help-10

[obtuse pebble]

@royal copper Has your question been resolved?

[hazy marlin]

huh? which angle exactly?

looks like you've found all the angles already ?

how do you find any angle ?

usually angles add up to something
so you simply add or subtract

well the total angle of the x axis is 180, since the x axis is a line, and therefore a flat angle

why would it have to be perpendicular ?

if the total angle of the x axis is 180 degrees, and 136 of those degrees are subtracted
what is the remaining degree then ?

exactly

well

in physics

well in general

you're entitled to define your own axis

and it's direction

so you can TAKE 100N to be along the x axis

you can define your point of reference, always

but no matter how you choose to define it, the angle between the forces is always gonna be 136

I think I understand where your confusion stems from

the 100N force was simply taken to represent the direction of the x axis, which is, in terms of angles, a single line

if we position the x axis such as it's along the 100N vector, it means the degree between F1(100n vector) and x Axis is 0
the degree between F1 and F2(140N vector) is 136 since it's a given
and 44 degrees is simply the complementary angle to the x axis

yea

because the y axis is defined to be perpendicular to the x axis

[obtuse pebble]

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[timid silo]

I’ve been trying to solve this but I can’t

[timid silo]

Because you always take x + 4 - 4 to get rid of it and you stay with x left and then you do the same on the other side

But this is more harder than the easy one

I don’t understand what to do

<@&286206848099549185>

[obsidian isle]

Just add 7,2 to both sides

Then subtract 4

[timid silo]

Can you show me how you would solve this in a picture?

I won’t understand like this

[tardy epoch]

i don't know how to draw a picture for this, but maybe you can draw your own picture from the steps

[copper latch]

, is just decimal

[tardy epoch]

x + 4 - 7.2 = x + (4-7.2) = x + (-3.2) = x - 3.2

[timid silo]

Ok

WHAT

How

[tardy epoch]

x - 3.2 = 1.8

[copper latch]

Bruhhhh

[tardy epoch]

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-of-operations/v/more-complicated-order-of-operations-example#:~:text=The order of operations is,(from left to right).

[timid silo]

I don’t understand

[balmy mortar]

Ok step 1

add 7,2 to both sides

x+4 - 7,2 + 7,2 = 1,8 + 7,2

[timid silo]

But why do I do that?

Do get it away?

[balmy mortar]

because

-7,2 + 7,2 = 0

They cancel.

[timid silo]

Ok

Yeah

[balmy mortar]

x+4 + 0 = 1,8 + 7,2

ok?

x+4 = 1,8 + 7,2

Now this looks simpler.

[timid silo]

He

[balmy mortar]

You can work out what 1,8 + 7,2 is to simplify the right.

[timid silo]

Yes

9

I think

[obtuse pebble]

@timid silo Has your question been resolved?

[uncut yoke]

hey do you still need help

[obtuse pebble]

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[eternal anvil]

I'm not so sure how to get the antiderivative of this equation.
I thought you had to do this:

f(x) = (2x+1)/(x^4+2x^3+x^2)
f(x) = (2x+1) * (x^4+2x^3+x^2)^-1`
But I have no clue how to proceed (if this even is the right way to approach this problem)

[eternal anvil]

(Sorry for the lack of sub/superscripts. I'm not sure how to use those in Discord)

[balmy mortar]

partial fractions

and also quickly check -1/2 isn't a root of the bottom

[eternal anvil]

Oh I see. I have never solved integrations by partial fractions before so I'll have to study the theory first. Thanks for pointing it out.

.close

[obtuse pebble]

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[timid silo]

I gotta solve this

Ik it's pretty easy but I didn't listen to my teacher

[lavish socket]

try to see what it looks like

[timid silo]

Basically I have to find a when x is any possible number

[lavish socket]

what does it remind you of?

[timid silo]

WdymM

?

[lavish socket]

do +1 -1, try to bring it to (x+1)^2 form

[true rain]

You have to solve for a?

Or solve for x

[balmy mortar]

complete the square

[timid silo]

Like it's hard for me to translate

Idk math language in English

Basically I have to find a when x is any possible number

[lavish socket]

yeah, so complete the square and simplify the inequality

[timid silo]

It's not square

It's parabola

[sage geode]

You don't know what completing the square means?

[timid silo]

since that function don't intercept x-axis and is always above x-axis(from coeff. of x^2>0)
its discriminant must be less than 0

No I don't sorry

[timid silo]

Ye

so find its discriminant and make it less than 0
you'll get the interval of a

[sage geode]

For example in this case you what you could do is
x^2 + 2x + a > 0
x^2 + 2x + 1 + a > 1
(x + 1)^2 > 1 - a

Or you could do that yeah

[timid silo]

no they just need interval of 'a' where domain is all real

Ok one sec

[sage geode]

In both of the methods the answer depends on the sign of 1 - a

[timid silo]

I can't find discriminant

I feel so dumb

I used to do this easily wth

uhh then you can refer to what beans said
(x+1)^2 > 1-a
lowest value of (x+1)^2 = 0 which is greater than 1-a
so
0 >1-a

btw discriminant for ax^2+bx+c
is b^2-4ac
compare that with this

[timid silo]

Ik that

then what's the problem?

Idk i think I'm just tired

But I got homework to do so

Wait.can you help me with one more thinf

x^2-3px+p^2-9=0

I have to find p

When

One of the idk if I'm saying it right but in my language it's called root

So if one of the root is negative and other is 0

[sage geode]

When there's just 1 root?

Oh

You could use quadratic equation for that one

Or

You could first make p^2 - 9 = 0

[timid silo]

use vieta's

[sage geode]

So that x = 0 is a root

[timid silo]

Can u show me quadric equation cuz idk what that means in english

Oh u mean discriminant?

[timid silo]

Yea yeah I get it now

B is 3p right?

b is -3p

Ye forgot to put -

So d is what?

I got -9p - 36

you can solve this question easily if you know that:
sum of roots = -(coefficient of x)
product of roots = constant term

since they just mentioned that the other root is negative and nothing more

It is 0 too

One of the root

And one is negative

yes that'll give you 2 values of p you need other root to eliminate one of p

so
sum of roots = 0+negative = negative
and as I mentioned above its equal to -(coefficient of x)
which means - (-3p)

so
negative root = -(-3p) = 3p
from this you can conclude that p is negative ___(2)

and
product of roots = constant = p^2-9 ___(1)
since one root is 0 product of roots =0

Oh

So

can you solve for 'p' from (1) and (2) I labeled as above

Damn this is so hard for me

its not just look at this picture

for us here p = 0 and q = negative root

a = 1, b = -3p and c = p^2-9

what?

Wait nothing one min

ohh sorry the p in image is different from p we're finding

Ok I wrote it down

How do I find every possible equation for p now

you just need 2
one you get when you put x =0 in the original equation
another by vieta (sum of roots)

So that's all?

yes then find 'p' that satisfies both equations
that's the answer

Ok

Thank you

So much

I'm just gonna practice equation and systems now

yes that's best way to get things

Laziness is killing me tho

.close

[obtuse pebble]

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[wispy bobcat]

not schoolwork btw

[spiral maple]

what have you tried?

[wispy bobcat]

what do you mean?

[spiral maple]

I mean... what have you tried in order to solve the problem?

[wispy bobcat]

the elimination method

[spiral maple]

ok, and what did you get from that...?

[wispy bobcat]

nvm i did it myself ty fr the help 😶

[tardy epoch]

feel free to .close

[obtuse pebble]

@wispy bobcat Has your question been resolved?

[obtuse pebble]

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[rotund pecan]

mY ANSWER WAS

4 Integral sign to 10

x^3

It was marked incorrect

Not sure why

[raven spire]

$\int_4^{10} x^3 \dd{x}$?

[warm shale]

Ansh

[raven spire]

I can't see what else could be wrong except for you missing out the "dx" part

[obtuse pebble]

@rotund pecan Has your question been resolved?

[obtuse pebble]

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[timid silo]

Could someone help me step by step for the long division please?

[timid silo]

not sure what Idid wrong

[haughty elm]

i can tell you that at the very least, you missed an exponent in this line near the beginning

and of course that has to carry through the rest of your division

[timid silo]

thanks, 1 sec

@haughty elm not sure what happened but uhh

[haughty elm]

hmm

[timid silo]

so umm

[silk galleon]

verif: $x^3 = (x^2 + 16x + 63)(x - 16) + 193x + 1008$

[warm shale]

xdk1235

[timid silo]

why 16?

[obtuse pebble]

@timid silo Has your question been resolved?

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[warm inlet]

How do I find the height of a point along the normal distribution curve

[spiral maple]

plug it into the density.

like any other function

[warm inlet]

What do I plug in?

How many standard deviations it is from the mean?

[spiral maple]

whatever the x value is

sure if you have a standard N(0,1)

[warm inlet]

Yeahhhh I gotchu. Thanks my guy have a good day/night/whatever

.close

[obtuse pebble]

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[frozen burrow]

Can someone help me understand this

[obtuse pebble]

@frozen burrow Has your question been resolved?

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[rose mesa]

So I was wondering what the motion of the car is I’m confused on what it is asking and ho to answer it

[rose mesa]

I’m not in a test rn it’s just homework

[spiral maple]

when you turn, do you accelerate?

[rose mesa]

If you turn you would decelerate right?

[spiral maple]

decelerate isn't a thing

you accelerate forward or backwards

[rose mesa]

Then it would accelerate backwards

[spiral maple]

Not quite backwards, but yes

there's a change in velocity so there's acceleration

[rose mesa]

So I would put it is accelerating?

Wait

Wow

Thank you a lot

[spiral maple]

it's accelerating as it turns, then comment on the speed and velocity on the straight bits

[rose mesa]

K thanks

How do I close to is

This

[spiral maple]

.close

[rose mesa]

.close

[obtuse pebble]

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[subtle jasper]

Im not sure why you can do this

[silk galleon]

that is the definition of |a+bi|

[subtle jasper]

like would this not work if it was abs(x + y) ?

[vast wren]

z=x+yi is a complex number

oh wait

you’re asking

why we can go from

abs((x-1)+yi)=2

to sqrt((x-1)^2+y^2)=2

[subtle jasper]

yeah

[spiral maple]

again, definition of |z|

[vast wren]

^

[subtle jasper]

ohhh right i remember thanks

.close

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[sterile tusk]

i am struggling with 36 a

,rotate

I got close to the same answer but instead of (60 - t) - (60 - t)^3 /3600

I got a positive so (60 - t) + (60 - t)^3 /3600

so it must be an issue with the integral on the right hand side that is Q(x) * I(x) (I(x) being the integrating factor for linear differential equation)

,rotate

[balmy mortar]

w(0) = 60
s(0) = 0
w'(t) = -1
s'(t) = 2 - 3s(t)/w(t)

Is this right?

[sterile tusk]

I know that y(0) = 60 from the question

But I’m not sure what the function s(x) is for

Oh

U sub

[balmy mortar]

water, salt

w(t) = -t + 60
s'(t) = 2 - 3s(t) / (60 - t)

[sterile tusk]

Yeah

That’s the differential equation

I have to solve for y

[balmy mortar]

(60 - t) s' + 3s - 2 = 0

(60 - x) y' + 3y - 2 = 0

separable i hope

(60 - x) y' = 2 - 3y

kk

[sterile tusk]

Actually I think it needs to be linear

It’s mixing problems using linear differential equations

[balmy mortar]

1/(2 - 3y) dy = 1/(60-x) dx

Don't think you need integrating factor here

it's separable?

int 1/(2 - 3y) dy = int 1/(60-x) dx

(-1/3)int -3/(2 - 3y) dy = -int -1/(60-x) dx

[sterile tusk]

I think we should the chapter is called linear first order equations

Chapter 1.4 was separable

[balmy mortar]

???

[sterile tusk]

1.5 is linear

[balmy mortar]

But I mean unless i fcked up

its separable

which means theres no reason to bother using integrating factor

(-1/3)ln |2 - 3y| = -ln |60 - x| + C

|2 - 3y|^(-1/3) = A|60 - x|^-1

y(0) = 0

|2 - 3y|^(1/3) = A|60 - x|

|2 - 3y| = A|60 - x|^3

y(0) = 0

|2| = A|60|^3

|2 - 3y| = 2|60 - x|^3 / 60^3

D:

probably mistake by me somewhere

ah i see it

rip

[sterile tusk]

i think in that case it is linear or at least thats how the textbook wants me to solve but i am not that good at solving these

my answer is close but

instead of -(60 - t)^3 I got + (60 - t)^3

idk why it is a negative i tried integrating the right hand side of the equality that has the integral of Q(x) I(x) and got a positive number

wait i think this means that the constant would be C = -1/3600 instead of +1/3600

,rotate

[balmy mortar]

ok i got it

your workings so squashed D:

https://i.imgur.com/0Q4hvyK.png

The error might be here?

There should be a minus sign ?

The power ^-3 should bring a minus sign outside

@sterile tusk

[sterile tusk]

if i did the integral though the -t also has a negative

[balmy mortar]

in that case

it should be the sign of your C?

0 = 60 + 60^3C

You should get C negative

[sterile tusk]

This was my attempt at that integral

,rotate

[sterile tusk]

I don’t understand how to get it to be negative since there is a - from the u sub and a negative after taking the anti derivative

[balmy mortar]

its the sign of your C

C has to be negative.

[sterile tusk]

Ohh

Actually I’m not sure how to solve for C now even though I did it already

,rotate

[sterile tusk]

I’m missing something but idk what

[obtuse pebble]

@sterile tusk Has your question been resolved?

[sterile tusk]

<@&286206848099549185>

[balmy mortar]

why are u multiplying that out

just write it as 60^3

how the heck do you get 60 on both sides

y(0) = 0 salt

[sterile tusk]

I got 60 on both sides using this formula we got solving for y

,rotate

[balmy mortar]

y(0) = 0

its salt

not water.

[sterile tusk]

Oh

Ah I got it now

Thanks

.close

[obtuse pebble]

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[sly bridge]

Find all roots for polynomial and write from least to greatest: x⁴=256

[brittle swan]

256 = 4⁴

[sly bridge]

I'm getting response that's not the answer.

Already tried -4 and 4

[distant raft]

complex roots?

[obsidian isle]

There is no total order on C

[balmy mortar]

Maybe prime factorise 256

[brittle swan]

i suppose you’re solving for real roots? since you want to compare the roots

[brittle swan]

this helps

lol

[obsidian isle]

This question has a flawed premise

[balmy mortar]

oh we have the answer

[sly bridge]

i suppose you’re solving for real roots? since you want to compare the roots
@brittle swan yes

[balmy mortar]

hell does it want

-4, -4, 4, 4 ???

cus thats just wrong

[zenith dove]

do you mean factors?

[obsidian isle]

4i > -4i

Hahaha

[haughty elm]

please order complex numbers hmm yes

[mental solstice]

no partial orders thanks hahaha

[balmy mortar]

order them by argument

4, 4i, -4, -4i

[brittle swan]

lmao

[balmy mortar]

,w x^4 = 256

[warm shale]

Results provided by WolframAlpha

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

Requested by Shuri2060#9525

[sly bridge]

The answer should be real roots or zeros.

[balmy mortar]

-2^2, 2^2

[obsidian isle]

The lexicographic order of C is left to right top to bottom

I think

Or bottom to top actually

[balmy mortar]

try 4, -4

least characters to greatest.

[obsidian isle]

Can you screenshot what it looks like

The input field

[mental solstice]

separated by comma, or separated by no spaces?

cause if it's comma no spaces, it's gonna be -4,4
...or it should be

if we ignore complex roots

[haughty elm]

its algebra 2 so I guess no complex shenanigans are involved

?

[sly bridge]

Has to be separated by commas and no spaces in between

its algebra 2 so I guess no complex shenanigans are involved
@haughty elm correct

#help-10

Correct answer @everyone

Thx for help. @close

#close

[obtuse pebble]

@sly bridge Has your question been resolved?

[sly bridge]

Yes

[obtuse pebble]

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[valid oracle]

Not sure which answer is correct to the problem

2 different answers

[high arrow]

$4,351.14 in interest definitely sounds like pain

[valid oracle]

lol

Think he meant pay

Do you know which one is right

[obtuse pebble]

@valid oracle Has your question been resolved?

[obtuse pebble]

@valid oracle Has your question been resolved?

[obtuse pebble]

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[fringe pollen]

I am actually a beginner right now, and in 10th grade from India , I can solve 40-50% of the NT , Quadratics, Trigno , Inequalities and Summations from AOPS vol 1 . Can someone suggest me how to get started and what are the best resources+ any other source for questions other than AOPS?

[frank shell]

hi

i would like to help you

[fringe pollen]

@raven spire here

[frank shell]

may i?

[fringe pollen]

Sure

Please

[frank shell]

okay but like i will help you pinging other ppl

[fringe pollen]

Well will they be annoyed?

😅

@frank shell sir?

[raven spire]

Hmm

tbf, starting with Excursion in Mathematics, and Pearson Pathfinder would be for the best

[fringe pollen]

Oh I didn't knew about those

Are they beginner friendly?

Like what are the pre requisites?

@raven spire sir?

[raven spire]

Yeah

they're absolutely beginner friendly

[fringe pollen]

Oh great

Thanks for the help

[raven spire]

Note: since you might be used to the routine maths, the sudden change into non-routine math would be a bit difficult to grasp

[fringe pollen]

Oh

Well wdym by routine maths?

[raven spire]

Like, uhh... what you're taught in school

[fringe pollen]

Yeah well that transition, I've already gone through that

Preparing for JEE

[raven spire]

And you're in class 10 rn?

[fringe pollen]

Yep

[raven spire]

decent

[fringe pollen]

I started jee coaching from 10th

[raven spire]

Hmm

[fringe pollen]

Yep

[raven spire]

Good luck! Note that no textbook is 100% beginner friendly btw..

[fringe pollen]

Ok

Thanks

[raven spire]

both excursion and pathfinder were my first reference choice because of how vastly they covered each topic plus the basic thinking of everything... But the motive was mainly to adapt to getting familiar with the question patterns, and to get flexible with your thinking process

👍

[fringe pollen]

Oh sounds cool

Thanks again for the help

.close

[obtuse pebble]

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[obtuse pebble]

@wanton dagger Has your question been resolved?

[royal basin]

@wanton dagger do you still need help with this?

do you perhaps already have an answer but aren't sure whether you got it right?

[obtuse pebble]

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[worn shard]

say i have
a = ±b
since saying is basically the same as saying
a = ∓b
does that mean i have
a = ±b = ∓b
or
±b = ∓b?

[worn shard]

from what i know writing
±b = ∓b
isn't right since then i'll have
b = -b or -b = b

[sage geode]

They aren't the same thing

Unless b is 0

[worn shard]

but i believe i can write
a = ±b
as
a = ∓b

[sage geode]

Yes you can

But not in the same line

[worn shard]

but can i substitute a?

[worn shard]

i don't understand why not

[sage geode]

You found the contradiction yourself

±b = ∓b is wrong

[worn shard]

good point

but still, i just don't get it for some reason

cause if they're equal then i should be able to substitute them

a=b
b=c
a=c

[sage geode]

Because those symbols mean different things when they're together

But if they're separated

Then there's no trouble

[worn shard]

so i can't apply the transitive property of equality then?

[sage geode]

Not really, due to how ± and ∓ are defined/used

[worn shard]

but that doesn't show that the transitive property is wrong?

[sage geode]

Yeah because when you write a = ±b, you're saying (a = b) or (a = -b)

Which isn't really just one statement

[worn shard]

i see

and a = ∓b means (a =-b) or (a = b) which is the same thing as (a = b) or (a = -b)

i'm sorry but i thought i almost got it

it's a straight forward idea but i can't seem to accept it since it's breaking the transitive property

[sage geode]

Yeah, S or Q is the same as Q or S

[worn shard]

is there a way of thinking about this that won't like break that property?

[sage geode]

I don't think you'll come across the same mistake in problem solving

[worn shard]

i hope so

so like to sum things up, ± and ∓ have the same meaning when only one of them is used in an equation but different meaning when they're both in the equation

hence, breaking the transitive property because the definition has changed

[sage geode]

Yeah kinda

[worn shard]

i appreciate that

.close

[obtuse pebble]

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[stone vigil]

Had this question on my math test, does the answer seem correct?

[stone vigil]

I translated the problem so ask if I need to clarify something

[raven spire]

Yes it does seem correct. Although you could've used a calculator to verify on your own..

Did you have any issues regarding any steps?

[stone vigil]

Ah im dumb. Actually this answer came pretty naturally so no further questions, thanks.

.close

[obtuse pebble]

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[rain mirage]

P = the amount of money spent by a person in one year

I'm not completely sure if this is a discrete or continuous random variable, but I lean more on it being discrete. Anyone wanna help me out?

[obtuse pebble]

@rain mirage Has your question been resolved?

[hazy marlin]

do you have more context ?

without any context it could be anything

i suppose it most likely represents a parameter but ...

[obtuse pebble]

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[heady fiber]

pls help me in this

<@&286206848099549185>

[sage geode]

The digit in the tens place of a two-digit number is three times that in the units place, so the first digit of the number is 3 times bigger than the 2nd one, right?

[heady fiber]

yes

[sage geode]

So if we had 10a + b, then a = 3b

[heady fiber]

ahh

ic

am in 8th

going to 9th

[sage geode]

Now if the digits are reversed, then the number becomes 10b + a

And the question says that this number is 36 less than the original number

[heady fiber]

ye

[sage geode]

So 10b + a + 35 = 10a + b

Here you can collect the similar terms

To get that 9b + 35 = 9a

So we're given two equations

a = 3b
9b + 35 = 9a

Here you can substitute 3b instead of a into the 2nd equation and then solve for b

And then, knowing the value of b, you can solve for a as well

[heady fiber]

ahh thnx

i already solved tho but thnx and thnx

.close

[obtuse pebble]

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[glass igloo]

https://cdn.discordapp.com/attachments/887295239914684437/938033844014166026/unknown.png

It says that a reflection moves a point perpendicularly so that the image is the same distance from the line as the preimage

what happens if it does not move perpendicularly? would the distance not be the same? you could definitely make it so that the distance is the same even without it moving perpendicularly (but then it wouldn't be reflection, but you know)

[balmy mortar]

Perhaps demonstrate what you mean with a sketch

[obtuse pebble]

@glass igloo Has your question been resolved?

[obtuse pebble]

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[glass igloo]

.reopen

[obtuse pebble]

✅

[glass igloo]

As you can see in the picture that I sent, it says that in order for the image to be the same distance from the line as the preimage, a reflection has to move a point perpendicularly(and we can see that happening in the image)

but if we don't do it perpendicularly, as in..

L and L`

i know that this wouldn't be a reflection anymore

but it would still maintain distances if we do it correctly, right?

the distance from L to the line of reflection can be the same as the distance from L prime to the line of reflection

I basically did not understand why they phrased it the way they did

" a reflection moves a point perpendicularly so that the image is the same distance from the line as the preimage"

they phrased it in a way so that it basically says "If you don't do it perpendicularly, the distances wouldn't be the same"

[high lily]

if you don't do it perpendicularly, you won't get a reflection

[obtuse pebble]

@glass igloo Has your question been resolved?

[obtuse pebble]

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[glass igloo]

.reopen

[obtuse pebble]

✅

[glass igloo]

Yeah, I understand that.

I was just confused by the way they phrased the statement.

because they phrased it as like you can't get the same distance from L to the reflection line as the distance from L prime to the reflection line if you don't do it perpendicularly

[high lily]

if you move perpendicularly and the distance is the same, you get a reflection

is pretty much what its saying

[obtuse pebble]

@glass igloo Has your question been resolved?

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[deft cipher]

I didn't understood that how did they did "3X2X2X2", in my opinion it should be "3^4", am I wrong somewhere in thinking so?

[balmy mortar]

You have not considered condition (ii)

[obtuse pebble]

@deft cipher Has your question been resolved?

[deft cipher]

Oh, yes, I thought to solve for the two conditions separately, thanks

[obtuse pebble]

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[river storm]

Idk what I've done wrong but I can't prove true for n=k+1

It's supposed to be rearranged to k+1/2k+3

[brave bramble]

After "show true for n = k + 1"
You're putting k into the Σ, which is no good. That's r in there, not n.

Wait, you maybe saw that already haha

Yeah okay the mistake is fixed below.

[river storm]

Yeah I noticed lol

The bottom statement looks true

But if I try to get just k+3 as denominator I can't

[novel knoll]

Put the two terms on common denominator

[river storm]

I got to 1+k(2k+3)/(2k+1)(2k+3)

But I can't just cancel because of the 1

Can I?

No

I tried expanding but I just get a +1 term so there's no other factor

To cancel

[obtuse pebble]

@river storm Has your question been resolved?

[obtuse pebble]

@river storm Has your question been resolved?

[obtuse pebble]

@river storm Has your question been resolved?

[brave bramble]

@river storm
Simplify then factor numerator

[river storm]

But it doesn't give me the expression I need

[hazy marlin]

looks like a telescoping series

@river storm it also works amazingly lol

do you still need help ?

[river storm]

Yeah

[hazy marlin]

Okay

so basically yea
that's a telescoping series

heard of those ?

[river storm]

Nah we're just doing proof by induction

[hazy marlin]

Oh

damn

I didn't see it required induction

I missed that
you can prove it without tho

hmmm

aight

@river storm are you familiar with partial fractions ?

[hybrid gull]

#❓how-to-get-help

[obtuse pebble]

@river storm Has your question been resolved?

[brave bramble]

I agree with this. Then:
(2k² + 3k + 1) / (2k + 1)(2k + 3)
= (k + 1) / (2k + 3)

Which is the form we want.

[river storm]

I didn't realize that the numerator was divisible by 2k+1

Thanks, I got to the very end and didn't even think about trying to simplify

[obtuse pebble]

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[wooden jay]

If cos (x+180) = a what is cos x

[granite thorn]

cos(x)=-cos(x+180) so cos(x)=-a

[wooden jay]

oh yeah im so stupid

thanks

[gilded needle]

Unless it's a trick question and they mean 180 radians. 😁

[wooden jay]

nah dw i was being retarded

.close

[obtuse pebble]

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[fickle cave]

I understand it's 9 sin

but what do I put in the box?

[short spruce]

sin(9) is a number

so not that

[fickle cave]

oh

y=9sinx

[short spruce]

yep

[fickle cave]

so I put that in the box?

[short spruce]

yes

[fickle cave]

thanks disappointing son

what about this 1?

[vague tundra]

Has anyone done mensuration?

[fickle cave]

wrong chat

this is mine boi

[vague tundra]

Which then?

[fickle cave]

lol

look at the math help (available)

not the math help (occupied)

[vague tundra]

Oh my bad am sorry I literally just joined

[fickle cave]

ik I did the same

lol

[vague tundra]

ty tho!

[hazy marlin]

@vague tundra #❓how-to-get-help

[fickle cave]

ayy my boi

Demarkus

I mean Deus

can you help me

[vague tundra]

Thanks

[short spruce]

why'd you select cos(x)

as your parent function

[fickle cave]

cuz the highest points

forgot the name of it is called

termastat or something lol

the math term of it

[short spruce]

cos(x) doesn't pass through the origin

[hazy marlin]

oh snap did I help you inthe past ?

[fickle cave]

naw lol

[fickle cave]

So I write 0?

[short spruce]

huh no

you have the sin(x) function filled out correctly

you just selected the cos(x) function for some reason lol

[fickle cave]

alr lemme think

yeh I got no clue

cuz cos wouldn't start from origin

[short spruce]

right...

so possibly your other answer that is already correct is right lol

[fickle cave]

so I put 1.5 again?

1.5 and 1.5?

[short spruce]

no

[fickle cave]

X_X

eh

[short spruce]

it tells you to select the correct function

only one of those is gonna be right lol

[fickle cave]

ohhhhh

ok ok

omg lol

what a tricky sneaky question

that was bs

[short spruce]

indeed

lol

[fickle cave]

.close

[obtuse pebble]

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[meager belfry]

since H_t must be a vector space, does t=0?

since the 0 vector must be within a vector space

and does that imply that s must remain a constant, since the vector that results from the subtraction of two points in an affine space must be contained within its tangent space?

[balmy mortar]

H_t isn't a vector space in general

H_t is an affine space

?

Or am I misinterpreting notation

<x, y, z> is just a normal vector or not

[meager belfry]

H_t is the tangent space and H_s is the affine space I think

and yea it's a normal vector

[balmy mortar]

I don't understand what tangent space means in this context then

[meager belfry]

For us it was just defined as

[balmy mortar]

Geometrically, isn't H_t flat?

[meager belfry]

Subtraction of two points in H_s will result in a vector in H_t

and adding a point in H_s with a vector in H_t will result in a point in H_s

[balmy mortar]

ohhhhhh ok I get it.

Then yes the tangent space is a vector space

In particular

Think about a general plane in 3D space.

the equation is

x.n = a.n = D

Do you recognise this?

[meager belfry]

What does the . represent?

[balmy mortar]

dot product

[meager belfry]

No, not really if I'm being honest I don't think we've introduced the dot product in the class yet

[balmy mortar]

This is university/college stuff or not?

[meager belfry]

Yes but it's an intro class

[balmy mortar]

Did you not see plane equations in high school

cartesian equations?

[meager belfry]

Yea

[balmy mortar]

ax + by + cz = D

[meager belfry]

Ok got it yea

[balmy mortar]

But in vectors, you haven't seen dot product?

[meager belfry]

Is that the inner product?

[balmy mortar]

That's kinda odd

yes

[meager belfry]

Ok yes

[balmy mortar]

ax + by + cz = D

(a b c) . (x y z) = D

if I write those vectors as columns

you can see?

[meager belfry]

Yes

[balmy mortar]

x.n = a.n = D

So we have this form

The (a b c)

is n

[meager belfry]

got it

[balmy mortar]

For one sec, lets think if D = 0

x.n = 0

This means variable x is orthogonal to n

[distant raft]

yea

[balmy mortar]

Your plane is all vectors perpendicular to n

[distant raft]

sorry I got off my phone I'm here now

[balmy mortar]

So if D = 0, it turns out n is the normal vector to the plane

ok

That make sense so far?

[distant raft]

So what does this have to do with affine space and the tangent space exactly?

yea I do get it so far

[balmy mortar]

Because I think it's v. related

In this case uhh

I'm pretty sure you have a plane, do you not?

[distant raft]

yea

since the z is constant

[balmy mortar]

Right

So for a shifted plane

x.n = a.n = D

You are shifting the plane by vector a

If n is a unit normal vector

And D = a.n

So actually, I think H_s will be the shifted plane. H_t will be the unshifted plane

So back to this, H_s in general is the plane parallel to the xy-plane, s away from the origin

[distant raft]

Sure

[balmy mortar]

t is the plane at the origin

And I think Hs and Ht have to be parallel

[distant raft]

Aren't they already parallel

[balmy mortar]

yh I guess lol

[distant raft]

since we define H_s and H_t with constant z

[balmy mortar]

So t = 0 is a must

[distant raft]

and s = any element of R

[balmy mortar]

Yh

thats what I figured

[distant raft]

is H_t just displacing it up and down then?

[balmy mortar]

(but am slightly confused by that)

It's a bit strange they ask about values of s if it turns out it can be anything

[distant raft]

thanks shuri

[balmy mortar]

👌

I agree with your answer

[distant raft]

Yea I was kinda confused since it seemed like the problem was too simple? idk

[balmy mortar]

yh I didnt realise it was just parallel to xy-plane

until I reread

[meager belfry]

.close

[obtuse pebble]

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[timid silo]

im in calculus 12

[timid silo]

I dont know how to factor (a-b)^5 + 4(b-a)^3

its doomed

[short spruce]

consider the fact that b-a=-(a-b)

[timid silo]

but wtf do i do with the 4

[short spruce]

that's ambiguous

[timid silo]

so is it just like

-3(a-b)^3 and a (a-b)^2

and the 4 is just like

chillin

[short spruce]

where did you get -3 from

[timid silo]

you can split the 5th power to a 2nd and a 3rd power right?

and since mr (b-a) is a naughty negative man

naaaaaaaaaaaah

nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[short spruce]

i still don't know where the -3 came from

[timid silo]

is it just
(a-b)^5 - 4(a-b)^3

im gonna be a very sad boy if it is

no x-box this week

[short spruce]

i mean that's how you'd rewrite it, yeah, but that's not fully factored

[timid silo]

do i have to

expand this

because if i do its a skip

[short spruce]

you don't have to expand anything that isn't easy, no

[timid silo]

common factor (a-b)^3 right

[short spruce]

yep

[timid silo]

calculus is doomed

its doomed

[short spruce]

you don't actually have to expand anything

[timid silo]

(a-b)^3((a-b)^2-4)?

[short spruce]

mhm

note that you have a difference of squares now

[timid silo]

https://tenor.com/view/sad-cry-crying-tears-broken-gif-15062040

idk what i have to do anymore

[short spruce]

$(a-b)^2-4$ is in the form $x^2-y^2$

[warm shale]

a disappointing son

[timid silo]

(a-b+2)(a-b-2)? I dont remember

[short spruce]

yes

[obtuse pebble]

@timid silo Has your question been resolved?

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[torpid current]

Please write up your solution to the following problems:

Let L(x,y) be the statement "x loves y", where the domain for both x and y consists of all the people in the world. Use quantifiers to express the following statement.

"There is someone who loves no one besides himself/herself/themselves."

[torpid current]

so far i have ∃x∀y(L(x, y) ↔ x = y)

but im not sure how to get thermselves in the equation

[quaint glen]

what do you think is wrong with what you've written?

[torpid current]

i dont know how to get themselves

[quaint glen]

You already have that x loves themselves by x=y -> L(x,y)

[torpid current]

OH LOL

bro i was honestly guessing that was correct

im jat not sure why himself herself and themselves are seperate instead or "everybody"

is that the teacher just making it more confusing?

or just throwing in a loop

[quaint glen]

So based on the way its written i would assume the teacher is just trying to make the question gender neutral lol

Personally i would just have used themselves

since thats a gender neutral pronoun but

[torpid current]

but so if i rewrite this could it be written as "there exists someone who everyone loves besides herself/himself/themselves"

[quaint glen]

uh no.

[torpid current]

why not

[quaint glen]

Why could you? It says something about there existing a person, let's call them John, who only loves themselves and noone else. It doesn't say anything about who loves John.

[torpid current]

im trying to understand how to rewrite it so could it be

uhh im trying to think

wait

could what you wrote be a rewritten version

also i think i got it confused by putting everyone loves him lol

i meant it the other way around

so "there exists someone who only loves themselves and no one else" would be the right way to rewrite it?

[quaint glen]

that would be another way of saying it yeah

[torpid current]

okay and the domain would be themselves?

or somebody?

[quaint glen]

Uh, not sure what you mean by that

[torpid current]

she wants us to find a domain

and an exampke was "there is somebody whom everybody loves"

and the domain is set d = set of all people in the world

[quaint glen]

Uh so like the domain of both x and y here is already defined in the question, and its the set of all people in the world no?

[torpid current]

yes

but for my question it would be someone because its only about "john" correct?

[quaint glen]

My understanding is that the domain of discourse for both x and y would still be the set of all people in the world, even though you're only making a statement about some specific x here, I don't think that "changes" what the domain is

[torpid current]

ill be honest with you i think im overcomplicating it but i do that so i can understand it

[quaint glen]

that's fair

[torpid current]

so you believe my answer is correct?

and that i dont need to swithc y and x

[quaint glen]

yeah

this stackexchange thread also correlates it

https://math.stackexchange.com/questions/1981191/use-quantifiers-to-expressthere-is-someone-who-loves-no-one-besides-himself-or

[torpid current]

oh dude ive never seen this website

[quaint glen]

if you continue doing any sort of math you probably will, its very useful (don't overuse the internet for getting answers where you can though, like looking up the answer for a problem should be your last resort imo)

[torpid current]

yeah google cant help you on tests

thank you sm!

.close

[obtuse pebble]

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[obtuse pebble]

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[river rune]

i got no clue

tan i find to be the hardest ones to solve

all i know is that its in quadrant 2

[short spruce]

draw a triangle

[river rune]

https://tenor.com/view/mind-blown-shocked-face-whoa-really-wow-gif-17146534

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[light karma]

I'm having trouble understand what exactly you're doing when taking a line integral over a vector field. I understand the intuition for a line integral over a surface, it's like you're finding the area under a path that traverses a surface, but I just can't wrap my head around what you're doing when you take on over a vector field

[light karma]

can anyone help me out ?

this channel is taken

I see a visualization like this, but I just still don't get it
https://cdn.kastatic.org/ka-perseus-images/fa9ace38dc24278776fe55f8fa3489f60734032d.gif

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[hasty harbor]

Is this valid notation (einstein)?

[hasty harbor]

Am I using einstein notation correctly here? Should I leave in the sub 1 and 2 for the v's?

[obtuse pebble]

@hasty harbor Has your question been resolved?

[hasty harbor]

<@&286206848099549185>

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[timid silo]

.close

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[worldly beacon]

how to start this problem?

[short spruce]

get all non constant terms to one side

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@worldly beacon Has your question been resolved?

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[cloud spear]

Why is this wrong

f' of tan is cos

[short spruce]

because you should be getting a value

[cloud spear]

We can't plug t in though

[short spruce]

so manipulate it until you can

or use lhopital

whichever works

[cloud spear]

How could we manipulate it though

The only thing I can see is multiplying by T^2

But then T ends up in the numerator

Making it zero

[azure glacier]

do you know abuot lhopital's rule

plug in 0 for all the t

if the numerator and denominator of the fraction both equal zero after doing that then you can take the derivative of the top and the bottom and try plugging t in again

[cloud spear]

I'll try that

I think it slipped my mind

[short spruce]

:(

[azure glacier]

if doing that makes it 0/0 again then take the derivative again

[cloud spear]

I hate to do this

but

Is the derivative of sin(5t)^2 cost(5t)^2?

The derivative of sinx is cos x

[short spruce]

no

chain rule

[cloud spear]

right

i forgor

So sin(5t) is g right

In which case it would be cos?

cos5t?

[short spruce]

2 chain rules

you have 2 inner functions

[cloud spear]

wut

Sin(5t) is the inner, and x^2 is the outer tho

t^2 works with lhospitals rule

it's just two

[short spruce]

?

[cloud spear]

How are there two inner functions

[short spruce]

5t and sin(5t)

the first inner function being sin(5t), the second being 5t

[cloud spear]

How does chain rule work with more than one inner function

[short spruce]

chain rule v2