help-0

[fast mantle]

64% < 82.6%

[stone minnow]

Same for the other values

[viscid harbor]

ya i found it but for science i got 32 and for maths i got 4.5 and i was like WHAAAAAAAAAAAAT

[stone minnow]

For example, f(0) = 2(0) + 5 = 5

[alpine sable]

i need a break i am doing math for more than 5 hours now

[heady kindle]

like this

[viscid harbor]

Yes

[stone minnow]

???

[fast mantle]

okay then come backlater

[stone minnow]

How

[fast mantle]

you're wrong there...

[viscid harbor]

@stone minnow

[viscid harbor]

uhh

what

[forest sage]

Math is higher

[wary stream]

Science score, 96/150 = 0.64 = 64%. Math score, 62/75 = 0.822 = 82%

Which is bigger

[stone minnow]

g (-4) = -(-4) - 1 = 3

[fast mantle]

the percentages you've ended up with are wrong

[viscid harbor]

WAIT WHAT

so u were right @wary stream

im sry

[fast mantle]

oh yes i thought it was the other way round hmm

[heady kindle]

i didnt want the answer just how to solve it

[idle bloom]

the delta of x in the first equation gives you a f(x0 + delta(x)) - f(x0))
But when i find the delta of x for the function f(x) = 1/x, they are not using f(1/x0+delta(x) - 1/x0) instead they are using 1/x0+delta(x) - 1/x0
the f part is missing

[viscid harbor]

i told u i was dum

[stone minnow]

Same for the other values

[stone minnow]

You just need to substitute the given value into x

Like idk how to explain

Just 1 step

[harsh swallow]

@heady kindle evaluate means that you find the value of the function when x =

[forest sage]

@idle bloom Well the function is given as f(x) = 1/x

So theres no more f when u sub it in

[harsh swallow]

this means inserting the x you are given into the function

[wary stream]

If you were reading how I explained by calculating the percentages for each score, you would have know what to do instead of stating, "it's a math problem". I know it's math, the concept was percentage

[harsh swallow]

for example

[viscid harbor]

But i did

[wary stream]

Parts of a whole, bigger number in denominator

Smaller in numberator

Hence 96/150 is science

Hence 62/75 is math

[idle bloom]

okay

[viscid harbor]

For Science i did 96/100 * 150 and i got 32 and for math i did 62/100 * 75 and i got 4.5

@wary stream

[wary stream]

It's $$\frac{96}{150} \cdot 100%$$

[ocean seal]

dldh06

[wary stream]

Because percentages are out of 100%

[viscid harbor]

$rotate

[wary stream]

Meaning you have to multiply by 100%

[viscid harbor]

%r

[lone heart]

#questions

For a list of rules about asking on this server, please see #❓how-to-get-help.

[wary stream]

To get a value out of 100

[lone heart]

#questions

For a list of rules about asking on this server, please see #❓how-to-get-help.

[forest sage]

Formula for percentage is fraction * 100%

[viscid harbor]

^r

[glad mural]

ayo could anyone help with this

[viscid harbor]

how u do this

,r

.r

WTF

'r

\r

[forest sage]

Say a number x is increased by 81%

Then x is now 181%

So it is 181% times of the original number

[lethal lichen]

can anyone help please?

[inner storm]

@lethal lichen i believe you set them equal to eachother then take the derivative but I could be wrong

[lethal lichen]

the derivate for that: y = 2x+2

[inner storm]

one sec

i have the exact problem worked through in my bag

[glass lichen]

yeah, so when does the parabola have the same slope as the line?

wait no

[lethal lichen]

wow, the chances of that are quite slim

[glass lichen]

that isnt the derivative

[inner storm]

its -2x+4

[glass lichen]

$-x^2+4x-1$ doesnt differentiate to $2x+2$

[lethal lichen]

$$2x=x^2+4x=1$$

[ocean seal]

Mosh

NiLo

[glass lichen]

??

"2x=x^2+4x=1"

[lethal lichen]

i got it wrong

forget that

$2x=-x^2+4x-1$

[ocean seal]

NiLo

[glass lichen]

yes

[lethal lichen]

$so x^2-2x+1=0$

[ocean seal]

NiLo

[lethal lichen]

therefore

[flat widget]

What's 9992 rounded off to hundreds?

[lethal lichen]

$frac{dy}{dx} = 2x -2$

[ocean seal]

NiLo

[heady kindle]

uhh

[devout summit]

Write \frac{dy}{dx}

[lethal lichen]

$\frac{dy}{dx} = 2x -2$

[ocean seal]

NiLo

[short agate]

seems this channel is not occupied, i got question

square shape cuboid(length and width is same)

how to find the length and width if given volume is 2020 , and the height is 15

so its gonna turn out to be like this?
2020/15 = x^2?

[crisp grove]

yes

[short agate]

so answer gonna turn out to have a points regardless?

[crisp grove]

by points you mean 12.3223 something like this? yes

[short agate]

okay, thank you for answering

[alpine sable]

could someone please help me?

the difference between 2 natural numbers makes 116
that one divided by the other makes something like a quotient of 4 and a rest of 8

would c - k = 116 <=> c = 116 + k work?

[runic sluice]

Do you mean a remainder of 8?

[alpine sable]

i do yes sorry

[runic sluice]

Ok

It would work but you'll need a second equation for that

@alpine sable You're assuming that c is bigger than k, and given the division relationship, what's the equation you'll get

?

[alpine sable]

i really do apreciate the help but i am honestly not sure, i am completly lost

[runic sluice]

Ok

I'll send you a dm

[alpine sable]

thank you so much

[alpine sable]

Are the complex zeroes here 2?

[patent shoal]

if $e^{x} = 2$ then $x = ln(2) $ or $x \approx 0.69314718056$, right?

[ocean seal]

homo-genius-dude

[alpine sable]

Confused by these instructions

i got this, what format should i put it in?

the top and bottom numbers?

[hard garden]

Hello.
How can i transform x1-x2in such a way that i can use Vietа's formulas ( x1+x2 or x1*x2)?

[glass lichen]

Square it

[alpine sable]

@glass lichen any help on my question above?

[glass lichen]

Just do the synthetic division....

[tough ice]

Hi guys, would this be 15!/4! ?

[alpine sable]

I did

[glass lichen]

So then you're done

[alpine sable]

ok ig

the instruction said for me to write the numbers "in the box"

any idea what that is @glass lichen ?

like the -83?

[stone minnow]

I think so

[proven heart]

May I please know which math this is.like whats the topic called

[royal meadow]

?

who are you talking to and what are you talking about

[late parcel]

Is this channel open?

[royal meadow]

sure

[late parcel]

49

If that graph helps

[royal meadow]

that's tiny

better screenshot

[late parcel]

Thx

[royal meadow]

what have you tried

your graph is also crap btw

the squares aren't small enough

[late parcel]

I have begun to consider the possibility of adding everything up and dividing my the number of years

[royal meadow]

no

why

[late parcel]

Ok

[royal meadow]

draw a proper graph, like on squared paper

[late parcel]

The thing is, it specifically says to use excel

[royal meadow]

or find better software

what

are there smaller squares

on the graph

that i can't see

[late parcel]

Smaller squares?

Want me to take a better picture?

[royal meadow]

are there smaller lines than just

'1000'

'2000'

[late parcel]

How do I change it

[royal meadow]

idk

i don't know enough about excel sorry

[late parcel]

Can we just try use this graph

[royal meadow]

no

it's not

accurate

[late parcel]

How

Are you doing that the increments are to big

We have the exact points

@royal meadow I figured it out

[royal meadow]

ok then hf

[late parcel]

Should I make it go by 500

Would 500 be ok

[acoustic glen]

hello

[late parcel]

Really hard to make it less than that @royal meadow

[royal meadow]

why

[acoustic glen]

e^(x^(2+1))-e^(2x)=ln (2x)- ln (x^(2)+1)-x^(2)+2x-1

i have to find the x

if anyone can help me dm

i need help with the e at the first part

[royal meadow]

can you post a picture of the original q

[acoustic glen]

ye

[late parcel]

Would 250 work

[alpine sable]

if I have for example 2 numbers: a = 12, b = 5.

12/ 5 will be 2.4 . how can I find out that answer only by using + and -

i managed to find to 2 from 2.4, but how can I find out the 4?

[acoustic glen]

@royal meadow

so here is what i have done

but i dont know what to do with the first part

i dont remember if there is anything that i can do

i can see that it maybe can apear a x^2 -2x + 1

but how i can prove it

[royal meadow]

is that ln

[acoustic glen]

yes

[royal meadow]

huh

that's

impossibly complicated

probably unsolvable with pure algebra

where did you get this q

[acoustic glen]

well

i have to solve 20 more of these

[alpine sable]

you can prob equate them with your calc

[acoustic glen]

i dont want just to find the x

i have to prove it too

its for final exams in greece mathimatics @royal meadow

[alpine sable]

find the intersect

[royal meadow]

i don't know how

gimme a sec

[acoustic glen]

i need help with the e at the first part

[late parcel]

@royal meadow know a better software?

[royal meadow]

no sorry

[acoustic glen]

the problem gives me this function f(x) = e^x + ln(x) + x +1

and if you see the one i send

there are kinda similar

[alpine sable]

wait but what are u trying to prove

[acoustic glen]

find the x so the thing i send in the photo exists

[late parcel]

@acoustic glen

I got it

@royal meadow I got it

How’s that look

[acoustic glen]

lmao

[late parcel]

Their was a way to change to axis

And now it’s by 250

Is that small enough @royal meadow

[alpine sable]

i legit have no clue

[acoustic glen]

nvm i found it

[alpine sable]

HOW

[acoustic glen]

lmao it was easy

anyways thanks yall

[royal meadow]

incredible

well the hints would have helped lol

[acoustic glen]

how to solve it?

[alpine sable]

anyone know haw to find both values

A and D

[acoustic glen]

@royal meadow the answer was 1

[royal meadow]

incredible

[alpine sable]

How would i solve this

is it just (x+5)/(x-5)?

[acoustic glen]

What you want to find

The x?

[buoyant kayak]

trying to find g(x)?

[alpine sable]

It says find f(x) * g(x)

[patent shoal]

he wanna know $f(x) \cdot g(x)$

[ocean seal]

homo-genius-dude

[alpine sable]

yeah

[buoyant kayak]

that is weird formatting

[alpine sable]

yeah

[buoyant kayak]

so $f(x)=\frac{x+5}{x-1}$ and $g(x)=\frac{x-1}{x-5}$

[ocean seal]

a disappointing son

[patent shoal]

@alpine sable yes $f(x) \cdot g(x) = \frac{x+5}{x-5}$

[ocean seal]

homo-genius-dude

[alpine sable]

ok so do i get a new function like h(x)?

also it says list any domain restrictions, but there aren't any, I don't think

[patent shoal]

make it up idk

[bleak wren]

hi! can someone help with a truth table?

[buoyant kayak]

well, when is your function undefined?

[patent shoal]

me

[bleak wren]

can we talk in dms?

[patent shoal]

yes

[alpine sable]

ah x < 5

how do i solve 1.66/0.59=(asin(3.63-d)-asin(2.73-d))/(asin(5.21-d)-asin(3.63-d))

[bleak wren]

ive messaged u 🙂

[patent shoal]

@alpine sable try $(x + 1)^{2} < 36$

[ocean seal]

homo-genius-dude

[crystal narwhal]

Can som1 help pls i cant figure out how to do the end

[velvet osprey]

Show that ... ?

[crystal narwhal]

So I have to express the area of the shape with the given algebraic sides and then turn tht into a quadratic eq

[velvet osprey]

Oh actually you did answer the question

[crystal narwhal]

How?

[velvet osprey]

You finished ?

[crystal narwhal]

I can turn the -14 to -39

Cant*

[velvet osprey]

-14-25=-39

[crystal narwhal]

Of fk me

Im an idiot

[velvet osprey]

You found the area equal to ... But you also know it's 25

So substract 25 on both sides and you have your equation

[crystal narwhal]

I did erithemtic error

Thanks for help

[velvet osprey]

Did you get what you couldn't find ?

[crystal narwhal]

Yh

Anybody know how to do any of these?

[raven valve]

Expand the square, compare the coefficients of x, x^2 and constants on either side

You'll get values of p and q

[small laurel]

Anyone know how to draw the first one? (i) 105 students passed only S121. Thanks!

[sonic wyvern]

can someone help me with an integration by parts problem?

if possible i think it would be easiest if you could join vc and watch me write it out

im doing it a different way than the solution says, so im not sure why im wrong

[tough ice]

Can you send a picture of your working

[sonic wyvern]

yes, hopefully you can read my writing

[tough ice]

try u = cos(x) so that you can cancel the sin(x)

[elder sedge]

i cant see the problem well

[sonic wyvern]

where

for my integral of sin(x)cos(x)?

[sonic wyvern]

yeah that's why I wanted to stream it so I could write digitally

[elder sedge]

just tell me what it is and ile show it in latex
integral of sin(x)cos(x) on [0,2T] ?

[sonic wyvern]

it's xsin(x)cos(x)

for the entire indefinite integral i got [xsin^2(x)]/2 - x/4 + sin(2x)/8

[alpine sable]

hello @everyone can you help me with this problem of limits and graphics

[elder sedge]

this channel is being used

#❓how-to-get-help

[alpine sable]

sry m8

i didnt know

[elder sedge]

anw \
$\int_{0}^{2\pi} x\sin(x)\cos(x),dx$

[sonic wyvern]

yes

oh sorry

its 2pi

0 -> 2pi

[ocean seal]

james_ash_

[sonic wyvern]

yes

[elder sedge]

for the most part what you chose was correct
using u = x and v'=sin(x)cos(x)

your answer is incorrect however

[sonic wyvern]

did i properly find the integral of sin(x)cos(x)?

if i let u = sin(x)

then du = cos(x) dx

so i get the integral of u

which is u^2 / 2

[elder sedge]

you dont need by parts

[thorn kindle]

Isnt it xsinxcosx though

[sonic wyvern]

i didnt use parts

[elder sedge]

in fact sinxcosx will lead you no where

with by parts

[sonic wyvern]

i didnt

[elder sedge]

as both loop infinitely

[sonic wyvern]

i used substitution

[elder sedge]

oh

ye

[elder sedge]

its hard to read but ile try

[sonic wyvern]

sorry discord camera is dumb

[elder sedge]

so whats dx?

[sonic wyvern]

if i have integral of sin(x)cos(x) dx

and my u is sin(x)

and thus my du is cos(x) dx

then i have everything i need

it can be rewritten as integral of u du

[elder sedge]

ye seems fine

[sonic wyvern]

ok good

but the solution's answer included cosine

as well as sine

mine wont

[elder sedge]

move to next step you're not done yet

whats the rule for by parts

[sonic wyvern]

uv - integral(v du)

pls flip latex

i used the identity sin^2(x) = [1 - cos(2x)] / 2

@elder sedge im an idiot

[elder sedge]

ye thats how you integral sin^2 and you should be done i don't see the problem

[sonic wyvern]

this was the old answer to this problem, which i am practicing

[elder sedge]

you just fix it by an identity at the end

[sonic wyvern]

but obviously, this answer is equivalent to -pi/2

which is what i got

im just fuckin stupid

[elder sedge]

i missed the identity at the end as well soz

you did fine all alone

[sonic wyvern]

i had the right answer all alonG

thanks for your time tho

[elder sedge]

[alpine sable]

Hi! How would you find the sum in terms of n, for k from 1 to n:

[ocean seal]

The Singularity

[glass lichen]

Split it by linearity, then you have 2 geometric sums

@alpine sable

[alpine sable]

Ah, that's right

Thanks!

23rd one

[rapid nova]

PSR is a right triangle, so by Pythagorean theorem we have
[PR^2 = PS^2 + RS^2]
$PR = 2 RS$ because an altitude of an equilateral triangle is also a median
[(2 RS)^2 = PS^2 + RS^2]
[PS^2 = (2 RS)^2 - RS^2 = 4 RS^2 - RS^2 = 3RS^2]

[ocean seal]

rept1d

[silk trellis]

Hey guys if anyone can help to solve this

A^5+B^5+C^5+D^5=E^5 it must be real numbers no 0 1 or negs or irational

[rapid nova]

so it should actually be in positive rational numbers without 1?

[silk trellis]

yes

u cannot use 1 or 0

[rapid nova]

and what do you mean by "solve"?

[silk trellis]

finding the combination

[rapid nova]

just one?

[silk trellis]

using diofants equations

[alpine sable]

Oo 3RS^2. Ya that's the right answer

Sorry for late reply

[silk trellis]

or some logic also

i got an idea for this alrdy

[rapid nova]

don't diofant equations imply it should be in integers only?

[silk trellis]

no clue

im in high school still

so i cant really know diofants

[alpine sable]

Ooo i just made a mistake in the very last line
2RS^2 - RS^2 = RS^2
Just a silly mistake 😅
Sryy

[modern dagger]

Hi. How to apply partial fraction decomposition to this fraction $$\frac{-p-1}{p^{2}-4 p+13}$$?

[ocean seal]

OleG

[rapid nova]

are you allowed to use complex numbers?

[modern dagger]

Yes

[real ether]

If i know what is I_0(start intensity), I, mu(absorbtion coefficient), and l (lenght) can i find out what the concentration or the molar absorbion coefficient?
I know there are 2 unknown variable, but can i subsitute one of them?

[modern dagger]

But I don't fully understand how to break this into the complex numbers...

[surreal abyss]

Hello, maybe it’s a stupid question, but does anyone know how to solve this?

[rapid nova]

you know how to find the roots of a quadratic equation, right?

[modern dagger]

Yes

[rapid nova]

you can use the same formula for complex roots

and all the remaining process is also the same

you just find such p that it nullifies A or B so you can find the other one

in this case such p would be complex

[modern dagger]

So in this case I'll get (p-firstroot)*(p+secondroot) in the denominator?

[rapid nova]

Since $p^2-4p+13 = (p - (2+3i))(p - (2-3i))$ you just need to find such $A$ and $B$ that:
[\frac{-p-1}{p^2-4p+13} = \frac{A}{p - (2+3i)} + \frac{B}{p - (2-3i)}]

[ocean seal]

rept1d

[rapid nova]

(p-firstroot)*(p-secondroot)

[strange comet]

Am i right 2/5 = 20/8

[alpine sable]

to get from 2as ---> a
2as / 2s = a
is this right

[rapid nova]

sorry to disappoint you

but you are not

[strange comet]

10/4

[alpine sable]

need help with last q

[alpine sable]

Make one comparison with the mean/median

and another comparison with the range

[formal fossil]

A ball is thrown upwards and its height h meters after t seconds can be described with the function h ( t ) = −5.0 t 2 + 20 t + 8.0.
a) Determine the maximum height of the ball.
b) What is the speed of the ball when it hits the ground?

can anyone help me with part b

[alpine sable]

a) completing the square

[formal fossil]

i'm working with derivators

[alpine sable]

one sec

[formal fossil]

i can solve it physically, but it is math

[alpine sable]

$h(t) = -5t^2 + 20t + 8

is this the equation?

[formal fossil]

yes,

[alpine sable]

I don't know how to use the bot 😅

[formal fossil]

mee too

hh

[alpine sable]

so u need help with part b right?

[formal fossil]

yes

[alpine sable]

ok

[alpine sable]

can you give 1 example

I think u need to calculate the gradient

I have a feeling it's calculus @formal fossil

[thorn vortex]

It is.

[formal fossil]

do you mean the slope

yes, i know, but how

[glass lichen]

find v(t), then find the time the ball hits the ground

[alpine sable]

Point 1: The first/second experiment has a higher/lower mean/median with Quoted data, therefore on average they have an increased/decreased estimated measurement, of the length of the rod.

Point 2: The first/second experiment has a higher/lower range. And to finish this, interpret your answer to the range. Higher range = less consistent with the frequency and lower range = more consistent

[alpine sable]

differentiate

[formal fossil]

i don't know how.

[dull olive]

I put this in the #math-discussion channel, but got drowned out... so I'll post it here.

There's a non-symbolic way to do auto differentiation to find the accurate derivatives of a function, but can you do that for finding the zeros of a function in a similar way? Without any trial & error?

[sour hemlock]

Jane started jogging 5 miles from home, at a rate of 2 mph. Write the slope-intercept form of an equation for Jane’s position relative to home.

its not y = 2x-5

and its not y = 2x+5

is the asnwer y = -2x+5?

[sour dove]

yes nicely done

if you're 5 miles away from home and you want to return home, you're going to have to decrease the miles

[sour hemlock]

ah

ty

[foggy scroll]

confused on what this question means

<@&286206848099549185>

[sour dove]

@foggy scroll what is the def of a limit?

[foggy scroll]

point where something can’t exist?

[sour dove]

nope

it's the value that a graph "approaches" that point

[foggy scroll]

oh i see

what does that have to do with function value tho

[sour dove]

if your left limit (coming towards your point from the left side) and your right limit (coming towards your point from the right side) are approaching the same value, then your limit to your function at that point is that value

so the limit of x^2 as x approaches 0 is 0 right? because as the left hand side and right hand side are decreasing towards 0 from -inf and inf repsectively

[foggy scroll]

yeah

wait so

[sour dove]

but what if have something like this?

$f(x) = \frac{x^2 - 4}{x-2}$

[ocean seal]

Bohemian_Jack

[sour dove]

?

[alpine sable]

Can you do point 1?

I have 0 clue on what to write for that one, but I have an idea for range

[foggy scroll]

i’m not sure

[sour dove]

Graphing it, we have the following:

so you notice how x^2 -4 is (x+2)(x-2)

and now the (x-2)'s can be cancelled out

so we're left with the equation y = x+2

[foggy scroll]

oh i see

[sour dove]

however, x = 2 does not exist becasue in the original equation the denominator equaling zero is not defined

so what is the lim as x approaches 2 here?

[foggy scroll]

4

[sour dove]

perfect!

so even though the value 4 doesn't exist

the limit still approaches it

[alpine sable]

Room free?

[dull furnace]

I need help to solve a problem I have 2^x times 3^y = 1.5 and then I have 1.5^x times 2.5^y = 3 How do I solve this?

[alpine sable]

solve for either x or y then substitute either x or y into one of those equations

https://www.cliffsnotes.com/study-guides/algebra/algebra-ii/linear-sentences-in-two-variables/linear-equations-solutions-using-substitution-with-two-variables

you can do the same thing with nonlinear equations

[dull furnace]

So I dont have to substitute with log?

How do I isolate x if its a power?

[alpine sable]

to solve it u must use log I think

[dull furnace]

Yeah that’s my problem

[foggy scroll]

thanks a lot

need help with another if u can

i’m confused on how to go about this

<@&286206848099549185>

[buoyant kayak]

well, what happens with direct substitution?

[foggy scroll]

it worked

on mathway at least

lemme try calculator

[buoyant kayak]

don't use a calculator

use direct substitution

[foggy scroll]

so like sin1/1

?

[buoyant kayak]

why would you plug in 1 for a limit going to 0

[foggy scroll]

idk

sin -1/-1

[glass lichen]

if you dont know why you did something, why did you do it?

why are you plugging in random numbers when a list of numbers to plug in has been provided

[foggy scroll]

well

when i plug in the numbers provided

it works

[glass lichen]

yeah... cause none of those numbers are 0

[buoyant kayak]

i'll ask again

what happens with direct substitution for the limit?

[hallow sphinx]

can someone help

[foggy scroll]

0?

0/0 doesn’t exist

[glass lichen]

yes

0/0 is indeterminate

[buoyant kayak]

there you go, you answered part a

part b is pretty self explanatory

[subtle seal]

I'm trying to understand why is the angle between the Fe force and that line alpha/2. Can anyone help?

[alpine sable]

whats a t-table

it says question 2: the first number in the t-table corresponds to x (t or f)

[foggy scroll]

am i allowed to use calculator?

or is it possible to do with hand

[buoyant kayak]

yes, use a calculator

[foggy scroll]

ok

thanks

[robust marsh]

helppp

[buoyant kayak]

do you know implicit differentiation?

[robust marsh]

yes

like the dy/dx

[buoyant kayak]

well that's just leibniz notation for a derivative

[robust marsh]

i'm just confused on the tangent line thinng

[buoyant kayak]

point slope form

[robust marsh]

still catching up on work

[buoyant kayak]

once you find your derivative, plug in your points, that will get you the slope

then use point slope form

[alpine sable]

y-y0=m(x-x0)

[quartz osprey]

little question like how do i find the intiial deposit is it when t=0?

[tawny dawn]

How many lbs of Coffee worth $5 a pound should be added to 30 lbs of Coffee worth $2 a pound to get a mixture worth $3 a pound?

[alpine sable]

It will be A only?

[quartz osprey]

i trieds that

but its not lol

my second guess is wehn t=0

[crystal raft]

Turn into equation

[alpine sable]

Ok it's a different formula

U need to put in t=4

it works in reverse

A is the amount 4 years later. And you have to get back to present by going 4 years backwards

Try that and see if it works.

[quartz osprey]

alright let me try that

ohhh i see

yea i see

its the equation 😒 to 21000

i didnt read

equals

[thorn marlin]

thoughts?

[silver goblet]

look up hyperbolic trig functions

[thorn marlin]

yeah?

I've got them in front of me

I cannot have e in the answer

[north needle]

Coth is 1 / tanh meaning you need e

[thorn marlin]

impossible

[silver goblet]

the bottom seems easy to simplify into what you want

[thorn marlin]

exactly

[silver goblet]

the top less so

you get a leftover e^t right

[thorn marlin]

yes

[silver goblet]

well, hm

maybe fractions

[thorn marlin]

debatable

[silver goblet]

have you tried adding and subtracting the uh

the missing negative part on top

[thorn marlin]

yes

but then cannot get rid of e in any way

[silver goblet]

maybe the answer is multiplying by something weird

if you multiply both top and bottom by like 2e^2t + 2e^-2t maybe it simplifies to something workable

no, it'd have to be -4t for the negative exponent

wait nvm

also, 2t = 4t - 2t

[thorn marlin]

that is true

I'm giving up

[thorn marlin]

aaah

[silver goblet]

dang, it was just clever identity stuff

i mean, they did just add and subtract 5e^-2t

[thorn marlin]

truue

[late parcel]

Is this channel open

[raven juniper]

can someone help me, im unsure of what to do first

[north needle]

Expand the bracket?

[raven juniper]

so a^2+b^2

[placid zinc]

Every time you do that, a puppy dies

² doesn't distribute

[north needle]

No whenever you have a bracket squared it means:
( a + b ) ( a + b )

[placid zinc]

(a + b)² = (a + b)(a + b)

[raven juniper]

oh okay

so after expanding the brackets you get
a^2 +2ab + b^2= ( a + b ) ( a + b )

how do i prove the left hand side?

[north needle]

You just have

Expanding the bracket gave you the left so factorising it would give the bracket

[raw shard]

a(a+b)+b(a+b)

[raven juniper]

help im still confused

so the left hand side now looks like
a(a+b) + b(a+b) ???

[raw shard]

no the right side

look at it with actual numbers

4*5 = 3*5+1*5

[raven juniper]

is that meant to be showing how the left side = the right

[raw shard]

no that’s supposed to show that (a+b)*(a+b) = a(a+b)+b(a+b)

with actual numbers for proof

[placid zinc]

You might have heard of FOIL before?

[raven juniper]

oh okay, sorry 😭

[raw shard]

oh yeah that will help

[raven juniper]

FOIL???

[placid zinc]

Some kind of method for multiplying out (a + b)(a +b)

[hybrid plume]

Is anybody here ok with trig substitutions?

[raw shard]

first outers inners lasts

[raven juniper]

this makes a lot of sense

thank you

🙏

[raw shard]

rather firsts+outers+inners+lasts

[placid zinc]

There's a glaring u-sub

[raw shard]

seems like normal u sub

[hybrid plume]

I was trying trig subs

[raw shard]

you know that’s unnecessary right

[placid zinc]

In general, if you've got a tough function like sqrt in your integral, consider subbing out everything under it

So in this case, u = x^2 + 1

[hybrid plume]

Don’t include the sqrt? I guess that makes differentiating difficult?

[raw shard]

u is the inside function

although i assume you already knew that

[placid zinc]

Usually don't.
Of course, there's no "always works" rules

[hybrid plume]

Yeah sometimes we’d include the sqrt that’s why I asked

[raw shard]

oh

[raven juniper]

so now i have all the numbers for foil- a^2, ab, ba, b^2... now do I add them all up?

[raw shard]

yeah

[placid zinc]

With practice, you'll be able to check quick u-subs in your head

[raven juniper]

thank you @raw shard and @placid zinc sm!

[raw shard]

no problem

[late parcel]

Help in channel 3 needed

[raw shard]

don’t go to different channels asking for help in other channels

[late parcel]

Ok sorry

Should I just post here if nobody is helping me their

[hybrid plume]

Just multiplying out the last bracket is left

[fresh parcel]

ye

[raw shard]

@late parcel no you shouldn’t post in multiple channels

[hybrid plume]

Quantum do u see any mistakes there?

[raw shard]

yeah maybe

2/3*5^(3/2) doesn’t equal 2/3*25^(1/3)

other than that it’s fine

you did ^2/3 instead of ^3/2

[hybrid plume]

Ohhh yes

[raw shard]

2/3*sqrt125

obvious but still posted

[hybrid plume]

5sqrt5

[raw shard]

yeah

10/3sqrt5

never actually use that rule lol

[hybrid plume]

Lol

[fresh parcel]

you raised it to 2/3 in the last line

[hybrid plume]

You said u self taught calc?

[raw shard]

yeah

[fresh parcel]

oh nevermind

[hybrid plume]

What YouTube vids were helpful?

[raw shard]

i’m on integrals right now

i don’t do youtube videos

i do articles

[hybrid plume]

Which website?

[raw shard]

i’ll send the site i use

[hybrid plume]

Ok

[fresh parcel]

3b1b videos are pretty nice

[hybrid plume]

I’ll check that out

[raw shard]

@hybrid plume https://tutorial.math.lamar.edu/classes/calci/calci.aspx

[chilly quiver]

i tried to solve it 3 times now and i always get x^(33/16). Solution says x^(7/8)

[hybrid plume]

Wait I forgot to put 2 and 0 in respect to u

So I should redo those last calculations?

[raw shard]

you deleted your image

looks good

[alpine sable]

is this channel busy for a quick question

[raw shard]

i’m at about the level you are

[hybrid plume]

When it’s a definite integral tho the bounds 0 to 2 must be solved in terms of u

[alpine sable]

is b={10}.

[raw shard]

no they don’t

[fresh parcel]

is it possible to just square it a few times to get the answer?

[hybrid plume]

Why not?

[raw shard]

i convert u to x and then sub

it’s just a different way of doing it

both are correct

[alpine sable]

its almost 2 am really need to get that question over with pls

very simple yet im not sure

[hybrid plume]

But I didn’t convert u to x

[chilly quiver]

i try to upload a pic of my process 1 sec

[hybrid plume]

Wait I did

Lol

[raw shard]

it doesn’t matter what you do

but i find u to x easier i think

[hybrid plume]

Yeah I get what ur saying and yeah I do too

[raw shard]

makes me sure i didn’t make any mistakes

[raw shard]

wow that looks annoying lol

[chilly quiver]

it is

[hybrid plume]

What class is that

[chilly quiver]

first mathclass of university

[raw shard]

i did it in my head and it’s x^(7/8)

[chilly quiver]

@raw shard yep it is

but where did i do the mistake

[raw shard]

i know you already said it is

hmm

i’ll try to see

why is there a x^(3/2) outside the whole thing

[chilly quiver]

i solved the first root

root of x^3

-> x^(3/2)

[raw shard]

oh

[fresh parcel]

bruh i went through it like 2 times

i still cant find the mistake

.

[junior talon]

Quick question a nice book started using this weird notation

I mean I believe this is supposed to be equivalent to saying f(x) = x^2
but what is this I even for though?

[raw shard]

for me what you do makes sense, but it confuses me so idk if i would be able to spot a mistake

the way you write it rather

[raw shard]

i’ll still look

[chilly quiver]

alternative writing

same solution but it is wrong

[raw shard]

not sure what you did wrong honestly

[chilly quiver]

haha

thank god i'm not alone

with that

[raw shard]

i just rewrote them as fractional powers to not confuse myself

[chilly quiver]

i wonder how you made it in your head tho 😄 but somehow we don't find the mistake

[raw shard]

i thought of it as fractional powers lol

it was still hard to keep track

maybe do it without all that expansion you’re doing

so focus on only the innermost layer at a time

[chilly quiver]

from inner to outer?

[raw shard]

yeah

[full linden]

Can I get help on this ?

[raw shard]

occupied bruh

at this point i should start saying this channel is obviously occupied lol

[fierce pebble]

If a = 1 and b = 0
ab would equal to 10 or 1? (I'm doing this cause I don't wanna know I was bored.)

[raw shard]

0

[fierce pebble]

Reasons?

[raw shard]

n*0 = 0

[fierce pebble]

Were not multiplying

I just did ab.

[raw shard]

so like 10a+b

[fierce pebble]

So like

10(a)?

or

[raw shard]

10*a+b

10(a)+b

however you write it

[fierce pebble]

Thats gonna be 10.

[raw shard]

but yes 10

[fierce pebble]

ok

any more thoughts

[raw shard]

nope

that’s all

[fierce pebble]

1= face down card
0 = face up card
What is the final card, which side is up?
0010101101

[chilly quiver]

Still the same...

[fierce pebble]

Hello there! What you need help on.

[raw shard]

bruh

[chilly quiver]

@fierce pebble the solution is x^(7/8) but i get as solution x^(33/16)

[fierce pebble]

I'm sorry im only in 7th grade. Im learning portional relationship

[chilly quiver]

OMG

i think i found it

[raw shard]

not to sound repetitive, but you expanded it again lol

[fierce pebble]

What grade of math is this? 💀

[alpine sable]

I just need help with the second one

[chilly quiver]

@raw shard i guess i didnt understand you quite right since i'm not native

[chilly quiver]

first class of uni

@raw shard the first "3" is over the root. not x^3

going to kill myself quick

brb

[alpine sable]

ab=0

[fierce pebble]

I'm not ready 💀 💀

[fierce pebble]

Reasons

[raw shard]

@fierce pebble you’re writing it weird

[fierce pebble]

what does x = to

[raw shard]

ab = a*b

[alpine sable]

ab = a*b

[fierce pebble]

kk

[alpine sable]

1*0=0

Understand?

[hybrid plume]

Then u sub from here

[raw shard]

they’re talking about 10a+b lol @alpine sable

[fierce pebble]

This is a fun app

[hybrid plume]

Are u 13 in every time zone tho 😡

Jk

[alpine sable]

Wtf

[alpine sable]

but your account isnt new?

Why didnt you just write that @fierce pebble

[fierce pebble]

In my mind was only about Pog

[chilly quiver]

@raw shard ty for checking!

[glass lichen]

$10a+b=a||b$ for common concatenation notation.

[ocean seal]

Mosh

[glass lichen]

or $\overline{ab}$

[ocean seal]

Mosh

[fierce pebble]

Help

[raw shard]

@hybrid plume i honestly don’t know

[glass lichen]

dont troll

[hybrid plume]

Np

[fierce pebble]

Sorry.

[hybrid plume]

Mosh can u check the beginning of my integral up a bit ^

[fierce pebble]

Wait this bot is smart

[hybrid plume]

If there’s any easier way to start it

[glass lichen]

I wanna say complete the square

then it should be inverse trig after a u-sub

,w complete the square on y=-9x^2+12x+12

[ocean seal]

Results provided by WolframAlpha

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

Requested by Omegabet_#9771

[fierce pebble]

Do we have to know the variables of each ones or we figure it out.

[glass lichen]

wasnt directed at you

[fierce pebble]

Oops

Brb

[hybrid plume]

You’d sub in a trig function for x?

[glass lichen]

no

$\int\frac{1}{\sqrt{16-9(x-2/3)^2}}\dd{x}$

[ocean seal]

Mosh

[glass lichen]

actually yes, I think it's when you do the tan trig sub

no, wrong signs

[hybrid plume]

Don’t have experience with this but I found a YouTube vid explaining, thanks

[glass lichen]

$0.25\int\frac{1}{\sqrt{1-\left(0.75(x-2/3)\right)^2}}\dd{x}$

[ocean seal]

Mosh

[glass lichen]

then u-sub and you get arcsin

[raw shard]

isn’t it 9/16 instead of 0.75

[glass lichen]

9/16=0.75^2

[raw shard]

oops didn’t catch that

[glass lichen]

it's 0.75(x-2/3) all squared

ye

cause then you sub u=0.75(x-2/3) and get (constant)arcsin(u)+C

[hybrid plume]

How do I complete the square?

Just factor out a 9?

[glass lichen]

$-9x^2+12x+12 \ =-9(x^2-4/3)+12$

[ocean seal]

Mosh

[glass lichen]

then add and subtract the needed constant in the brackets, then simplify

[hybrid plume]

Where do I add and subtract the needed constant? Haven’t done completing the square before

[glass lichen]

You should've done comp the square in High school when you first learn quadratics

but I said "in the brackets"

[hybrid plume]

So I add -4/3?

[raw shard]

isn’t it like adding and subtracting a value c so you can do something like (x+y)^2

plus something including c

[glass lichen]

yes, you make a perfect square trinomial

so you halve the new linear co-efficient then square it

then add and subtract that

[hybrid plume]

I’m lost on this part can u tell me what I need to add and subtract so I can continue integrating?

[glass lichen]

$-9(x^2-\frac{4}{3}x+\frac{4}{9}-\frac{4}{9})+12$

[ocean seal]

Mosh

[glass lichen]

But yeah, comp the square is HS content, find videos on it if you dont remember doing it

[hybrid plume]

Is that all ^ for completing the square tho?

I can continue integrating?

[glass lichen]

no, you need to finish.

If you just want to focus on integrating, I posted the quadratic in vertex form when I had wolfram do it.

it's the same process.

[hybrid plume]

?

[glass lichen]

yes.

$-9(x-2/3)^2-9(-4/9)+12$

[ocean seal]

Mosh

[undone isle]

ikr

[hybrid plume]

At this point I factor out the 8 to make it 1-…

But what should I do with the -9?

@glass lichen where should I go from here?

[glass lichen]

when was 4+12 equal to -8?

[hybrid plume]

Cancelled the 9s

Wait 16

Ok 16-9(x-2/3)^2

Does the 9 matter?

$16-9(x-\frac{2}{3})^2$

[ocean seal]

H4

[hybrid plume]

@glass lichen I think this is the last thing, what do I do with the 9?

[glass lichen]

no that's right.

[hybrid plume]

So what trig identity should I sub in? And will it have a coefficient of -9?

@glass lichen

[glass lichen]

I already said what happened after cause I thought you had figured it out

[glass lichen]

.

[hybrid plume]

The 3/4 though isn’t that another coefficient?

Will the trig sub have a coefficient of 3/4? @glass lichen

[glass lichen]

No...

you sub u=(3/4)(x-2/3)

you're also missing the dx

[hybrid plume]

Oh lol sorry and thank you

[alpine sable]

Could someone please help me with questions 2 and 6?

[north needle]

For 2).
Log 7 + log 5

[north needle]

For 6).
Log 3 + log 5 + log 5 - 2

[alpine sable]

I can’t use base 10 logs

[north needle]

I couldn’t write base 7

[alpine sable]

o

[north needle]

It looked messy

But yeah they are all to base 7 hence why the -log 49 became -2

[alpine sable]

ah okay

[hybrid plume]

@glass lichen I know this has got to be wrong but do u know which part is?

I’m not sure if I can do back to back substitutions like that

[glass lichen]

There's no trig sub

[raw shard]

are you just trying to find a way to do a trig sub? lol

[glass lichen]

3rd line is a known primitive

[raw shard]

it really seems like you are

[hybrid plume]

Whats the primitive?

Quantum do u know what mosh means?

[raw shard]

nope i actually don’t know/remember what primitive means lol

[hybrid plume]

@glass lichen what is the primitive?

[glass lichen]

Anti derivative

[raw shard]

wait i’m curious, can you do multiple substitutions like that?

i would assume yes but idk

[hybrid plume]

So do u integrate (1-u^2)^-1/2?

[raw shard]

yeah

[hybrid plume]

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

Any chain rule?

@raw shard is there any chain rule?

[raw shard]

no you already integrated

[hybrid plume]

Forgot the -

u=3/4(x-2/3) was the sub

Calc2

@raw shard that look right?

[raw shard]

this is calc 1 isn’t it

wait are you sure that original function with u wasn’t a trig derivative

[rancid rapids]

im dumb

[rancid rapids]

pls do question i need within hour or ccp will come for me

[devout summit]

On what basis did you go from second to third line?

[raw shard]

oh my gosh people stop sending questions

this channel is obviously occupied

[hybrid plume]

Wdym?

Is there any mistake?

[raw shard]

most of the other channels are dead and you two go for the 1 channel where people are currently talking

[rancid rapids]

can u do it and send all answers i bet you can

t

[devout summit]

8th line to 9th line

[rancid rapids]

oh so u dont know it do u

[hybrid plume]

Eighth line counting from the original step?

Whats the mistake Euclid?

[raw shard]

@alpine sable @rancid rapids go to a different channel

one person per channel

[devout summit]

The first line where you got rid of the integral sign

[devout summit]

Yes

[hybrid plume]

What is the specific mistake tho?

[devout summit]

You simply can’t do that

[hybrid plume]

Do you know what I should’ve done?

A trig sub?

[devout summit]

Yes

[hybrid plume]

Which one?

[devout summit]

The one you did before

[fresh parcel]

a quick question but why can't you do that?

[hybrid plume]

u=sintheta?

[devout summit]

Ye

[devout summit]

There is involvement of trig functions

[fresh parcel]

hm

[hybrid plume]

Int 1 dtheta equals 1?

Multiplied by 3/16?

[devout summit]

It equals theta plus some constant

[hybrid plume]

And is 3/16 multiplied by theta final?

Plus C

[devout summit]

You have to re substitute back all the substitutions you have done

[hybrid plume]

How do I go backwards from here?

Inverse sin u?

[devout summit]

Yep

And substitute back in terms of x

Wait there is another slight error

[hybrid plume]

Where?

[devout summit]

That 1/4 on the outside converts to 1/3 and not 3/16

Since dx= 4/3 du

[raw shard]

@hybrid plume i think you’re asking is this right too much lol

i’ve noticed that you’ve asked that like 5 times for this 1 problem

[hybrid plume]

Apologies I’m done after today

[devout summit]

And, (4/3)*(1/4)=1/3

So the last line you get should have been just theta/3

[hybrid plume]

Understood

[eternal osprey]

help pls fine g prime

[hybrid plume]

sin^-1(3/4x-1/2)?

Final sub and no simplification from there yes?

[devout summit]

Umm, sin^-1((3x-2)/4)

[sour dove]

wow your teacher must hate you. That's an intense derivative lol.
It's just a lot of chain rule though

[devout summit]

Combined with that (1/3) outside

[fresh parcel]

use chain rule?

[hybrid plume]

How do u get 3x-2?

[eternal osprey]

will it be easier to ln both sides first

yeah I want to die

[hybrid plume]

Isn’t it multiplying 3/4 by within the bracket?

[devout summit]

Just the u=(3/4)(x-2/3)