help-33

[solar nimbus]

Anyone???

I got $25 for anyone that can do it

[fallen galleon]

I dont want $25

but drawing a diagram might help

just draw a circle 2 cm off the ground

with radius 8

4 revolutions every 60 sec

so 1 rev every 15 sec

so 1 revolution is 360° ye

360° every 15 sec

so 24°/sec

so after t seconds

24t°

[solar nimbus]

So what would the final cosin equation be?

[marsh citrus]

@solar nimbus Has your question been resolved?

[fallen galleon]

try it and find out

have you drawn the circle?

take a picture of ur work

[solar nimbus]

I drew a graph not circle

I was able to get this

But then I realized this is sine

The question asks for cosine

[frank rose]

the general equation for uniform circular motion is

,,\vec{r}(t) = (R\cos(2\pi\omega f (t-\phi)), R\sin(2\pi\omega f (t-\phi)))

[elfin berry]

vin100

[solar nimbus]

Is that the cosine equation?

[frank rose]

the first component is the horizontal position, and the second component is the vertical position.

in this formula the motion is centered at the origin

in your question, the center of the wheel (and the wheel itself) is above the ground

so you need a vertical shifting

R is the radius

f is the frequency

$\omega$ is the angular speed

[elfin berry]

vin100

[frank rose]

oh sorry the formula shud be

,,\vec{r}(t) = (R\cos(\omega (t-\phi)), R\sin(\omega (t-\phi)))

[elfin berry]

vin100

[frank rose]

$\omega = 2\pi f$

[elfin berry]

vin100

[frank rose]

$f$ means rotations per second

[elfin berry]

vin100

[frank rose]

in each rotation, one travels $2\pi \mathrm{rad}$

[elfin berry]

vin100

[frank rose]

multiplying them gives how much angular displacement per second

$\phi$ is the phase shift

[elfin berry]

vin100

[solar nimbus]

Hmm ok

So I just plug in the numbers into the formula?

[frank rose]

you may try $R = 8$, $f = 4$. note that the initial position is at the bottom, so $\vec{r}(0) = (R\cos(2\pi f \phi),R\sin(-2\pi f \phi)) = (0,-R)$.

[elfin berry]

vin100

[frank rose]

,,\sin(-2\pi f \phi) = -1 \iff 2\pi f \phi = \pi/2

[elfin berry]

vin100

[frank rose]

so you see that the vertical displacement from the center is

,align
&\quad R\sin(2\pi f (t - \phi)) \
&= R \sin(2 \pi ft - \pi/2) \
&= -R\cos(2\pi ft)

[elfin berry]

vin100

[frank rose]

the wheel is $h$ from the ground, so the vertical position is

[elfin berry]

vin100

[frank rose]

,,h + R - R\cos(2\pi ft)

[elfin berry]

vin100

[frank rose]

i suggest that you leave the substitution at the final stage to avoid careless calculations mistake

[marsh citrus]

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[marsh citrus]

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[naive mist]

y=-6cos(πx/6)+10≥12 domain 0≤x≤24

can anyone help with this inequality (solve for x)

[naive mist]

pls

<@&286206848099549185>

[marsh citrus]

@naive mist Has your question been resolved?

[naive mist]

useless server tbh

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[still temple]

How do I answer 6iii?

[marsh citrus]

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[marsh citrus]

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[still temple]

what?

this question's composition makes little to no sense

okay it finally clicked

[cobalt zealot]

The vertex of question a

Ye

How does one do that exactly

[still temple]

they are all in vertex form so the vertex is just (h,k)

[cobalt zealot]

Ah ok so

What wluld.be h,k

So I can do all the vertex's rn

[cobalt zealot]

So 1,-3?

For a that is

[still temple]

axis of symmetry is just the line running through the vertex either vertically or horizontally

[cobalt zealot]

Alright and how does one do that

[still temple]

you only have up and down parabolas so it is just the vertical one

its the h value

the range, i will leave that one to you

[cobalt zealot]

Alright well thanks so

For symmetry its always just h

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[marsh citrus]

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[ivory laurel]

For this question do I assume one side exists and then prove the other side exists and vice versa getting two inequality showing that they’re equal?

[warm breach]

I would do this too as sup doesn’t even make sense if the set is not bounded

[marsh citrus]

@ivory laurel Has your question been resolved?

[ivory laurel]

I’ve came up with the first inequality but it lacks justification, I think I get the idea but I can’t seem to write it out?

[marsh citrus]

@ivory laurel Has your question been resolved?

[marsh citrus]

@ivory laurel Has your question been resolved?

[gentle sierra]

well sup(AUB)=sup{supA,supB}. but we have infinitely many, so it's not as simple as just proving that by induction.
suppose that s=sup(S1US2U...). then s is an upper bound of S1. but since supS1 is the least upper bound, s>=sup(S1). repeat this logic to conclude that s is an upper bound for {supS1,supS2,...}, so it is >=sup{supS1,supS2,...}.

so that would give you the <= side for the original problem. you then have to show the >= direction.

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[rough crow]

which two consecutive intergers is the fraction 50/8

A. 6 and 7
B. 7 and 8
C. 8 and 9
D. 9 and 10

[hidden plaza]

I don’t understand the question

[rough crow]

help solve

if can

[silent cave]

can you simplify 50/8?

[rough crow]

yea

i dont get the wording tho

[sleek lake]

"between"

essentially add one word

[silent cave]

i believe the question is asking in between what numbers it is

[rough crow]

what

[silent cave]

50/8 is in between which two numbers

[rough crow]

ah ok

ohhhh

6 and 7 right?

[silent cave]

yeah

[rough crow]

ah ok thanks

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[rough crow]

x:15 = 18:27

for what value of x is the proportion shown above true

e. 6
f. 10
g. 11
h. 12

[rough crow]

i think its e

but idk

[trim quest]

Can you simplify the ratio 18:27?

[rough crow]

no

i cannot

[trim quest]

Do you mean, you don't know how? Or you're saying it's already simplified?

[rough crow]

oh

i dont know how

wht i meant

sorry

[silent cave]

@rough crow
18 = 9x2
27 = 9x3
That means 18:27=2:3
Does this make sense?

[rough crow]

uhhh

somewhat

oh oh yes

ok

thx

[silent cave]

can you solve the rest of it?

x:15 = 2:3

[rough crow]

hope so

ok so like

yes thanks

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[limpid hemlock]

this is in organic chemisty tutor's video for convergence/divergence, i dont understand why he's multiplying both the top and bottom by 1/n?

[limpid hemlock]

at first i thought it was to use l'hopital's rule but it multiplies all of it by 1/n, including constants

[marsh citrus]

@limpid hemlock Has your question been resolved?

[limpid hemlock]

<@&286206848099549185> pls help im in dire need of support

[marsh citrus]

@limpid hemlock Has your question been resolved?

[marsh citrus]

@limpid hemlock Has your question been resolved?

[main idol]

you don't need l'hopital for this problem

you just use limit laws

quotient law for limits

the main thing is to manipulate the fraction so that when you take the limit of each separately, you get a finite number. which isn't the case in the beginning, but it is when you divide the top and bottom by n

[limpid hemlock]

i see, thank u

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[stiff yacht]

,w critical points (1500z)+(500(sqrt(16^2-z^2)))

[stiff yacht]

.close

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[main bolt]

I want to know the integration limits, i know those are wrong but how can i know them?

[marsh citrus]

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@main bolt Has your question been resolved?

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[hollow heron]

would this be (3T - 14) mod 3?

[hasty ruin]

yes, but can you simplify?

[hollow heron]

uh

so T - 14/3?

[hasty ruin]

oh actually i think your expression is wrong .-.

[hollow heron]

oh

well T (mod 3) if we were only to use 3 cent stamps would be 0

but idk where to put the 14

[hasty ruin]

the starting step is to express T in terms of the number of 14c stamps (which is 1) and the number of 3c stamps

[hollow heron]

ye

[hasty ruin]

and reminder that you're not solving for T, you're solving for T mod 3

[hollow heron]

3c + 14?

since 14 is already given (1)

if we were to set 3c as a and 14c as c

If a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ b + d

is what the theorem says

so

3c ≡ 0 (mod 3) and 14 ≡ 2 (mod 3)

so

3c + 14 ≡ 0 + 2 (mod 3)

would this be correct

or am i completely lost?

so final answer I would get is
3T + 14 ≡ 2 (mod 3)

[marsh citrus]

@hollow heron Has your question been resolved?

[hollow heron]

<@&286206848099549185>

[marsh citrus]

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[lean cargo]

I don't know how to solve c

[hasty ruin]

relate the conditions stated by c to the inequalities you've written in parts a and b

[lean cargo]

Like graphing?

Or without

[hasty ruin]

no, not necessary

under the conditions of c, what must be true about the inequalities in parts a and b?

[lean cargo]

They're connected

Would I input the second inequality to the first one?

[marsh citrus]

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[marsh citrus]

@lean cargo Has your question been resolved?

[marsh citrus]

@lean cargo Has your question been resolved?

[marsh citrus]

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[tight pasture]

Can someone help me with Exponential function word problems

[cursive echo]

What’s your problem

[tight pasture]

A town has a population of 19000 and grows at 4.5% every year. To the nearest year, how long will it be until the population will be until the population will reach 51600

[cursive echo]

Population = initial population times e^(rt)

[tight pasture]

I'm not understanding 😕. Sorry math has never been my strength

[cursive echo]

plug and chug into the formula

r being the este

being the rate and t is what you’re solving for (time)

[tight pasture]

Ohh ok

So like this

[cursive echo]

51600=19000e^(.045t)

[tight pasture]

Alr

Sorry for taking long

So it should be 23 years

[marsh citrus]

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[marsh citrus]

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[calm jacinth]

how do limits x rising to infinity work?

[calm jacinth]

like x with an up arrow to infinity

or a down arrow to infinity

[marsh peak]

Same thing as before, but instead of |x - a| < epsilon you have x > M for any M

[crystal lintel]

idt that was the question?

[wise iris]

may i pls get some help

[calm jacinth]

.close

[marsh citrus]

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[trim quest]

Hi, is there anything you've tried yet?

[fair pagoda]

I tried deriving the problem and pluggun in k

[trim quest]

You're half way there

You want to find k such that the derivative at k is equal to the derivative at k+1

[fair pagoda]

Okay so i plug in both x's then set them equal?

[trim quest]

both x's being

k and k+1 ?

[fair pagoda]

Yep

[trim quest]

Yeah, then you can solve for k

[fair pagoda]

So i got 18k=-10

[fair pagoda]

So is k just -5/9

[trim quest]

I get 18k = -9

[fair pagoda]

If possible could i send my work and you just review it quickly?

[trim quest]

sure

[fair pagoda]

Nvm i just saw it when rewriting it ouy

I forgot to subtract the 1 from the 9 on equation

I appreciate the help lots!

[trim quest]

Ahh, that'll get ya

No problem 👍

[fair pagoda]

So k=-1/2 is just the final answer to the problem?

[trim quest]

Yes, that's the value of k, such that f'(k) and f'(k+1) are equal

[fair pagoda]

Alr tysm!!!!

[trim quest]

Sure thing!

[fair pagoda]

.close

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[fierce belfry]

@fierce belfry hello

[fierce belfry]

@hushed egret

hi

.close

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[wraith trench]

hello, how can I find out what the constant ratio is?

[stoic saddle]

well it's the ratio of any two adjacent terms

so either divide 27/5 by 81/25 or divide 9 by 27/5

[wraith trench]

how can that help me find the constant ratio?

[still temple]

because thats how u get it

[wraith trench]

so to get the constant ratio I should divide a number by the number before?

[sleek lake]

yes

[wraith trench]

alright but that gave me a number with infinite decimals, how might I apply that to find the next number in the sequence?

<@&286206848099549185> Could someone help me with this

[still temple]

can you show us?

what you mean

[wraith trench]

surely, this is what I get when I divided 27/5 by 81/25

so how can I use that to figure out the next number in the sequence?

[stoic saddle]

you know what a geometric progression is, right?

also you could have just divided the fractions by hand and gotten 5/3 for the common ratio

[wraith trench]

increase or decrease with constant ratio

I don't understand

how I can calculate the common ratio

[stoic saddle]

a geometric sequence is a sequence in which each term is obtained from the previous by multiplying it by a fixed number

this fixed number is called the common ratio

[wraith trench]

yes i'm aware

but I just can't figure out how do get the fixed number

[stoic saddle]

but you already did

it's 5/3

[wraith trench]

how do you get 5/3?

[stoic saddle]

9/(27/5)...

or (27/5)/(81/25) if you want. it'll give the same result

[wraith trench]

but I did the same calculation and got this

[stoic saddle]

did you use a calculator?

[wraith trench]

yes

[stoic saddle]

why not do it by hand?

the true value is 5/3, but the calculator cannot work with fractions and instead gives you the closest it can do to 5/3

[wraith trench]

I can do it by hand just figured it would be easier

[stoic saddle]

well it isn't.

[wraith trench]

I can't grasp how to solve this I get the same value when I do it by hand

[stoic saddle]

...

show your work?

sounds like some issue you're having with fraction arithmetic.

[wraith trench]

and if I convert to fraction I get 15/9

[stoic saddle]

15/9 is the correct value but it is not fully simplified.

you can still cancel out 3 from numerator and denominator.

[wraith trench]

oh yeah I could get 5/3

okay so I shouldve converted to fraction

I got the right answer now

@stoic saddle Thank you for the help

.close

[marsh citrus]

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[kind pike]

A question on how to write out a formal proof:

Im trying to prove that a choice function K: P(X) \ {∅} --> X: A --> a with A ∈ P(X) \ {∅} and a ∈ X, is surjective. I know that it is surjective because for every a in X, there is a K(A), namely the singleton {x}. Or in other words, every singleton {x} in P(X) \ {∅} gets mapped to x for every x in X.

[kind pike]

I have no idea how i would make this into a formal proof, can anyone help me along please?

[marsh citrus]

@kind pike Has your question been resolved?

[kind pike]

I realise that i can prove the equivalent statement K(A) = X by proving that K(A) is a subset of X and vice versa. Im gonna attempt this but meanwhile i'll keep this channel open in case i run into trouble

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[still temple]

how do you do this limits to +inf?

[distant peak]

the first one is easy
$\sqrt[n]{2} = 2^{\frac{1}{n}}$

[elfin berry]

Ｈｅｒｅｌｓ

[distant peak]

and thats something we know the limits

[marsh citrus]

@still temple Has your question been resolved?

[hazy grove]

So what?

[distant peak]

you want me to do all the exercises or what, I just gave a hint that could make the limits complicated to calculate, the rest is easy

[hazy grove]

I doubt it will help much

[still temple]

i didnt help me much, because i still cant lift the indetermination

got to a point where i got stuck at e^((ln(2)/n) + ln(n))

but the solutions say its : ln(2)

[distant peak]

n(2^{1/n} - 1) is equivalent to n2^{1/n} = n*exp((ln(2)/n) which is equivalent to n x ln2/n = ln(2)

taylor works well here

[hazy grove]

Try using e^a(n)=1+a(n)+o(a(n)) as a(n)->0

I guess taylor is too much in this case, since its a limit of a sequancr, not function

[distant peak]

not really taylor, but equivalence

[still temple]

why?

[distant peak]

2^{1/n} grows faster than 1 at infinity

[still temple]

thx

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[waxen heron]

Can somebody give me some hints regarding this problem?

Ig the point m is (0,m) is that true?

because in the second part of this question, I am asked to prove this so m should not be just a naming point

<@&286206848099549185>

Anyone?

This is the rough figure

When i used the two point formula to find the equation of the line p1(-1,0) and p2(cos theta, sin theta)

I got an equation and i did dy/dx on it and got the result as 1

I'm not sure if it's right, if it is then the slope of the line is 1 , but I feel like i should use m somewhere

Because in all the follow up questions m is used , so that's my doubt..if someone could help please

<@&286206848099549185> sorry for spamming

[marsh citrus]

@waxen heron Has your question been resolved?

[waxen heron]

<@&286206848099549185>

[marsh citrus]

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[lucid hinge]

second derivative of the critical point 0 is 0 tho?

after you first deriviative, what is the subject of the second derivative

is it derivative the critical point or second derivative the original function?

[spice verge]

2x is it

And then you get 2

And plug in 0 for x

[lucid hinge]

ik but the instructions says F''(x*)

[spice verge]

And still have 2

[twin girder]

F’’ is 2nd derivative of F

What is 2nd deriatvive of F?

[lucid hinge]

eh i guess

can someone explain why this is true?

[twin girder]

Why what is true

[lucid hinge]

like the entire process of determining local min and ma

[lucid hinge]

this

i understand that the min/max must have slope 0

what to go from there

2nd derivative determines concavity

wait so ig that makes sense

since the 2nd derivative is positive

it's concave up

so it has a min

hmm ill just wait til someoe confirms me

and close channel

[marsh citrus]

@lucid hinge Has your question been resolved?

[lucid hinge]

@tight furnace

@sharp vessel

@sage heath

can i be confirmed

[sharp vessel]

what

[lucid hinge]

read

[sage heath]

[lucid hinge]

greenstone

[sharp vessel]

ok I read

[lucid hinge]

🥬

[sharp vessel]

my name is literally redstone

[lucid hinge]

redstone is green, contradiction derived

redstone is not red

[sharp vessel]

@lucid hinge yes, if f'(x) = 0 it means there is a min/max

and since f''(x) > 0, it means the function is concave up so its a min

[lucid hinge]

no but is my rasoning correct

ok

nice

thx greenstone

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[sharp vessel]

it's very common to check for min/max using second derivative

np

[marsh citrus]

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[crisp crypt]

Prove (A∩B)∪(A∩B̅) = A using set builder notation and logical equivalences.

[marsh citrus]

@crisp crypt Has your question been resolved?

[marsh citrus]

@crisp crypt Has your question been resolved?

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@crisp crypt Has your question been resolved?

[marsh citrus]

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[upbeat pivot]

i need those steps in order anyone please help

@everyone

help

its due at 11:59 pm

[marsh citrus]

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[mortal flax]

I'm a bit rusty so I'm having trouble with this question

[mortal flax]

.close

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[hasty holly]

chaange it into sin

one term

[hasty holly]

no only one term

sin^2(72)+ cos ^(72)

like thiss

and then property

[marsh citrus]

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[analog kestrel]

any one help

[silk vector]

Whats the question

[analog kestrel]

solve with distance formula to see if congruent

[still temple]

start by skectching a diagram?

[analog kestrel]

??

you dont sketch it

[analog kestrel]

this is an example

[still temple]

yes

[late pasture]

Do you know the distance formula?

[still temple]

it just for u to understnad better what u r doing but ok

[silk vector]

Its easier to think of a solution by sketching the diagram first.

Just a rough sketch, for your better understanding

[analog kestrel]

yes

[analog kestrel]

oh ok

[analog kestrel]

i state if its congruent or not yes

at the end

[silk vector]

Use the distance formula to find all side lengths of the triangle

[silk vector]

If the sides of the two triangle match, then they will be conguent by SSS congruency principle.

And if they don't, they will not be congruent, because corresponding sides of congruent triangles are equal.

[analog kestrel]

so if two of them are equal they match

but they dont match

[silk vector]

So, they aren't congruent

[analog kestrel]

can you make sure that i did it correctly?

because there was another question and they werent congruent either

[silk vector]

Ok, Lemme see.

They are congruent

I think you did something incorrectly @analog kestrel

[analog kestrel]

oh?

i did distance formula

im not sure what i did wrong

[silk vector]

These are congruent

[analog kestrel]

the one i showed isnt right?

the one i just did

[analog kestrel]

botj?

[silk vector]

These ar not

[analog kestrel]

i got the number correct right?

[analog kestrel]

i did it correctly right?

[silk vector]

You need to find all three sides of triangle PQR

You didn't find PR

[analog kestrel]

found my mistake

[analog kestrel]

oh i do?

[silk vector]

Exactly.
The way I will do it is calculate all three sides of both triangles.
And check if we can make pairs of equal sides.

For example, if sides of PQR are 3,4 and 5

And sides of XYZ are 5, 3, and 4

They are congruent

[analog kestrel]

so for pqr and xyz i would have to do PQ QR and PR

and then XY YZ and XZ?

[silk vector]

Yep

[analog kestrel]

also for 10. im confused

it would be UWV= GIH?

@silk vector

so this would be correct right?

and this

[silk vector]

You want to prove triangles UVW and GHI are congruent By ASA.
You know angle U equals angle G
Angle V equals angle H

In ASA congruency, you have to show two angles and the side between are equal.
You know currently that two pairs of corresponding angles are equal.
What is the side between?

[analog kestrel]

so it would be congruent if two sides are equal

[silk vector]

Yes. Which two sides?

[analog kestrel]

U,G V,H

[analog kestrel]

right?

[silk vector]

Hmm
You have shown the correspondence correctly.
U corresponds to G
V corresponds to H

But in ASA congruency, a side of triangle UVW must be equal to a side of triangle GHI.
Which side of triangle UVW should be equal to which side of triangle GHI?

[analog kestrel]

W and I

[analog kestrel]

W and I right?

[silk vector]

Is W a side?

Sides are UV, VW and WU, correct?

[analog kestrel]

ohhh yes

that would be V H then though its a side

@silk vector

[silk vector]

How come V H is a side?

What are the sides of triangle GHI?

[analog kestrel]

H?

its okay ill ask my teacher

you dont have to help me but thanks so much

[marsh citrus]

@analog kestrel Has your question been resolved?

[marsh citrus]

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[thin bison]

Why I got diff answer?

Where did I go wrong??

[hasty ruin]

the answer is just wrong, you're correct

[twilit arrow]

i think the answer they gave you is wrong

[thin bison]

Ok

Thx

.clos3

.close

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[still temple]

Help

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

What does A.O.S mean

Anyways this is all graphically shown, so what's the problem?

Idk

Idk how to solve this

I’m trying to help my son with homework

[marsh citrus]

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[marsh citrus]

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[upper gust]

is this correct

[main idol]

not quite

you can only simplify the denominator after you take the limit. but you still have the limit expression out front because you haven't taken the limit in the numerator yet

so the denominator stays 3 + 5/n

[marsh citrus]

@upper gust Has your question been resolved?

[upper gust]

ok thx

[marsh citrus]

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[stuck jasper]

can anyone help me with this question

[marsh citrus]

Please don't occupy multiple help channels.

[stuck jasper]

I cant make out a performance function

[main idol]

I closed your other channel

[stuck jasper]

sorry i didnt know how to close it

thanks tho

[marsh citrus]

@stuck jasper Has your question been resolved?

[marsh citrus]

@stuck jasper Has your question been resolved?

[marsh citrus]

@stuck jasper Has your question been resolved?

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[drifting siren]

is it a better way to do this without my pc crashing?
z initial value= 100000
z=0.9995*z
this is based on "per second"
aand i would like to know what the value is after x days...
soo iterate over 70000 times

[sleek lake]

yeah exponentiation

assuming python, **

[drifting siren]

thx

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[green reef]

Someone can help me with that: Tina sold bags of popcorn at a bake sale. In the morning, Tina paid the booth fee of $36.50 and sold the bags for $0.83 each. In the afternoon she sold the bags for $0.68 each. Her profit in the morning was the half as her profit in the afternoon. How many bags of popcorn did Tina sell in the morning?

[green reef]

I dont know how to solve this problem

<@&286206848099549185>

<@&286206848099549185>

Tina sold bags of popcorn at a bake sale. In the morning, Tina paid the booth fee of $36.50 and sold the bags for $0.83 each. In the afternoon she sold the bags for $0.68 each. Her profit in the morning was the half as her profit in the afternoon. How many bags of popcorn did Tina sell in the morning?

.close

[marsh citrus]

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[green reef]

.reopen

[marsh citrus]

✅

[green reef]

please

Tina sold bags of popcorn at a bake sale. In the morning, Tina paid the booth fee of $36.50 and sold the bags for $0.83 each. In the afternoon she sold the bags for $0.68 each. Her profit in the morning was the half as her profit in the afternoon. How many bags of popcorn did Tina sell in the morning?

[still temple]

Can you take a photo or screenshot of the whole problem

[green reef]

ok

ready

<@&286206848099549185>

[marsh citrus]

@green reef Has your question been resolved?

[ionic lava]

x: sold bags in the afternoon
y: sold bags in the morning

(0.83)*2*y = (0.68) * x
y = 68/166 x

there's something missing in the problem

[green reef]

I told it to my teacher buy he ask me that the problem is correct

[ionic lava]

at least he need to give you how much she gains

to solve this problem

[green reef]

ok

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[burnt abyss]

$x^2-2x-63\geq 0$

[elfin berry]

Master Oogway

[burnt abyss]

now i usually find the roots

then solve graphically

is there any other method?

perhaps a shorter one

?

[high pine]

you can do sign chart but it's harder

I guess

graphing schematic plot is the fastest method I think

[crystal wraith]

yeah, it depends on what YOU find easy or hard.

[burnt abyss]

quick

not easy or hard

i want quick

[high pine]

usually hard is connected with long time (e.g. calculations, strategy etc.)

[burnt abyss]

so my method is the quickest?

[cerulean rover]

I think so.

[wet zenith]

Wavy curve algorithm

[burnt abyss]

yeah thats what i use i think

ok thanks

.close

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[cerulean rover]

Isn’t it just a shaded area of a parabola? No need to FOIL even

[marsh citrus]

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[burnt abyss]

wdym

[marsh citrus]

@burnt abyss Has your question been resolved?

[cerulean rover]

You do need to solve for x so you know the 2 intercepts of 63 @burnt abyss

[marsh citrus]

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[copper drift]

is this right? is a positive?

i dont think it is

[marsh citrus]

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[upper plume]

can someone help

[hidden plaza]

should be 4+ show your work

[still temple]

how is this 40 points LMAO

anyway series solution should work

[upper plume]

its from homework

there are only 3 questions because first one takes like an hour to complete for some reason

[still temple]

$y = \sum_{n = 0}^\infty a_n x^n$

[elfin berry]

Maxim

[upper plume]

I tried power series

but the answer keeps going on forever?

[still temple]

yes because it's infinite

[upper plume]

how do I type that as answer

[still temple]

you just write down the first 3-4 terms

[upper plume]

ahh

it worked-_-

thanks

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[hallow kettle]

Is the interior of an open set always the set itself?

[marsh citrus]

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[marsh citrus]

@hallow kettle Has your question been resolved?

[hallow kettle]

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[still temple]

basic algebra, 8th grade 14yo level,

How do I resolve calculations with multiple different variables?
like

3x + 4y²(2x²*6xy²)+ 10y - 3x² = ??

I was sick during this and no classmate knows this either

[still temple]

Ill have a test for this thing

[tall umbra]

It's just expand and simplify right?

[still temple]

im not from an anglophonic country, what is exactly that

[tall umbra]

make the expression simpler

[still temple]

like this? yes

[tall umbra]

yes

Ok so

what have you tried

[still temple]

A classmate gave me this and I dont know following things:

Why the hell did they got -15a²b²?
I. Why didnt they calcule the 5² which is 25 and 3b² which is 9b (right?), or are you not susposse to do that?
I. Where does a² come from?

[tall umbra]

very unclear image

brb

[still temple]

Shouldnt 5²3b² be - 259b²

[tall umbra]

gotta get my glasses

[still temple]

Alrigjt

[tall umbra]

1ab * (-2ab) - 5² * 3b² + 3a * 10 * ab^2
this?

[still temple]

ill write it

7ab * ( -2ab) -5² * 3b² + 3a * 10 * ab² =

they write very blobby i know

[tall umbra]

ok so

first of all

he/she is wrong

second of all

3b² isn't 9b

the square is on the b

it means

3 * b * b

3b^2

[still temple]

oh

but where a² came from

[tall umbra]

and yeah, you're supposed to square the 5

[still temple]

yh she prob just copied wrongly from the board

but where did a² came from

i see they all have been gave an a²

why

[tall umbra]

ok you know the order of operations right?

[still temple]

yes

[tall umbra]

just to make sure

ok

lets just do it by parts then

first of all...

7ab * ( -2ab)
this

do you know what to do for this part?

[still temple]

-14ab

[tall umbra]

ok no

[still temple]

ahh

-14a²b²?

[tall umbra]

7ab means 7 * a * b
-2ab means (-2) * a * b

so
7ab(-2ab) = 7 * a * b * (-2) * a * b

or 7 * (-2) * a * a * b * b = -14a²b²

yes

[still temple]

alright so -14a²b² -...

5² * 3b²

[tall umbra]

yes

[still temple]

25 * 3b²

25x3 is 75

but

so

75b²

[tall umbra]

yes

[still temple]

but she put 75a²b²

[tall umbra]

she probably wrote the question wrong 🙂

she probably meant to write
5a² * 3b²

but forgot to wrote the a

so the question should have been

7ab * ( -2ab) -5a² * 3b² + 3a * 10 * ab² =

[still temple]

so -14a²b²*75b²+..

3ax10xab²

30a²b²

right

[tall umbra]

not * 75b^2

[still temple]

?

[tall umbra]

but yes 30a²b²

[still temple]

i was using the old version

[tall umbra]

yes still not * 75b^2

7ab * ( -2ab) - 5² * 3b² ≠ -14a²b²*75b²

it should be

-14a²b² - 75b²

[still temple]

oh yeah

i didnt see that

so -14a²b²-75b²+30a²b²

[tall umbra]

yes ok almost done

focus on the

-14a²b²-75b²**+30a²b²**

[still temple]

we need to do -14 and 30

[tall umbra]

yes

[still temple]

bcs common signs

[tall umbra]

yes

[still temple]

16

[tall umbra]

yes

[still temple]

16a²b²-75b² ?

[tall umbra]

yes

that's it

you're done

[still temple]

alright

yeah i was confused about the power and letter "a" it came out of nowhere

ty so much

.close

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[tall umbra]

you're welcome

[marsh citrus]

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[oak shell]

does infinity * 0 defined?

[marsh peak]

No, it's not defined

[marsh citrus]

@oak shell Has your question been resolved?

[marsh citrus]

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[ember wind]

<@&286206848099549185>

[proven timber]

!15m

[marsh citrus]

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[still temple]

Translation: ABC is a right triangle, where AB is perpendicular to AC, and [EF] is perpendicular fo [BC].

If |BF|=|FC|, then m(ADE)=m(EDC), m(DEF)=80°

Based on what has been said, how many degrees is m(DCB)?

[ember wind]

thanks

[still temple]

Yeah can speak a bit of Turkish so thought it would be helpful for others

[ember wind]

thanks again

[marsh citrus]

@ember wind Has your question been resolved?

[ember wind]

<@&286206848099549185>

[ember wind]

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[ashen flicker]

IB MATHS question) Im confused on what "show that" means and how should I approach a

[ashen flicker]

/close

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[pallid pine]

for ii), since its a gradient vector field, the answer should be 3 (since x and z are both start at 0 and end with 1)

[pallid pine]

yet doing the integral gives you 3.375

because the integral becomes 27t^7dt

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[ivory laurel]

How do i go about evaluating the lim. at x=0 for x^(-p)ln(x) where x,p>0

[marsh citrus]

Please don't occupy multiple help channels.

[sour relic]

$\frac{\ln (x)}{x^p}$

[elfin berry]

Fucktalogist

[sour relic]

limit of x to zero of ln(x) is -infinity

and denominator will be zero

so we have -infinity / 0

[marsh citrus]

@ivory laurel Has your question been resolved?

[ivory laurel]

So essentially the limit is divergent tending to negative infinity

[marsh citrus]

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[brisk scarab]

hey there, which one?

@jovial fractal ^

[jovial fractal]

7

[jovial fractal]

7

[marsh citrus]

@jovial fractal Has your question been resolved?

[brisk scarab]

my best guess is solving the whole of LHS and then comparing coefficients

what have you done so far?

[marsh citrus]

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[jovial fractal]

.reopen

[marsh citrus]

✅

[jovial fractal]

This

[brisk scarab]

Well

Lets try to solve it then

Okay so

Writing the question $$
p(x+2)(x+1)+q(x-3)(x-1)+r(x-2)(x-6)=2x^2+7x-13$$

[elfin berry]

n11

[brisk scarab]

Solving the LHS:
\begin{align*}
p(x+2)(x+1) &+ q(x-3)(x-1)+r(x-2)(x-6)\
&=p(x^2+3x+2)+q(x^2-4x+3)+r(x^2-8x+12)\
&=(p+q+r)x^2+(3p-4q-8r)x+(2p+3q+12r)
\end{align*}

[elfin berry]

n11

[brisk scarab]

Now
$$(p+q+r)x^2+(3p-4q-8r)x+(2p+3q+12r)=2x^2+7x-13$$
Therefore, we have
\begin{align*}
p+q+r &= 2\
3p-4q-8r &= 7\
2p+3q+12r &= -13
\end{align*}

[elfin berry]

n11

[brisk scarab]

Now you can solve these 3 equations and you'll get the values :^)

[marsh citrus]

@jovial fractal Has your question been resolved?

[marsh citrus]

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[normal pollen]

Can anyone help

[still temple]

What does Hesablayin means?

[still temple]

Calculate/compute

Source: I can read the language

[still temple]

Amazing. Turkish is wonderful.

[still temple]

$\frac{\sqrt{42-\sqrt{42-\sqrt{42}-\cdots}}}{\sqrt{6-\sqrt{6-\sqrt{6-\cdots}}}}$

[elfin berry]

3317

[normal pollen]

It is Azerbaijani language which belongs to Turkic family group

Now this question

[still temple]

Yeah it hurts my brain too.

Wish I could help more, but still, what I'd do is figure out if there's something interesting when you convert the square roots to raising to the power of a half.

[marsh citrus]

@normal pollen Has your question been resolved?

[still temple]

I think you need to try to use exponents laws or try computing them to a certain amount and finding that value. Then continue computing to a higher and higher value until

You can find a limit it approaches

[marsh citrus]

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[balmy vault]

Calculate the volume of the body that appears when the area between the graphs of f(x)=e^x^2 for x in [0,1] and g(x)= cos(x) for x in [0,1] and rotates around the y- axis

[balmy vault]

im struggling a bit with this one

[cloud iron]

Want to start by graphing it?

[balmy vault]

i have graphed it i can send a pic 2 sec

[nova totem]

Sounds like washer method moment

[cloud iron]

Depending on which variable you want to integrate wrt it could be either

Washer might be easier

Yeah washer would definitely be easier lol

[balmy vault]

here

[cloud iron]

Looks good so far

[balmy vault]

yeah i think so too but i have a bit of problem actually finding out what the texts wants tbh

im assuming we want to find the triangle ish area

that then rotates around the y axis

which should be okay but e^x^2 is kinda tricky

[cloud iron]

Actually e^x^2 is very tricky because iirc we can't integrate it

Unless we use a sum

[balmy vault]

yeeee

and i really dont know where to go from here

since we are only going from 0 to 1

wont e^x^2 act the same as e^x

and that we can integrate

bc e^0^2 = e^0 and e^1^2 = e^1

is that possible?

[proper zodiac]

Sure they agree on 0 and 1 but try 1/2

[balmy vault]

i was hoping we could discount that 😔

<@&286206848099549185>

[marsh citrus]

@balmy vault Has your question been resolved?

[balmy vault]

.close

[marsh citrus]

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[vernal spear]

1

[marsh citrus]

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[still temple]

How do i even solve this omfg

is r = sqrt(+-i) even correct

But then again there must be 4 solutions not only 2

[marsh peak]

Yes there are 4 solutions

First pair comes from r^2 = i and the other comes from r^2 = -i

[still temple]

So

Can I come to this conclusion with r = sqrt(+-i)

[marsh peak]

No

[still temple]

(If its correct in the first place?

I see

[marsh peak]

You need to consider the cases separately

[still temple]

Alright

Tysm 🙏

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[balmy vault]

work done is w = F *s when the force is in the same direction as the displacement. if the force as a function of F(s) and the work done between the points s = a and s = b is defind by

work = integral from a to b F(s) ds

a block is pulled over the floor by a rope attached at the bottom of the block and goes the a pulley 1 m over the ground the F is constant and equal 10 N but the horizontal component of the force that does work

let x be the distance from the block to the point 1m under the pulley
calculate the work that be done to move the block from x=10 to x = 10
Hint: start by calculating the magnitude of the horizontal component of the force when the block is as in the figure

[balmy vault]

ill add the figure

.close

[marsh citrus]

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[balmy vault]

.close

[main idol]

@balmy vault bot is slow. Just wait a few minutes

[marsh citrus]

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[balmy vault]

work done is w = F *s when the force is in the same direction as the displacement. if the force as a function of F(s) and the work done between the points s = a and s = b is defind by

work = integral from a to b F(s) ds

a block is pulled over the floor by a rope attached at the bottom of the block and goes the a pulley 1 m over the ground the F is constant and equal 10 N but the horizontal component of the force that does work

let x be the distance from the block to the point 1m under the pulley
calculate the work that be done to move the block from x=10 to x = 2
Hint: start by calculating the magnitude of the horizontal component of the force when the block is as in the figure

[balmy vault]

ill add the figure

i can elaborate to the best of my knowledge if needed

[deft apex]

from x 10 -> x 10?

[balmy vault]

sorry typo

x = 10 to x = 2

[deft apex]

alr

[balmy vault]

any insight into this task would be wonderful

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[marsh citrus]

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[lucid hinge]

how to use the puiseux

wtv to solve

[stoic saddle]

puiseux what?

[lucid hinge]

puiseux series

maybe

im not sure

[stoic saddle]

have you been explicitly instructed to use those

bc like. yuck!

[lucid hinge]

no somebody told me i can use it

[stoic saddle]

who and where

[lucid hinge]

fairylog told me

anyway, herei s my other answer

it works

but fairylog said puiseux would be faster

[stoic saddle]

eugh

i have no idea how youd be expected to make a puiseux series out of this shit

[lucid hinge]

eh ok thx