help-38

[clever pawn]

u can ask yourself

1. if i had 1 vector, how will my span be like in R3
2. now i have 2 vectors, are they linearly independent or not
3. if they are linearly (in/)dependent, how will my span look like

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[twin mortar]

where does the vx come from

[wraith hinge]

$$\abs{x} = \sqrt{x^2} = \sqrt{x}\sqrt{x}$$

[solid kiln]

What should I do

[wraith hinge]

$$ x = x^1 = x^\frac{1}{2} x^\frac{1}{2}$$

[solid kiln]

What should I do

[twin mortar]

but there is no x^2

im still confused

oh

wait

but isnt 3vx v9x

@wraith hinge

[wraith hinge]

yes

[twin mortar]

.close

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[twin mortar]

.reopen

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✅

[twin mortar]

its still confusing to me

@wraith hinge

[wraith hinge]

do you know what $a^\frac{1}{2}$ is ?

[solid kiln]

What should I do

[twin mortar]

no but yes

[wraith hinge]

https://www.youtube.com/watch?v=GipavLCnke0

basically

$a^1 = a^\frac{1}{2}a^\frac{1}{2}$ you will have to understand this to understand the way they solved the problem

[solid kiln]

What should I do

[wraith hinge]

Also the way they simplified this is dumb asf imo

$$\frac{12}{\sqrt{2}}$$

[solid kiln]

What should I do

[wraith hinge]

instead of doign weird fractional exponent stuff

you can just multiple the top and bottom by the same amount

the best amount to multiply by would be $$\sqrt{2}$$ because it takes the square root out of the denominator and moves it to the numerator

[solid kiln]

What should I do

[wraith hinge]

$\frac{12}{\sqrt{2}} \frac{\sqrt{2}}{\sqrt{2}} = \frac{12\sqrt{2}}{2} =$ You should be able to do the last step

[solid kiln]

What should I do

[twin mortar]

.close

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[stiff locust]

Couple questions

[stiff locust]

What is 0 and why is the interval notation not (-inf, 1) Y [8, inf)

Question two

4 - sqrt(u+7) = 0 gives us nine

So 4 - sqrt (16). Can you think of this being

[round crypt]

i think u can rewrite that like, 8<= x < 1

[stiff locust]

Both :
4 MINUS sqrt(16)
And 4 + -sqrt(16)?

Can the minus also be within the sqrt?

Like -2sqrt

[zinc ginkgo]

$\varnothing$ is the empty set

[solid kiln]

riemann

[twilit kraken]

Ah. Better.

[stiff locust]

What does that mean

[stiff locust]

Why is this wrong

[twilit kraken]

An empty set is the set which has no elements.

Because there's an "and" in between.

[stiff locust]

Whats wrong with that??

A lot of things have and no?

[twilit kraken]

Lol.

Sorry.

"And" means that both conditions have to be true at the same time.

Are you at all familiar with set theory?

[stiff locust]

No

[twilit kraken]

So, your x needs to be smaller than 1 and bigger than or equal to 8 simultaneously.

Can you think of any such number?

[twilit kraken]

Well, know that "and" between two statements demands the solutions which satisfy both statements.

If it was an "or", you would have been correct.

[stiff locust]

Huh, I see

[stiff locust]

Can you help with this?

[zinc ginkgo]

Simplify the sqrt

[stiff locust]

About my question here

[random token]

are you trying to solve for x

if so, just use the quadratic formula

[stiff locust]

Right

But I want to find out how to do it with this

[random token]

why would you solve by completing the square

[stiff locust]

Its something I don’t know. Why not learn?

[tidal jolt]

move -11 to the other side

[random token]

i mean ig?

[stiff locust]

Then square?

[tidal jolt]

(x-3)^2 = 11

[random token]

square root

[tidal jolt]

no then square root

[stiff locust]

Right

[tidal jolt]

yes

[random token]

and then make sure to have the +- in front of the sqrt11

[tidal jolt]

x-3 = plus minus square root 11

yes

[stiff locust]

Ok I see

when you square root

Two things happen

You get +-

[tidal jolt]

yes

[stiff locust]

And there is | | around the number?

[random token]

no

[tidal jolt]

no

[stiff locust]

Though usually you don’t care about the | |

[tidal jolt]

yes essentially

[random token]

there isn't one, and it would matter a lot

[tidal jolt]

dont confuse yourself

[random token]

because that would get rid of any negative roots

[stiff locust]

Wdym there isnt one

There is

???

I remember going over function inverses

And for them to be inverses

They have to be f(x) = x

So if you square rooted and it became = |x|

[tidal jolt]

ok this is completing the square

[stiff locust]

Thats not valid

[stiff locust]

I am talking about square root absolute value

[random token]

I feel like you are overcomplicating this

[tidal jolt]

yes

[stiff locust]

How

[random token]

you just move the 11 over, square root, and add 3 to isolate x

[tidal jolt]

you’re trying to look into the logic of how +- is related to absolute value

[stiff locust]

And whats wrong with that ?

[tidal jolt]

just complete the square and that is all you need, considering completing the square is not 100% needed

[stiff locust]

Buddyyyy

Do you think I care about this problem

I don’t

Im just trying to learn the compexities of square rooting and it being -+

And | |

I am not trying to solve a problem

[tidal jolt]

Then that should be the question not “how do I solve (x-3)^2 - 11 = 0

[stiff locust]

Well I already got past “how to solve”

[tidal jolt]

Good Job

you can close this chat and open a new one if needed or continue on

[stiff locust]

Well if you don’t wanna explain how square rooting gives | | you don’t have to

[random token]

square rooting does not give ||

it gives +-

[tidal jolt]

You need to understand the absolute value of an equation is positive

square rooting an equation can give you a negative

[stiff locust]

What about rooting

Does that give | |

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[thin vault]

Hi

[thin vault]

i was wondering if u can help me on ratio

[thin vault]

my bad

I need help for dis one

Hello?

Help

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[sage axle]

full problem in picture 1, relevant equation in picture 2, solving it for T and plugging in the given values in picture 3. what else could it possibly be asking me to do? I also tried positive 9.8 and it rejects that too

[sage axle]

oh, and the relevant part of the question zoomed in

oooh oopsie, it all becomes clear...

.close

erm lets try that again

.close

uhm

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[red mango]

Hi, i'm reading a real analysis book and I don't get why that is true 😦

[red mango]

I can translate if needed.

<@&286206848099549185>

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[manic jackal]

I have to show the antisymmetry of this equation, this is, if xRy and yRx then x = y

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[craggy saddle]

@manic jackal u still there>?

i can help u

[manic jackal]

yes

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[honest saddle]

how would you go about calculating this NxN matrix?

[raw magnet]

@granite cove

Do you know what this is

[honest saddle]

determinant of the matrix is what i meant

[granite cove]

I guess Laplace and you get a recursive formula

[wise dagger]

this is what i have for the first 2 steps

count carefully and you'll get a good recursion

[honest saddle]

i've never actually learned the recursive formula

[eternal adder]

maybe somewhat tangentially related, but I've used this in the past
https://www.webpages.uidaho.edu/~barannyk/Teaching/LU_factorization_tridiagonal.pdf

which works quite well, and the determinant is then easy to calculate from the triangular matrices

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[honest saddle]

@wise dagger this should be it right?

detA = 7 * 3^(n-1) - 2

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[tulip vector]

A survey of 100 undergraduates on the use of instagram and facebook are as followed: 86 use instagram, 52 use facebook, 10 do not use either product.

Given that x undergraduates use both products, draw a venn diagram and find x.

[wraith hinge]

Have you started a venn diagram

Given 10 do not use either the difficult part only considers 90 people

You can think of it as "only use Facebook, only use Instagram and use both"

The numbers they gave you aren't the "only" numbers -- it's not the case that 86 only use ig.

So you can express the above as equations

If x is the people that use both:

• 86 - x only use ig
• 52 - x only use fb
• x use both

That should be enough to start

[tulip vector]

ohh thanks so much

.close

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[tulip vector]

Please help 😭

A total of 100 students gave the following data: 41 students take spanish, 29 take french and 26 take italian. 15 take both spanish and french, 8 take french and italian, and 19 take spanish and italian. 5 students take all 3 languages.

Find the number of students not taking any of the 3 languages. How many take just one of the languages?

[wraith hinge]

You need to start by drawing a triple venn diagram

[tulip vector]

yep i did.
to find the number of people taking only italian, is this equation correct
only Italian = Total taking Italian - those taking Spanish and Italian - those taking French and Italian - those taking all three languages

[wraith hinge]

Well the thing is the way this is worded, "those taking Spanish and Italian" could be those "taking Spanish and Italian AND French"

Cause if you're taking all 3, you're defo in "Spanish and Italian"

What you want to do is start from the most specific, the center, and work outward

So start with the 5 people taking all 3

Then you can easily find the dual language numbers

If for example S&F = 7 and S&F&I=5 then those ONLY taking Spanish and French is 2

To use your numbers, those taking only S and F is 15-5=10

And those taking S and I is 19-5=14

Which means ONLY Spanish is 41-14-10-5

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[smoky saffron]

i dont want the answer

just the method

i feel like ive tried everything

clarify: i dont want the working

still want to do it myself

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[smoky saffron]

i dont want the answer
just the method
i feel like ive tried everything
clarify: i dont want the working
still want to do it myself

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[smoky saffron]

.reopen

[cloud beacon]

i take over

[cloud beacon]

Write complex number a) 1 for exponent form

cos0+i sin0= e^i0?

@dreamy oar

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<@&286206848099549185>

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[fiery loom]

I don't follow. What is your question / confusion?

[cloud beacon]

Hi

Want to know moivers formula to complex number=1

[fiery loom]

As you wrote, cos(0) = 1 and sin(0) = 0.

What are you confused about?

$e^{i0} = e^0 = 1$ is easy enough to double check.

[solid kiln]

chencking

[fiery loom]

1 is a positive real number, so you can just obtain the exponent by taking the natural log.

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[cloud beacon]

.close

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[simple jackal]

How do we get the last term in the second expression?

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[vale wharf]

for this question, the underlined equation simplifies to

x^4 - 8x^3 - 4x^2 + 80x + 84

which has 4 solutions

however, the underlined equation only has two according to photomath and wolfram

I checked if that is because of the sqrt in the original by doing an inequality, but all solutions satisfied that inequality

is it because of the power of 2 in the original? or something else
Image

[vale wharf]

I moved the square root to the other side, squared it and then moved everything to the left

[ornate hedge]

Have you checked when x > 0 ?

[vale wharf]

yh

I did an inequality

of the square root

[ornate hedge]

then I have no idea im sorry xd

[vale wharf]

= 0

[ornate hedge]

I never trust photomath or wolfram

[vale wharf]

fair enough

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[vale wharf]

<@&286206848099549185>

[tacit quest]

yeah, it has four solutions, but some might not be real

wait, are you sure -x^2+4x+9 is always positive

because it won't be only squaring both sides then

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[short star]

How do you redefine a recursive sequence by a function?

[short star]

For example $x_{n+1} = \frac{5}{6-x_n}$ and $x_1 = 4$

[solid kiln]

KN

[tacit quest]

u mean redefine in terms of n?

xn=f(n)?

[short star]

I want to show that this sequence is strictly decreasing

It would be nice if I can rewrite as a function

So like an explicit form

[tacit quest]

I would do something like this

suppose there is a limit as n->inf

then a=5/(6-a)

,w x=5/(6-x)

[solid kiln]

Results provided by WolframAlpha

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

Requested by _ils

[tacit quest]

since it looks like it's decreasing let's take 1 as a supposed lim

so an>1

an+1<?an

[worldly bay]

need to show
$x_{n+1}-x_n = \frac{5}{6-x_n}-x_n<0$

[solid kiln]

Amir

[short star]

I think i was able to do it with induction

Yeah

ok

$x_{k+2} = \frac{5}{6 - x_{k+1}} < \frac{5}{6-x_{k}} = x_{k+1}$

[solid kiln]

KN

[short star]

.close

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[graceful solstice]

is there a way to find all of the solutions by graphing or do you actually have to do all that work

[short star]

It is teaching you how to do long division

That usually means it is helpful and you don’t want to not know how to do it

It is not that much work

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[novel oar]

Can someone help explain b to me:

I trie the following, we first pick 2 signle digit and 2 double digit. That is, 9 choose 2 times 6 choose 2 and then we have 7 choose 1 single sigit last players left. Thats the numerator. And the denominator is then 15 choose 5.

I think I am overocunting because in this expression it overcounts for say the 3rd single digit comes in position 3 and then the last 2 are double digits

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[random token]

Let X_n be the maximum number of consecutive heads in n flips of a fair coin (eg, X_6(HHHTHH)=3 )
What is the expected value of X_n?

[random token]

(a summation works as an answer, I don't need closed form, so I basically need the formula of the distribution)

It seems like, to find P(X_n = k), you should start by finding the number of ways to place k consecutive heads and then the number of ways to arrange the rest so that there aren't k or more consecutive heads in the other flips

but I don't know how to do that second part

hi

<@&286206848099549185>

[rustic trail]

hi

[random token]

hi

help pls

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[spare junco]

Hello! I'm doing some discrete math studying before an exam, but Im kinda confused with the last step for induction. I understand you have to make the left side look like the right, but I guess after not doing any algebra for 6 months I may have forgotten a bunch..
Anyways, attached is 2 images, 1 is the before, and 2 is what I think is the after, after simplifying it. My question is are those 2 equations equal because for some reason it doesnt feel right, since both have a k+1 and a k+2, shouldnt it be (k+2)^2 + (k+1)^2 after combining? thank you!

[surreal bough]

waht can u factor out of both addends on the left image

[spare junco]

k+1 and k+2 and 1/3?

[trim jolt]

@spare junco Has your question been resolved?

[surreal summit]

hey

[spare junco]

hoi

[surreal summit]

You good?

[spare junco]

eh not really

i get that its the right answer but I dont really see why

[surreal summit]

Hmm

let me see

Ok

So you are having concern about how do you get the result

[spare junco]

yeah

[surreal summit]

Final answer

[spare junco]

yepyep!

[surreal summit]

Okay look

[spare junco]

this is how it started

[surreal summit]

I will show you a really good example of it

You get it?

We call this reduction of fraction to a common denominator

It's basically just use multiplication to get the same amount of denominator and doesn't change the final result

2/4=1/2

1/2=0.5

2/4=0.5

[spare junco]

uh huh, so why is the k+3 special, and gets combined into one set of parenthesis

[surreal summit]

oh yeah

I will show you that later

FIrst we gotta get the integer to a fraction

How do we do that

Pretty easy, All you have to do is turn the integer into a fraction by putting 1 to the denominator

for example

[spare junco]

so 2x+1 / 2

[surreal summit]

yes

Thats how you get the 3(k+1)(k+2)

And the next step of what we gotta do

[spare junco]

mhm i got that far, and then needed to simplify further to get the rhs of a proof

[surreal summit]

you have to combine those equations in one

don't look at the denominator

because they are already the same

you just have to worry about the numerator

k(k+1)(k+2)+3(k+1)(k+2)

You might not understand the next step

I'll show you an example

ka+3a

You get it?

Same base power

3a+4a=7a

which it means ka+3a=a(k+3)

(K+1)(k+2) might not equals to a

but this is an example

just to show you that the things in the bracket doesn't matter

[spare junco]

oh

so its a little like u subsitution?

[surreal summit]

it works the same as same base power

[spare junco]

from calculus?

[surreal summit]

Hmm

[spare junco]

you put a set of stuff in a variable and do it from there?

[surreal summit]

yeah

[spare junco]

so heres what the full equation looks like

[surreal summit]

you just do subsitution

[spare junco]

so itll be easier to see what im talking about

[surreal summit]

Yes

[spare junco]

erm oops

so if (k+1)(k+2) = a

ka + 3a = a(k+3)

[surreal summit]

yeah

[spare junco]

divide by a

i think

[surreal summit]

umm after that

you will have to simplify the equation if you could

[spare junco]

(k+3) = (k+3) which means lhs is = rhs

so thats the end of the proof?

[surreal summit]

yea

[spare junco]

cool thats a different way of doing it than I thought

but I guess it works

[surreal summit]

But most of the time i think people such as your teacher wouldn't let you replace the product into other values

Uhh wait

Where is your denominator

[surreal summit]

You can't just remove it, I mean you can ignore it while doing stuffs like that, But the final answer needs to keep it if its already the lowest term

[spare junco]

cant we multiple every part by 3?

[surreal summit]

no

[spare junco]

to get rid of the denominator

[surreal summit]

uhh yeah

you could though

the values of K won't change

[spare junco]

alrighty well thank you, ill try to do some more practice problems, how do I close this post

.close

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[lyric kiln]

hi

[lyric kiln]

<@&286206848099549185>

how do I do this

I have been trying to reach somebody for 1 hour now

maybe more

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[lyric kiln]

BRO

[austere cedar]

Could you graph (x + 9)² if asked?

[plucky walrus]

In order to find the domain of f(x) = (x+9)^2 we would need to graph it

[austere cedar]

#help-45 message

[plucky walrus]

yeah just like what kaynex said

[austere cedar]

It seems like you know the answer, but it didn't accept it. Not sure how to help with that.

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[dim python]

Can someone help me with Mathematical Induction?

I'm following youtube guides and I simply don't understand one part.

So I understand I have to replace n with k. Then replace the n for k + 1 for the second part. But where does the extra (4k-1) comes from in the bottom?
If I take 3 + 7 + 11 + ...... (4n - 1) = n(2n + 1) from the top and replace the n with k + 1, I get 3 + 7 + 11 ........ (4(k+1)-1) = (k+1)(2(k+1)+1). Exactly what's below, but without the extra (4k-1)

[tacit quest]

Sk+1=Sk + (4(k+1)-1)

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[main olive]

is there a function that satisfies $\int f(x)dx=0$

[solid kiln]

Jash

[dusty sleet]

Yes, think about which functions has 0 as their derivative

[main olive]

0

but when u integrate 0 u get C

[dusty sleet]

Sorry, I told you a shit 🙈 ignore it lol

I don't know why I thought the opposite ahah

I don't know if there's one such function for indefinite integrals

[delicate belfry]

Dosen't this seem right?

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[rigid vigil]

Hiya, could someone help me "derive the equation of motion of a freely moving particle with mass m" in cylindrical (and spherical) coordinates, from the Christoffel symbols?

[rigid vigil]

I have found all the christoffel symbols for these coordinates

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[wraith hinge]

Spare my horrible drawings

[wraith hinge]

What did i do wrong

Deriviing $arcsec(5x)$

[solid kiln]

What should I do

[wraith hinge]

Steps are from top to bottom

I don't understand where the absolute value sign is supposed to come from

is the absolute value from

$$\frac{1}{x\sqrt{25x^2-1}} \approx \frac{1}{x^2\sqrt{25-\frac{1}{x^2}}}$$

[solid kiln]

What should I do

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[next raptor]

Hi

[next raptor]

How to write All real number except x = -2

In mathematics way

[trim lichen]

$\bR \setminus { -2 }$

[solid kiln]

Ann

[next raptor]

Seriously?

[trim lichen]

yes

[next raptor]

I was doing (-infinity, -2) U ( -2, Infinity)

[trim lichen]

that works too

[next raptor]

Alr thx

👍

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[fallow ether]

Why is this wrong

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[zinc ginkgo]

doesn't look like you used the right formulas for breaking your acceleration into tangential and normal components

read this
https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/2%3A_Vector-Valued_Functions_and_Motion_in_Space/2.6%3A_Tangential_and_Normal_Components_of_Acceleration

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[frosty heron]

Can anyone explain me

The working is not mine

I'm not getting

Anything

[pure hatch]

Hmm

Okay what do you understand from the question?

[frosty heron]

I just understand that it's a cylindrical pipe and it has some water in it

And the diameter

Is 20

[pure hatch]

Are you sure?

Diameter?

[frosty heron]

Radius

Sorry

[pure hatch]

Okay

What else?

[frosty heron]

I don't get the triangle inside iy

[pure hatch]

R = 20 cm

Well

Can you find the side lengths and angles of that triangle based on what you saw?

[frosty heron]

Yes I think using the sine rule

[pure hatch]

Okay

Wait which drawing is the given one?

The right or left one?

[frosty heron]

Left

[pure hatch]

Alright

If that's the case then we don't need sine law

We can find it using basic trigs

Hey? @frosty heron

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[frosty heron]

Ye

[pure hatch]

What have you reached so far? :)

[frosty heron]

We can use Pythagorean theorem

Ig

[pure hatch]

Yep

If you notice also

The triangle you have is a 3-4-5 triangle

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[wraith hinge]

I was supposed to find the solution, which I did. However, I'm not sure which answer is correct. I think they are both right and they represent the same thing differently but I just wanted to make sure.

[waxen thunder]

The first one describes a rectangle, the solution set isn’t a rectangle, so it’s not correct.
The second one describes a ray, so that doesn’t seem right either

[wraith hinge]

I'm gonna give it another shot.

this time with more thought

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[wraith hinge]

The solution set is supposed to be in a set builder form right?

is that part at least right?

[wraith hinge]

I came up with another one.

[waxen thunder]

Honestly, in set builder form you’d just put the two inequalities in there, might they be just asking for you to graphically label the solution set instead?

[wraith hinge]

the sign should have been > and it =

[wraith hinge]

i used a proper graph paper and shaded the region where the inequities lie. I then cross checked with desmos and it was correct. would the shading count as labeling?

[waxen thunder]

Maybe draw an arrow to it and write S? Was there any exercise like this before? Maybe you can check how they did it

[wraith hinge]

here's the set builder one btw.

[wraith hinge]

eh it doesn't matter. I'm only doing it for practicing my algebra. I'm not actually giving a test.

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[dusty slate]

if a polynomial with a degree of 7 cant have 6 real roots,
then how is this possible ?!

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[vernal briar]

why cant it?

[tacit quest]

double root?

[dusty slate]

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:fta/v/possible-real-roots

this says it cant

[waxen thunder]

This has 7 real roots, there is a double root there

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[leaden hearth]

How do I show

[crimson pebble]

What’s the definition of a root of unity?

[untold ore]

hi :>

[leaden hearth]

each of them are separated evenly across a unit circle.

[crimson pebble]

Algebra-wise?

[leaden hearth]

w^n = 1

[crimson pebble]

Yep

[leaden hearth]

Oh shit, you are activating my asian powers.

Thank you so much, sensei

.quit

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[leaden hearth]

.reopen

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✅

[leaden hearth]

@crimson pebble could you please help me with the second part?

I got (z^5 -1)/(z-1) is that right?

[crimson pebble]

No

[leaden hearth]

how would we do it?

[leaden hearth]

how does one do the question.

[crimson pebble]

Which would you like first, over R or over C?

[leaden hearth]

lets go over C

[crimson pebble]

Ok, so the idea has merit but your expressiob needs double-checking

[leaden hearth]

I'm confused

Isn't this z^5-1 = (z-1)*(1 + z + z^2 +.. + z^4)

[crimson pebble]

Well we’re given 1+z+z^2+…+z^5

[leaden hearth]

Yes

[crimson pebble]

and so?

[leaden hearth]

ahh, (z^6-1)/(z-1)

How do I factor it over complex now

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[pure geode]

can somebody help me wit dis 😭

[ornate oasis]

So f(x) equals 1/2 (x) + 3/2
Do you know how to find the value of f(2) ?

[pure geode]

shii

no

[ornate oasis]

If you look at the table, what's the value of f(x) when x is 2

[pure geode]

2

[ornate oasis]

So that means f(2) equals 2

[pure geode]

yuh if my calculations is correct

which they prob not

[ornate oasis]

Let's go in order now, looking at the options, the first is f(-1/2)

Can you tell what f(x) is when x equals -1/2 from the table?

you probably can't right away

But you know that -1/2 is between -1 and 0

[pure geode]

ay ima keep it real i aint got a clue of what u saying

[ornate oasis]

that's alright, where should i start from

want me to explain how to find f(x)?

[pure geode]

yes that will work

thanks

[ornate oasis]

so f(x) is like an equation
They give you an equation for f(x), and that equation is (1/2) times x plus 3/2
If you replace the x in f(x) with another number, then you'll have to replace the x in the equation for f(x) with another number as well.

For example, if f(x) has the equation: (1/2) times x plus 3/2
Then, f(2) has the equation: (1/2) times 2 plus 3/2
If you do the math, in a calculator or something, you'll see that f(2) equals 5/2

The table lists values for x, and to the right, what f(x) would be equal to with these x values

[pure geode]

oh

okay

makes sense

so what would the answer be

[ornate oasis]

First of all, for the first one, try to find f(-1/2)
If f(-1/2) equals -2, then the first option is true, else, it's false

You can use the table, or the equation if the table doesn't have the x value you're looking for

For the first once, you want to replace x with -1/2 in the equation

[pure geode]

oh aight

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[severe stump]

This is the problem I am on.

[severe stump]

I could figure this out without using the contrapositive proof method, but I don't quite understand how this method works.

We have only been given 3 definitions thus far. Intersection, subset, and union.

I'm not fully at a conclusion right now, I'm just trying to get words on a page to try to pick stuff out.

<@&286206848099549185>

Can I imply that since there are values of S, that the union of S and T cannot equal T?

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.close

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[vapid kayak]

Hello!! I understand that this question is asking for one E-Tank + one - E-tank. however, I’m not really understanding where the yellow circles and red circles come in. I understand the value of them, but how many are actually in those tanks. I hope this makes sense. I don’t have any work for this since there’s not too much to understand I’m just not getting it.

a. 1
b. 2
c. -1
d. 0

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<@&286206848099549185>

:))

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[vague vector]

may i ask if this is the correct approach to this problem? i understand how to find the complementary solution, but i got a bit confused after i solved for that

[austere cedar]

You're just finding any particular solution

,w y" + 2y' + y = e^(3t)

[solid kiln]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by kaynex

[austere cedar]

Oh wait, you guessed the particular solution was Ae^(3t)t²? That's not the right guess here.

It's just Ae^(3t)

@vague vector

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[green oak]

I have to determine the domain and range of this function.

[green oak]

It is valid notation to say that the domain of this function would be R^3 - {(0,0,0)} ?

[vague vector]

oh! may i ask why? what role does the double root play in the particular solution?

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[austere cedar]

@vague vector
Open another channel and ping me there

@green oak
Yes.

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[rough vine]

find d^2y/dx^2 if 3y-6x^2 = 2x-y^2.

[rough vine]

i got dy/dx as (12x+2)/(2y+3)

and then I got this:

but the answer key somehow simplifies it to this:

where did the 100 come from??

[split chasm]

How'd you get that

[rough vine]

this one?

[split chasm]

yes

[split chasm]

expand the numerator

from the original equation you have a relation between x and y

that should allow you to simplify to a constant

[rough vine]

idk why I'm getting 100/48

instead of 100

[split chasm]

because you seem to just have divided that whole numerator by 48 here

[rough vine]

oops

i just need to factor it out and leave the 100 outside

or i couldve just divided the denominator by 48 and it would've cancelled

right?

yup that works

thank you

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[zinc crane]

wants me to get the ordered pairs and plot them right, but when i do it the first two y coords are -18 and -12 meaning i cant plot them cause the graph only goes up to 10...

am i doing something wrong

??????

?????

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[loud wasp]

Could someone explain this to me

Oops I'm sorry I didn't see you typing 😭

[timid bay]

There is a typo in the problem it should be x^4 +13x^2 +36=0

[loud wasp]

Ahh

Then it makes sense

Thank uu

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[real saddle]

trying to find sin theta of (-1, √3)

i try and get there by finding the radius

√x^2 + y^2 or

√4

so
√(3)/√(4)

and then i try to rationalize the denominator by multiplying both sides by √(4)

√(12)/4

then i simplify for 3√(3)/4 which is wrong apparently

which step did i mess up on?

[red loom]

$\sqrt{12}\neq3\sqrt{3}$

[solid kiln]

MrFancy

[red loom]

$\sqrt{12}=\sqrt{2^2\cdot3}$ :)

[solid kiln]

MrFancy

[real saddle]

ohhhhh

so 2√3?

[red loom]

[real saddle]

would that then simplify the sin too

√(3)/2 ?

[red loom]

Should be right

[real saddle]

tyty

doing the cos its -1/√(4) and rationalizing it by multiplying by both sides by √4

would that be -√4/4?

oh wait

[shrewd adder]

sqrt(4) is just 2, you dont need to rationalize

[real saddle]

-2/4 or 1/2

yah caught that last sec lol ty

should be all for now tyvm

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[severe narwhal]

Im so confused

How is MVT being applied here here at the very start of the solution?

er not too sure what that curly math symbol is called, i will refer it to it as "k".

How does MVT give us that both function's derivatives share the same k?

[zinc ginkgo]

Yea that proof is flawed

Use this one instead

Or Google another proof for "Cauchy's mean value theorem"

They should all look similar to the one I showed

[marble wharf]

(the letter is called xi, btw)

[zinc ginkgo]

Oh yea

$\xi$

[solid kiln]

riemann

[zinc ginkgo]

"kuh-see"

[severe narwhal]

ah okay i see whats happening here, thank you very much

[severe narwhal]

thanks for this too

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[severe narwhal]

.reopen

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✅

[severe narwhal]

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[wraith hinge]

i understand {A} is not a subset of P(A) but what is mean by {A}

[wraith hinge]

like what it means to represent subset like this {{1,2}}

[boreal dome]

P(A) is a set of sets

the notation {A} is a set that contains the set A

so we should write :
$${A} \subset P(A)$$

ah

[solid kiln]

Herels

[stoic iron]

Escape them \{

[wraith hinge]

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[sage cloak]

I have no clue how to solve these 🥲

[hallow spruce]

As x tends to infinity, x is negligible compared to x^2

So you can ignore everything aside from the term with the highest power

[severe stump]

I think the issue here is that it's a sqrt of x^2, so they have relatively similar trends.

[hallow spruce]

The num and denom do, yes

But that's step 2

[sage cloak]

What would step 1 be?

[hallow spruce]

Step 1 would be to simplify

As x tends to infinity, 4x+1 has basically no difference from 4x

Similarly x^2 - 2x is negligibly different from x^2

[sage cloak]

So I would simplify it to 4x/x^2?

[hallow spruce]

Don't forget the sqrt

[sage cloak]

Yeah I just saw that I missed it

What would I do after?

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[sage cloak]

<@&286206848099549185>

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[sage cloak]

<@&286206848099549185> is anyone able to help me with this question?

[wispy sparrow]

which question

$\frac{4x+1}{\sqrt{x^2-2x}}=\frac{4+\frac1x}{\sqrt{1-\frac2x}}$

[solid kiln]

chlamydia

[wispy sparrow]

i've just done this by dividing by x on the top and bottom which doesn't change the expression

next we can recall how 1/x behaves towards infinity

[sage cloak]

How does dividing x^2 by x = 1?

[wispy sparrow]

when you bring x into the square root, it becomes x^2

$x\sqrt{y}=\sqrt{x^2} \sqrt{y}=\sqrt{x^2y}$

bruh

[solid kiln]

chlamydia

[wispy sparrow]

so dividing by x becomes dividing by x^2 in the radical

[sage cloak]

So it's the square root of x^2 = x then x/x which equals to 1?

[wispy sparrow]

the other way around: x is the square root of x^2, so (x^2-2x)/x^2=1-2/x

[sage cloak]

I see, so we divide by x^2, not x?

[wispy sparrow]

yes, within the radical

[sage cloak]

Do you know why we divide by x^2 and not x?

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[stone torrent]

Nah he divided by x but the under the square root it becomes x²

[sage cloak]

How did it become x²? Didn't it have x² in the question?

[stone torrent]

Or u can visualise it by taking x² out of the expression

${\sqrt{x^2-2x}} = {\sqrt{x²}×\sqrt{1-\frac{2}{x}}$

[solid kiln]

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

[stone torrent]

Yeah something like that

And √x² = |x|

[sage cloak]

Okay and then like what would I do after this step?

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[wispy sparrow]

do you understand this now

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[sage cloak]

So we just divide everything on the numerator and denominator by x^2 and then we see which values can be ignored?

[fiery loom]

Not exactly. You can divide both the numerator and denominator by $x^2$ because $\frac{1/x^2}{1/x^2} = 1$. Here, you end up with a determinate form. And you can directly evaluate the limit of determinate forms.

[solid kiln]

chencking

[fiery loom]

The terms are not "ignored," however they go to zero.

[sage cloak]

I see, I understand this step but I'm just confused on what to do after this

[fiery loom]

The direct evaluation?

It's just plugging in the limit since it's determinate.

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[idle cloud]

!occupied

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[cinder swallow]

@sage cloak One approach is that you could try to visualise these functions in Desmos, for example: https://www.desmos.com/calculator/kj2dkuextk

We can also create a simple table for values of -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

See what patterns emerge

Try to write a table for powers of 10

Make conjectures

[cinder swallow]

Approximate

[fair bison]

@sage cloak do you still need help

[sage cloak]

Thanks for all the help, I think I mostly understand now

[willow thicket]

Please don't post spam links in this channel. (It disappears, but I'm not sure whether other people could see)

[fair bison]

Banned them, don't worry

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[digital thunder]

how to solve this inequality

[dusty sleet]

Multiply both sides by 15 (which is the common denominator)

And then do the usual calculations

If you have already done 1st degree inequalities, I don't see where the problem is

[digital thunder]

5-2x/3 . 15 > 2 + x / 5 . 15 like this?

[dusty sleet]

Yeah, of course 😅

[digital thunder]

😅 thank you

sorry im confused, can you explain me why 15 ?

[dusty sleet]

.

[tame solstice]

Actually we just want to vanish things down there to make the calculation easier

If u feel uncomfortable multipling 15 both sides
Consider cross multipling 🗿

[digital thunder]

the answer is x > -19/-13 right? 😅

[tame solstice]

I think it should be x < (19/13)

[digital thunder]

ouuu thank youuu

😭

[tame solstice]

[shrewd ridge]

we do separate channels for every question

[wispy sparrow]

they were basically done innit

[shrewd ridge]

scroll up, look for math help available

[red ridge]

oh shit sorry

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[molten comet]

Can someone tell me what I did wrong here?

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[upbeat mist]

I’ve never seen anything like this

No idea where to start

Where did A and B and C and D and E and F come from

[stoic iron]

You have to figure out what they are

By manipulating the given expression

[upbeat mist]

So should I evaluate it

Find the limit as h approaches 0?

[stoic iron]

No because the limit has not been evaluated anywhere in the problem

[upbeat mist]

Oh

So is this what not to do?

[stoic iron]

Everything is fine here up until you somehow ended up with 2h³

Note that you are not at any point evaluating the limit

Only simplifying the expression that appears in the limit

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[real saddle]

Trying to solve this and struggling

i do

y = x + 4

3x^2 + 2(x + 4)^2 = 20

3x^2 + 2(x^2 + 8x + 16) = 20

5x^2 + 8x + 16 = 20

5x^2 + 8x - 4 = 0

this and kind of struggle on factoring 5x^2 + 8x - 4

[polar skiff]

dont u know the quadratic formula?

[real saddle]

uhhh

dont rlly remember it off the top of my head no

oh

-b +- sqrt(b^2 - 4(a)(c)/2a

[polar skiff]

yes

if the discrimant is non negative

which is the case since u got one coefficient negative for the last coefficient and one of the oppositie sign in front of x^2

[real saddle]

-8 +- 12/10 is what im endin up with

which is 2/5th and -2?

[polar skiff]

yes

[real saddle]

which when plugging into y = x + 4 gives me

(-2, 2), (2/5, 22/5)

but im pretty sure it tried that and got it wrong? what did i mess up

[polar skiff]

here you messed up when u developped

my bad should've checked it

always read back the precedent line when u do some calculations

[real saddle]

wdym?

which part do u refer to when u say devbeloped?

[polar skiff]

last two lines before the last one

[real saddle]

3x^2 + 2(x^2 + 8x + 16) = 20 this?

[polar skiff]

yes

do u see whats wrong

[real saddle]

(x + 4)
x^2 + 4x + 4x + 16

no i dont think so

[polar skiff]

after that

u developped

check that the next line is right

[real saddle]

oh

[polar skiff]

always double check

[real saddle]

should be 5x^2 + 16x + 32 = 20

[polar skiff]

only way to not do the same mistakes again, especially on tests

and then u do ur things again

[real saddle]

5x^2 + 16x + 12 = 0

a = 5
b = 16
c = 12

-5 +- 4/10?

wouldnt that lead to

-9/10 and -1/10

[polar skiff]

(-16 + 4)/10 = ?

[real saddle]

oops

mixed -b with -a

[polar skiff]

no need to hurry take ur time

[real saddle]

-12/10 and -2

[polar skiff]

yes

[real saddle]

y = x + 4 so

x = -2
y = 2

x = -12/10
y = -12/10 + 4
-12/10 + 40/10
y = 28/10
y = 14/5?

[polar skiff]

yes

so u get two couples

and then what do u do

[real saddle]

just {(-2, 2), (-12/10, 14/5)} i think

[polar skiff]

what u should do then

[real saddle]

i thought that was it

[polar skiff]

it depends on what ur prof is waiting

if u write calculations like that

u should do analysis and then synthesis

analysis is what u did