help-26

[vague bramble]

I dont suggest using l'hopital rule because the question itself is basically the same as finding the derivative of sinx as a

If you know compound angle formular for sin(A+B), then you can try to use this

By first rewriting the limit into a form where the denominator is just a single variable h going to 0

[misty valley]

what about this

[sweet shard]

Change t = x-a

x goes to a implies t goes to 0

Then use sum angle formula for sine to expand sin(t+a)

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[graceful leaf]

pls

[graceful leaf]

ik its chem but numbers are involved

i took the exam oct 1 and still not been graded

but for this question i guessed i have to be honest

Anyone know if its right

[icy sky]

,rccw

[icy sky]

how does it violate pauli exclusion

also please go to the chem server for more chem related questions please

[little lantern]

oh

[icy sky]

[response to deleted message] i was trying to get them to reach that conclusion

[graceful leaf]

rip

i guess the plan is get my test and re study the whole chapters becuz they said this exam is the foundation for the rest of chem

and retake this exam without looking @ answers

thnx

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[little lantern]

gl @graceful leaf

[icy sky]

yes gl

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[crude cape]

pls someone help me understand this questions and how to do it.

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[cloud sage]

@supple hinge Hello

That is your problem?

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[tidal elk]

I need to discover wich affirmation is right
a) A + B = 5
b) A – B = 5
c) B – A = 2
d) A + B = 0
e) A – B = 2
I just get stuck, i dont know exacly what i need to do and i don't know what is this "j" 😭

[finite storm]

partial fraction

[tidal elk]

x =/ 1 and A and B are real

[finite storm]

is j a variable?

if not, everything will be easy

[tidal elk]

I don't know

The question doesn't mention about j

Mention

[finite storm]

it talks only about A and B

?

[tidal elk]

I will translate it and send

Knowing that (pic of equation) Solve the equation for any real values ​​of the variable x other than 1 and that A and B are both real numbers, it is CORRECT to state that:

[finite storm]

i see

[tidal elk]

Maybe it's and ortographic error, idk

Yeah, it's wrong

I searched for where the question whas taken for and the equation is diferent, sorry

[finite storm]

yeah

i couldn't find the last term that will satisfy B

[tidal elk]

Ignore that final letter

[finite storm]

alright

make sense

do a cross multiply

and compare coefficient

[tidal elk]

Where?

[finite storm]

on the right side

[tidal elk]

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[uneven dirge]

Determine whether the given equations are functions of the variable x.

could anyone help and give an explanation? i dont understand this topic

[hallow depot]

so it asks whether the set of points (x,y)\in R^2 could be described as the graph of one function y=f(x)

[uneven dirge]

yeah

[hallow depot]

i) it is pretty straightforward

[uneven dirge]

but how do you know if it could be a function?

[hallow depot]

in general you only need to check whether it is possible to isolate the y-variable without creating other cases

like in i) -y=|x| that implies y=f(x)=-2|x|

[uneven dirge]

what about in e) ?

ah, i think i got it. Thank you very much

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[ember fog]

Can anyone help me with this task please?

[ember fog]

Please its very important to me to do this task

And I ve already tried to solve this

But I just cant

[rigid star]

Show what you have tried

[ember fog]

this is my drawing for this task

[rigid star]

The points ABCD all have to be on the perimeter of the circle

[ember fog]

They're on it

[rigid star]

Oh, it's a faint little circle

Why do you have multiple copies of everything here?

This is impossible to see. Draw it once, and don't make ABCD a square

[ember fog]

okay

is it okay now?

[rigid star]

You seem to have put in many extra things, such if good because it means this trying stuff, but it does look confusing (first picture, not second)

[ember fog]

yeah i had many attempts but i still dont know how to prove that task

So if you could help me somehow I would be very grateful

[rigid star]

I'm actually not sure either.
Do you know that angles CMK and DFL are equal?

And I suppose you know that it's enough to die that two opposite angles in EFNM add to 180

[ember fog]

Yes i know this

[ember fog]

Are they?

i dont think so tbh

[rigid star]

Look at the two quadrilaterals they're in. Both have two right angles. And the MN is a transversal of parallel lines

[ember fog]

oh you're rigt

But what can i do with this fact?

[rigid star]

Which makes those similar quadrilaterals, which makes pairs of similar triangles

If you line it up, you get NFE=FEM

[ember fog]

Okay but what's next?

If I understand correctly, the quadrilaterals DNLF and MCEK are similar, so the angles LND and KEC are also equal, right?

But idk why NFE=FEM

[topaz sinew]

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[ember fog]

@rigid star pleas explain me this🙏

[rigid star]

NLFD and CEMK are similar

which means that when you cut it along the diagonal, the two triangles you get in one are similar to the triangles you get in the other

Specifically, look at DNF and MEK

[ember fog]

Okay i see this

But what after this?

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[rigid star]

You already have the other part

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[topaz sinew]

Please don't occupy multiple help channels.

[desert yew]

kk

[rigid star]

.close

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[wise vector]

how do you evaluate trigonometric expressions like sin15 = (sqrt6 - sqrt 2)/4 exactly

[cedar wagon]

Formula mostly

Here you use the fact that sin(15) = sin(45-30)

And using addition formula or whatever its called

Sin(45)cos(30) - cos(45)sin(30)

Simplify

And there you go with result

[wise vector]

this?

[cedar wagon]

Yup

[wise vector]

I see

[cedar wagon]

Second one

[wise vector]

many thank

thanks

[cedar wagon]

You're welcome

[wise vector]

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[tropic birch]

i would like some help on this question,

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[dense cosmos]

yo

[dense cosmos]

original problem: integrate x/(x^4+1)

i dif

did

u=x^2

du/2x=dx

so integrate x/((u^2+1)(2x)) du

so 1/(2(u^2+1)) du

from there i did .5(ln|u^2+1|)/(2u)

is that ok to do?

i just divided by the derivative of u^2

[sweet shard]

,w integral dx/(x^2+1)

[thorny flame]

Results provided by WolframAlpha

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Requested by rie.mann

[sweet shard]

that's an integral you'll need to have learned

[dense cosmos]

ok but why is what i did wrong

[sweet shard]

differentiate your answer and find out why

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[rigid meteor]

need help to understand some concepts related to calculus -
three functions are given f1(x) = 2x/(1+2x), f2(x) = log_e(1+2x) and f3(x) = 2x

[rigid meteor]

need to prove f1(x) + f2(x) < f3(x) / 2

in these cases how should the log function be calculated without calculator ?

one case could be using infinite log series

[sweet shard]

what's the range of x

[rigid meteor]

oh sorry

x > -1/2

[golden blade]

I would bring everything to one side and then try to show that there is an absolute minimum lower than 0 within that interval

[rigid meteor]

and range of f(x) is ( ((3)^(1/2) / 2), inf)

[rigid meteor]

ok, and how to estimate log function here ?

rhs = 2x/2 = x

what is the correct procedure to find lhs < x

[golden blade]

You can try to see how the monotony is using the derivative of that new function

[rigid meteor]

both f1 and f2 are monotonically increasing over the interval

f3 alse

[golden blade]

are you sure about that

[rigid meteor]

also

[rigid meteor]

yes

[golden blade]

ln(1+2x)

1+2x>0
1>-2x
-1/2 < x

[rigid meteor]

yes

[golden blade]

also are you trying to show this inequality holds for all x>-1/2?

[rigid meteor]

no only when x > sqrt(3)/2

basically need to show f1 + f2 < x

[golden blade]

aha

that makes now more sense

[rigid meteor]

need to simplify f1 + f3 in terms of some a.x

or something like that

[golden blade]

that doesnt seem to hold

[rigid meteor]

why ?

[golden blade]

look where sqrt(3)/2 is

until the intersection

f_1+f_2 is greater

[rigid meteor]

what is the intersection ?

[golden blade]

where x and f_1+f_2 meet

[rigid meteor]

x = sqrt(3)/2

and y = ?

[golden blade]

somethings off

https://www.desmos.com/calculator/hugd8zvljl

you can take a look for yourself

either post the original or idk

[rigid meteor]

but this graph actually confirms the statement

[golden blade]

How

you say for all x>sqrt(3)/2

where a little bit more than sqrt(3)/2 the inequality doesnt hold

[rigid meteor]

the y-value for y=x > y= f1 + f2

[golden blade]

the inequality holds if x > 2.7

orsome value like that

look at the red

f1+f2 is above x

[rigid meteor]

ok, can you tell me what is 2x/(1+2x) at x = 2.7

[golden blade]

i sent the link

[rigid meteor]

oh ok

[golden blade]

,calc 2*(2.7)/(1+2*(2.7))

[thorny flame]

Result:

0.84375

[rigid meteor]

may I type the entire question then ?

For ( x > -1/2 ) let ( f_1(x) = \frac{2x}{1+2x} ) , ( f_2(x) = log_e (1 + 2x) ) and ( f_3(x) = 2x ). Then which one of the following is true ? ( \ )
a) f3 < f2 < f1 for 0 < x < ( \sqrt(3) /2 ). ( \ )
b) f1 < f3 < f2 for x > 0. ( \ )
c) ( f_1(x) + f_2(x) < f_3(x)/2 ) for x > ( \sqrt(3)/2 ). ( \ )
d) f2 < f1 < f3 for x > 0

option C is correct

[thorny flame]

shanks44

[rigid meteor]

can you help @golden blade

[golden blade]

no

[rigid meteor]

ok

[golden blade]

literally a counter example

also you were really misleading

it seems you are doing a T or F thingy

you should always first see if the assumption is true by testing it, not assuming it's true immediatly

[rigid meteor]

no I was trying to clear my concept

how to prove the statement algebrically

that was what I was looking for

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@rigid meteor Has your question been resolved?

[rigid meteor]

anyway thanks

.close

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[stable wren]

got it nevermind

.close

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[thorny flame]

w

[sinful vault]

hmm

looks like we both are taking a very similar uni course in math

lol

uhh you know what the intermediate value theorem is?

replace

(f(a) + f(b))/2

with a constant k

and its literally the definition of the IVT

if you arent allowed to use IVT im not sure how to help you

yea

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[iron elk]

Write the piecewise function for f(x)

[topaz sinew]

@iron elk Has your question been resolved?

[iron elk]

<@&286206848099549185>

[crude anchor]

What are you struggling with?

[covert juniper]

Use slope formula

[iron elk]

idk how to find the piecewise function

[covert juniper]

Different function for different starting points

[iron elk]

what does that mean?

[covert juniper]

https://images.app.goo.gl/9bKZ6kdiZBDs4ZA18

See that statement above the graph? That's how you need represent the function you're given

[iron elk]

yes but how do i do that

[covert juniper]

Find slope

Then put it in mx+c=y format

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[limpid flame]

idk wat i did srong

wrong

[sterile finch]

You miswrote (x-3) as (x-5).

[limpid flame]

Oh

TY

.close

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[limpid flame]

.reopen

[topaz sinew]

✅

[limpid flame]

idk wat to do

[cedar sinew]

Do you know IVT

intermediate value theorem

Have you learned it yet

@limpid flame

[limpid flame]

yes

[cedar sinew]

So what does it say

[limpid flame]

omg

do i plug in 0 and 2

[cedar sinew]

Yes

[limpid flame]

wat is cos 0

that's like 1

[cedar sinew]

Yes

[limpid flame]

cos 2π is like

all the way around right

like

1

+4

[cedar sinew]

Yes

[limpid flame]

EASY

[cedar sinew]

So what is the value at x = 1

And the value at x = 4

Uh

I’m stupid

Ignore me

I forgot the interval

I meant at 0 and 2

Alr you got this

Just ivt

@limpid flame use .close if you are done

[limpid flame]

.close

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[viral fulcrum]

hey, what does skew means?

[viral fulcrum]

how do I even start?

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[tacit turret]

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[tacit turret]

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[sweet shard]

Use point slope of line

,tex .point slope

[thorny flame]

riemann

[tacit turret]

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[tacit turret]

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[agile harness]

the line perpendicular to the tangent line has a slope that is the negative reciprocal of the derivative at that point

it also passes through the point

then use point slope

derivative at 2 is 9

so perpendicular slope is -1/9

[tacit turret]

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[agile harness]

yuh

[tacit turret]

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[agile harness]

3(2^2) - 3

[tacit turret]

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[agile harness]

12-3 = 9

[tacit turret]

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[tacit turret]

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[agile harness]

the slope is a numerical value

[tacit turret]

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[agile harness]

always

[tacit turret]

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[agile harness]

we need the slope at the point so we can calculate

[tacit turret]

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[agile harness]

for perpendicular line yes

[tacit turret]

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[agile harness]

now use point slope

it goes through the same point

(2,3)

[tacit turret]

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[agile harness]

what

[tacit turret]

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[agile harness]

y - y1 = m(x-x1)

(x1,y1) = (2,3)

m = -1/9

[tacit turret]

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[agile harness]

it is

but you did it wrong

2-a?

and why is there a b?

[tacit turret]

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[agile harness]

sir

[agile harness]

^

y - 3 = -1/9(x-2)

[tacit turret]

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[agile harness]

y = -1/9 x + 29/9

[tacit turret]

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[agile harness]

you didn’t get that

[tacit turret]

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[limber cargo]

I was just messing around with what I had so I haven’t formally declared or concluded anything yet, but I just wanted to know if this was valid.

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[mellow aurora]

yo wait what I thought a set can't have duplicates

[mellow aurora]

[distant shadow]

Since a set is expressed without duplicates, including one doesn’t matter as it can just be ignored

[mellow aurora]

ah

.close

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[neon iron]

Hiii, i'm currently in my freshman year of college and I have no clue what to do for the homework, as my prof never taught us this, and they removed the example problem section on this question so I can't learn it from the math program. I tried just using chain rule, but it wasn't correct. When I tried submitting my answer, the second image is what I was given as a response, but I don't know what it means

[sweet shard]

Which part exactly do you get lost first

[neon iron]

i just don't know how to find the derivative of this

i got it wrong the first time and saw that i was supposed to rewrite it as e^xlnb

and i just tried doing chain rule from there

but either I did it wrong or that wasn't the correct way

[true coral]

Well you did the first step to change into e^something

Then you just need to differentiate that result using chain rule

[neon iron]

What should I do from there?

i tried doing that but that wasn't the answer

[true coral]

Was your answer the one here?

[neon iron]

Yes

[true coral]

I'm guessing then your g'(x) in the chain rule is wrong in this case

[neon iron]

checked with a derivative calculator and unless i'm blind I think I got it right

or do I gotta remove the parentheses

i was just dumb it was the parentheses

sorry

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[thorny flame]

utop!a

[versed basin]

specifically, 3d.

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[strong sable]

How is this yielded by Taylor?

[finite storm]

waht is taylor expansion in ur eyes

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[jolly agate]

Quick question 5) b, the mixed partial derivative of z’’xy

The z’x is y/x

Now derivate this with respect to y

Do I use product rule or the quotient rule ?

Either way I do it I will get a Y in the equation, and the solution says that there should only by 1/x

So how should I think?

If I use product rule, it will be :

It is not correct! How do I think🤨

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[dapper patio]

q. Find the number of ways in which a selection of 100 balls, can be made out of 100 identical red balls, 100 identical blue balls & 100 identical white balls.

wouldn't the answer be 3^100, just because there are 3 choices to every one of the 100 balls to be selected?

[dapper patio]

another question i didn't get:

what i did was i first chose 6 book out of 8 to distribute in groups of 2 to all 3 students (minimum requirement)
so 8C6 so after selecting 6 distinct books we need to split them among 3 students
so first I selected 2 out of 6
and then 4 books remained so 2 out of 4
6C24C2 ways of distributing
and because we selected 6 books out of 8 first multiply that into 8C6
and then we're left with 2 items which we can split in any way among 3 students so that i counted manually and it's 9
so obvoiusly we have to multiply 9 into the number we have
but that's wayyy bigger than the options (my answer is 25209)

[neon iron]

mathongo ?

[dapper patio]

yea

[dapper patio]

what did i do wrong

[neon iron]

im getting only 6

[glass maple]

books are distinct here

so it should be 9

[neon iron]

we are to distribute 2 books along 3 children so 3P2 ?

oh

:P

[glass maple]

well assuming the english at least since they said "different books"

[neon iron]

yeah mb

[glass maple]

allg, easy to miss

[neon iron]

yo bacc

xD

[glass maple]

the pfp change caught me off guard lol

ok well the way i counted was a little difference but im getting 2940

(hopefully thats right otehrwise it would be pretty embarrassing that im yapping like a madman)

8 objects into 3 groups, so really your distribution is either
4 books, 2 books, 2 books or 3 books, 3 books, 2 books to 3 ppl

which respectively has 3 ways and 3 ways of doing

if its 8 distinct books (different books since the english since we suggest that)

its $3 \cdot \frac{8!}{4!2!2!} + 3\cdot \frac{8!}{3!3!2!}$

[thorny flame]

Dootud

[glass maple]

which im getting 2940 from

[golden blade]

this would be correct, if you had 100 distinct balls, and from these you choose 3 colors

for this problem look up the stars and bars method

[dapper patio]

it is indeeed

[dapper patio]

right

[dapper patio]

oh shit order doesn't matter my bad i forgot

we could use integral equations ig

[dapper patio]

i wouldn't have thought of it that way thanks

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[lusty yacht]

It was my big brother homework

but i don't know anything bout physics

i only can do math

idk all the formula needed

pls explain

thank you

[stark panther]

when momentum changes its know as impusle and is worked out by I = m(v-u) where m is mass of object and v is final velocity and u is inital velocity and I stands for impulse

[stark panther]

we know v is 5 and m is 0.2 as given in the question

so we need to work out u

[lusty yacht]

what is l anyways

so like this :

$L = 0.2 \cdot (5 - u)$

[lusty yacht]

what is l btw

[stark panther]

yes

but its a capital i

and it just means the change in momentum

[thorny flame]

Newt

[stark panther]

measured in Newtons seconds

[lusty yacht]

i see

i am guessing so L is the 2N /s that we need to prove am i right?

[stark panther]

yeah

so we need to find u which is the velocity the puck is at when the other player intercepts it

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[lusty yacht]

yeah i will retype in here

[lusty yacht]

UPPP

[lusty yacht]

Is the u = 5/2 if yes why?

idk

i just did the step backwards

i have noo basic on physics

I am still grade 9

[stark panther]

i dont think it is

[lusty yacht]

So how to find u

[stark panther]

im pretty sure your gonna need to use calculus

have you done that before

[lusty yacht]

i don't think my brother has given any calculus

i know calculus but i don't think his teacher teach him

[stark panther]

i dont know how else you could work out the value of k without it

becuase that what we need to start finding u

[lusty yacht]

what is k?

[stark panther]

you can use calculs to work out its 1

[lusty yacht]

Or just explain me on calculus maybe i will get another idea

Nyeh ignore it

My brother prob doesn;t understand

i think he's smarter than me because he has learned and idk any lol

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[compact sequoia]

,rccw

[compact sequoia]

Physics problem I solved for time wrong it looks like

Can I have some help figuring out where I messed up?

Nvm I see it 🥲

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[unique quarry]

imagine this as a rectangle

and use pythagoras to find the side corresponding to CD

[hushed hull]

thanks

🙂

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[pale hill]

Im kinda stuck on this

[loud oasis]

what is the question?

[odd pagoda]

find all zeros

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[wispy burrow]

I have no idea on how to solve this

[golden blade]

The velocity vector of your curve r should be just r' and the speed the magnitude of r'

[wispy burrow]

What?

[wispy burrow]

I don't understand what that means

[golden blade]

By r' I mean the derivative of r with respect to t

[wispy burrow]

Are i and j constants?

[golden blade]

No, it's a notation

[wispy burrow]

What do I do with them when finding the derivative?

What is t?

Time?

[thorny flame]

bacc the sigma😔🤞

[wispy burrow]

Why is cos over sin?

Ah

I think I get it

But how do I use that when trying to find the derivative?

[golden blade]

You just differentiate component wise

[thorny flame]

bacc the sigma😔🤞

[wispy burrow]

Okay

[thorny flame]

bacc the sigma😔🤞

[wispy burrow]

I see

[golden blade]

And when you have r' which would be your velocity vector, then the speed of that is the magnitude of r' or also ||r'||.

[golden blade]

https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/mechanics/vectors-main/the-i-j-notation.html

[wispy burrow]

Do you do it like this?

[neon iron]

chain rule

we have 100t not t

also you missed the i hat and the j hat

[wispy burrow]

Idk how to impliment that into this

[neon iron]

d(sin(at)) / dt = cos(at) d(at)/dt=acos(at)

d(cos(at)) / dt = -sin(at) d(at)/dt=-asin(at)

[wispy burrow]

at?

[neon iron]

a is a constant

in this case its 100

t is time

[wispy burrow]

So this is what you wrote?

[wispy burrow]

I see

[neon iron]

absolutely not

[wispy burrow]

Wdym ;-;

[neon iron]

${d(sin(at))}/{dt}$= $cos(at)$ ${d(at)}/{dt}$=$acos(at)$

[wispy burrow]

Yeah?

[thorny flame]

Cnidarian

[neon iron]

ditch this

d(sin(at)) / dt = cos(at) d(at)/dt=acos(at)

whats d(sint)/dt?

[wispy burrow]

I don't know

[neon iron]

,w differentiation rules

[thorny flame]

Results provided by WolframAlpha

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Requested by cnidarian3103

[neon iron]

i wonder if thats the right command

[wispy burrow]

I know this

[neon iron]

okay

d(sinx)/dt = cosx

[wispy burrow]

But Idk how to use it with sine and cos and stuff

[neon iron]

note them down

d(cosx)/dt = -sinx

those will be sufficient for this question

now

try to find d(sin(at)) / dt

||hint : use chain rule ||

[neon iron]

missed the chain rule again

[neon iron]

your this would have been the case if there were no a

but we do have one

[neon iron]

so this would be cos(at) d(at) / dt

[neon iron]

which equals a cos(at)

get it ?

[wispy burrow]

?

[wispy burrow]

I don't

[neon iron]

yes

so

whats d(at) / dt ?

[wispy burrow]

Idk

[neon iron]

whats d(3x)/dx?

[wispy burrow]

Idk what you are asking for, I am sorry

[neon iron]

what is the reslt you get when you differentiate 3x with respect to x ?

are you familiar with the topic of differentiation?

[wispy burrow]

Not really

I hear about it

But I don't get it

[neon iron]

oh

thats where the problem is

1 min

https://www.youtube.com/watch?v=BcOPKQAZcn0

you could also try your organic chem tutor or bprp fast

[wispy burrow]

I'll watch this then

[neon iron]

jee ?

[wispy burrow]

Yeah

Or

Organic chem. Teach.

He's the goat

[neon iron]

they are teaching you magnetic feild before differentiation and laws of motion ?

[wispy burrow]

They expect me to know calculus and trigonometry

But I wasn't taught that in my home country

I need to go to bed

Thank you for your efforts

[neon iron]

you also need to master basic integrations and the concept of integration if you aim to ace JEE physics

[wispy burrow]

Yeah I know ;-;

Wait

Differentiation is derivatives?

[neon iron]

yes

[wispy burrow]

Ah

Alright

See you around

And thank you

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[cinder oxide]

Why Is it du not udx on left side

[mortal steeple]

?

like du / 2x = udx?

[cinder oxide]

It looks like dx being multiplied to both sides

[mortal steeple]

No bro

It's basically du/dx

Then we take dx to the other side and 2x

[cinder oxide]

If we cancel doesn’t that mean multiplication?

[mortal steeple]

We can cancel dx and all

Can you write and show what you are trying to say?

[cinder oxide]

The derivative of u = the derivative of x^2

That’s the first line right

[cinder oxide]

Why isn’t it written du = dx^2 for the first line?

If we start with u = x^2

[mortal steeple]

They skipped it lol

After some time you will start skipping such steps too

[cinder oxide]

Is it more like d(u) = d(x^2) or is this not a function?

[cinder oxide]

Horrible for learning tho

[mortal steeple]

Yeah

I'm gonna say that it's du/dx

[cinder oxide]

Why do teachers skip steps or explaining and expect us to follow

[mortal steeple]

But then they exchange 2x and dx

[cinder oxide]

So derivative on both sides is incorrect? Derivative is not a function? Or it’s written incorrectly as a function?

Argument is correct but function name is not?

[mortal steeple]

It is correct to think like this

But to find out d(x²)

[cinder oxide]

OK

[mortal steeple]

You will need chain rule

Which I'm guessing you haven't done yet

Derivative is a function

[cinder oxide]

Ok

[mortal steeple]

I don't get what your last q is?

[cinder oxide]

I mean should it be d() for the function name of the derivative or something else instead of d

In this context of u sub

[mortal steeple]

?

[cinder oxide]

It feels like they using different notation for left and right side of first line

To say d and dx

[mortal steeple]

dx is the same as d(x)

Mathematicians are just lazy ppl lol

[cinder oxide]

No I mean why not use this d(u) = d(x^2)

[mortal steeple]

They have done exactly that

What else do you think they have done?

[cinder oxide]

They are multiplying dx to right side and not showing work that it’s a function

You gotta do same thing to Lhs and Rhs and show the work to explain to newbies

[mortal steeple]

They are actually not multiplying dx

d(x²) = 2x dx

[cinder oxide]

Oh

That’s the chain rule?

[mortal steeple]

It's done using chain ruke

Rule

Yeah

[cinder oxide]

Two derivatives needed

[mortal steeple]

That's why I was preferring du/dx

[cinder oxide]

One for exponent and then the derivative of that

[mortal steeple]

You know what chain ruke is?

Rule

[cinder oxide]

Kinda

There is a song for it right

To remember it

[mortal steeple]

I don't know about that lol

You know these things might seem hard at first but after some time this will become second nature lol

That is why it's hard for me to understand what your doubt is

I hope you understand too

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[bold parcel]

hello i need some help,
21n^5w^4/21n^4w^2

i did these steps.

1. I divided the numbers first and got 1,
2. Secondly, i subtracted n^5 with n^4 and got n^1
   3.I did 4-2 on the last one

my answer was 1n^1w^2
i got it wrong, did i do anything wrong?

[bold parcel]

anyone avalible to help?

it’s this one

<@&286206848099549185> anyone

[outer delta]

You don't have to put the 1's, it can be just nw^2

otherwise it looks correct

[bold parcel]

ohh thank you so much

i do have one more question

if you can answer

[outer delta]

Sure

[bold parcel]

would this be 8/10?

cause it’s supposedly wrong (according to my teacher)

[outer delta]

Yes, but you can simplify 8/10

[bold parcel]

OH RIGHT

thank you so much for helping me

[outer delta]

No problem

[bold parcel]

see you 😁

.close

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[graceful leaf]

Just to confirm

there are 2 vectors

that will be in the

2nd quadrant??

it feels weird to draw

also

with vectors

I feel like

idk how to draw ax and by properly using tiptail method

like

let me show

,wcw

,wcr

Bro

I mean i guess th epic is clear enoujgh

like for the vector A

I found 2 scenarios

where the ay is - or +

Can i use either? is it proper tip tail method?

Like

as in the second vectors tail must hit the tip of the first vector?

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[hidden cypress]

Im stuck here, can anyone please enlighten me

[modern rock]

cos^2 (θ) = 1/2 (1+cos2θ)

[modern rock]

.

[topaz sinew]

@hidden cypress Has your question been resolved?

[hidden cypress]

for 3cos^2 (θ) does it become 3/2 (1+cos2θ)?

[modern rock]

yes

[hidden cypress]

Up until this point is it correct?

[modern rock]

you didnt pull out 3/2 properly

u missed the 1/3

also this isnt important, but for some reason u changed half of it to x's

[hidden cypress]

So should it be 3/6?

[modern rock]

2/9

[hidden cypress]

Oh yeah i wasn't focused earlier

[hidden cypress]

May i know how? 😭 sorry im so confused rn

[modern rock]

yeah u original had 1/3 but you pulled out 3/2, so you have to multiple 1/3 by 2/3 since 2/3 * 3/2 = 1, thus 1/3 * 2/3 = 2/9

[hidden cypress]

Where did 2/3 came from? Omg sorry im so slow

[topaz sinew]

@hidden cypress Has your question been resolved?

[hidden cypress]

.

[hidden cypress]

Ohhhh i just get it

Thankyou so much

.close

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[topaz sinew]

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[leaden jungle]

I just wanna double check but

[leaden jungle]

the only true statement here of this list would be

the last one right? im just a bit anxious about "the graph rises to the left and falls to the right"

which is.. true kinda but it rises again to the left then falls to the right

so the wording is kinda risky for me

[elfin sparrow]

The wording is a bit informal, but I'd say that it's true. It seems like they're just talking about the end behavior

[bold parcel]

yes the y intercept is 0,0

[leaden jungle]

okay so im completing the square right now but I ran into this

Am I right so far? I'm worried about the -1^2

Can't I make it a 1

[topaz sinew]

@leaden jungle Has your question been resolved?

[leaden jungle]

Okay I think I did it

But I'd appreciate some proof checking because completing the square makes me nervous

please png me if i dont respond

i think i got it right

.close

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[karmic cloak]

Could somebody explain why it would be cm cubed

[karmic cloak]

I have a quiz tommrow and I think I’ll just remeber more in context

[alpine mist]

,rccw

[alpine mist]

volume is (unit)^3
like area is (unit)^2

[topaz sinew]

@karmic cloak Has your question been resolved?

[topaz sinew]

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[ivory sorrel]

Trying to determine of this is a vector space

[whole geode]

Have you tried showing the axioms hold yet?

[ivory sorrel]

$((a+b)f)(x)= f((a+b)x)$. Which isn't necessarily equal to $f(ax)+f(bx)$.

[thorny flame]

Veni, vidi, perii is not f(wai)

[ivory sorrel]

It is thus not. a vector space

[whole geode]

Looks reasonable to me

Fails distribution

[ivory sorrel]

Thanks!

My intution tells me this isn't a VS

but P sure I'm going wrong somewhere

[whole geode]

On the contrary, this seems to me like an obvious vector space

Why do you think it might not be?

[ivory sorrel]

Wait

Yeah

Okay

[ivory sorrel]

Idk, just didn't feel like one

[whole geode]

Fair enough! They aren't always obvious to everyone

That's what we have axioms for

[ivory sorrel]

Thanks

.close

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[loud oasis]

a subset of R^n is subspace generally if its restriction is in the form of a (some linear combination of the entries) = 0 [possibly multiple equations like this]. similar things can be said of matrix subspaces

[topaz sinew]

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[arctic sundial]

Haven’t been taught this and instructions were to teach ourselves this section

But I’m lost

[leaden hatch]

set it up like a long division problem back in grade school

[arctic sundial]

X+3 on outside?

[leaden hatch]

yea

[agile harness]

outside the house

[leaden hatch]

and polynomial on the inside

[arctic sundial]

Got it what’s next step

[leaden hatch]

what do u have to multiply (x+3) by to get an x^2 term

[arctic sundial]

-?

[leaden hatch]

i explained that kinda poorly

so u multiply (x+3) by x to get x^2 + 3x

[arctic sundial]

So the first Leg is X

Right

[leaden hatch]

ur just tryna get the leading terms to match

[arctic sundial]

So X is the first number right

[leaden hatch]

yea it's the first part of the answer

[arctic sundial]

It will always be X

[leaden hatch]

no

it is in this particular example tho

[arctic sundial]

If it’s X+_ and X^_

It will always be X

[leaden hatch]

what does that mean

[arctic sundial]

Nvm

So we have X

What’s next

[leaden hatch]

bring down the 31

get the leading terms to match

[arctic sundial]

Idk all that

So wdym bring down 31

[leaden hatch]

so what do u multiply the divisor by to get 8x as a leading term

[arctic sundial]

What bro

Where did -X^2+3x come from

[agile harness]

x(x+3)

then subtract

it’s how we perform long division

[arctic sundial]

Why’s it a negative tho

And why is it 0 and not blank

If X^2-X^2 cancels out

@leaden hatch @agile harness

How’s bottom wrong

[agile harness]

if it divided evenly then the remainder is zero

[leaden hatch]

remainder is 7

calculation error?

[agile harness]

or that

,w (x^2 + 11x + 31)/(x+3)

[thorny flame]

Results provided by WolframAlpha

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Requested by c.knief

[agile harness]

so annoying

[arctic sundial]

How if it’s X+8

And that was correct

[agile harness]

remainder is 7 though

[arctic sundial]

How if it’s X+8

[agile harness]

quotient + remainder

you had the quotient part

[arctic sundial]

How do I find reminder then

[agile harness]

$\frac{f(x)}{g(x)} = q(x) + \frac{r(x)}{g(x)}$

[thorny flame]

knief

[agile harness]

q is quotient

r is remainder

[arctic sundial]

How do I find it tho?

With what I have

[agile harness]

the long division results in this form

[arctic sundial]

I’m so lost

Ik how to find the quotient

What’s next

For remainder

[agile harness]

notice here

[arctic sundial]

What do I plug in where

[agile harness]

the next step would be to put +
8 in the quotient because 8x/x = 8

then you multiply the divisor by 8 and subtract

you’ll get (8x+31)-(8x+24)

which is 7

notice

x doesn’t go into 7

so the remainder is 7

[arctic sundial]

Where did 8x+24 come from

[agile harness]

i multiplied the (x+3) by 8

i recommend you watch khan academy

or organic chemistry tutor or something