from?

like you have 4-1

where does 4 and 1 come from?

is there more to the problem?

seems like the important stuff is blocked from the picture

[valid raptor]

its the bounds of the integral

<@&286206848099549185>

[pearl pond]

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[opaque lantern]

need help on where to start

[pearl pond]

@opaque lantern Has your question been resolved?

[opaque lantern]

😩🤔

would it still be -13,3

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[undone hill]

Could someone help explain how we get the solution at the end

[tough token]

,w expand (x^2-36)^2

[jolly parrot]

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[tough token]

they just did the reverse of that

[undone hill]

wouldn't the second step be this tho

where do we get the 1296 + 676.8 from?

[tough token]

,w -1296+676.8

[jolly parrot]

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[tough token]

hmm

seems it is not quite correct

[undone hill]

ahhhh but it's positive in there must be a mistake

[tough token]

,w expand b((x^2-36)^2+676.8)+1

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[tough token]

yeah should be negative, guess this solution isnt correct

[undone hill]

yeah thank you tho 🙂

[tough token]

👍

[midnight haven]

anyone pls im in help 15

[undone hill]

,w expand b((x^2-36)^2-676.8)+1

[jolly parrot]

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[undone hill]

,w (x^4-72x^2+1296)

[jolly parrot]

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[pearl pond]

@undone hill Has your question been resolved?

[pearl pond]

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[proper geyser]

So the anti derivative of 1/x is log(|x|) and that’s fine and I know that but let’s say we had log(x) then I differentiated that and got 1/x so when I integrate 1/x shouldn’t it be just log(x) since I already know if x is negative or positive or does that not make sense

[lone belfry]

Same thing if I understand the question correctly

[proper geyser]

Alright thanks

[lone belfry]

Anti derivative = indef integration

[midnight haven]

idk if thats valid tbh

seems a bit weird but maybe someone smarter can confirm

[pearl pond]

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@proper geyser Has your question been resolved?

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[olive pivot]

Since any non zero to the power of 0 is a 1 then Why is -9^0 = -1 but (-2)^0= 1?

[toxic lichen]

-9^0 reads as -(9^0)

[marble sonnet]

When you write -9^0 in calculator
It does -(9⁰)

[olive pivot]

Oh I see ty

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[pearl pond]

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[plush bramble]

fun

!show

[pearl pond]

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

[midnight haven]

Have I done this properly? It's the right solution, but I'm unsure if I did the full steps

Oh, I see. I should have solved for x
3x^2 + 2 = 14
3x^2 = 12
x^2 = 4
x = 2
or a = 2

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[opaque hearth]

Is there a simpler way to find the derivative of this function without having to plug in H(x) + H(x+h) into the quotient formula and do a bunch of fraction simplification?

[broken ivy]

rewrite the denominator to make it into a vastly simpler chain rule

[opaque hearth]

[\frac{2\sqrt{x+1}}{x+1}]

[jolly parrot]

dopediscorduser

[opaque hearth]

?

[broken ivy]

wait, the denominator is still there

thats not much easier at all

try removing it

like, $2\cdot (x+1)^{-0.5}$

[jolly parrot]

Jigglyproff

[broken ivy]

this should be much more attractive to solve

[opaque hearth]

It'd be like

[\frac{2\cdot (x+1+h)^{-0.5} - 2\cdot (x+1)^{-0.5}}{h}]

[jolly parrot]

dopediscorduser

[opaque hearth]

?

[broken ivy]

wait no

$2\cdot (x+1)^{-0.5}$ is h(x)

[jolly parrot]

Jigglyproff

[broken ivy]

just chain rule on this

or inner times outer

[opaque hearth]

[2(-0.5)\cdot (x+1)^{-0.5 - 1 } = -1x^{-1.5} -1]

[jolly parrot]

dopediscorduser

[broken ivy]

mhm, how did you get 2(-0.5)

[opaque hearth]

[\frac{dy}{dx} \text{ for } 2x^{y} = 2(y) x ^{y-1}]

[jolly parrot]

dopediscorduser

[opaque hearth]

No?

[broken ivy]

so chain rule is $f(g(x))$ becomes $g(x)\cdot f(g(x))$

[jolly parrot]

Jigglyproff

[broken ivy]

so your g(x) is x+1, and the derivative of that is not -0.5

ah right im sorry

[broken ivy]

you were actually right

,w derivative 2/sqrt(x+1)

[jolly parrot]

Results provided by WolframAlpha

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Requested by Jigglyproff#4511

[broken ivy]

I mean almost, the right side is wrong

[pearl pond]

@opaque hearth Has your question been resolved?

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[midnight haven]

how do i solve c. find the 1/2 unit growth/decay factor?

[midnight haven]

i already know the answer to a. which is 1.018 i just don't know how to solve c.

[midnight haven]

<@&286206848099549185>

...

.close

[pearl pond]

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[fast heart]

Hello, I know this is a physics problem, but there is some algebra to it and I'm so rusty how he got this to this

[fast heart]

isolating t how was he able to do this?

[plush bramble]

$at + bt^2 = 0 = t(a + bt)$. if $t \neq 0$ then divide by $t$

[jolly parrot]

riemann

[fast heart]

okay so it will turn out to be 0 = t(viSinThetai + 1/2(-g)t), t is not 0 so I divide it on both sides which is?

1/(viSinThetai + 1/2(-g)t)?