help-33

[pallid agate]

so the 4th one?

[sleek lake]

take the number pi

take first 2 digits, take first three digits...

they are rational numbers

[devout mauve]

bit overcomplicated. just take the negative integers

[sleek lake]

could be rational from the beginning, of course
0.3
0.33
0.333

only a bit maybe

[pallid agate]

you say one of the choices is clearly wrong?

[devout mauve]

all 4 sets are infinite

[pallid agate]

thats what I thought

.close

[marsh citrus]

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[marsh citrus]

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[lucid fossil]

Hi! I am trying to solve a differential equation, but can't find good material to solve this one. I found ways to solve it where r(x) is just a constant, but not a function, any help?

u"(x)-r(x)×u'(x)=0

[fathom ridge]

Sub u' = w

w' + rw = 0

Now it's seperable

w'/w = -r

ln(w) = -rx + C

[lucid fossil]

Then exp(•)?

[fathom ridge]

yeah

[devout mauve]

somewhere along the way you forgot that r isn't necessarily constant

[fathom ridge]

They said r is a constant

[lucid fossil]

It's not tho

[fathom ridge]

Oh wait

I misread

Stupid me

[lucid fossil]

No worries x)

[devout mauve]

either way, same approach

[fathom ridge]

Yeah well then isn't it just a Bernoulli equation otherwise

or yeah

[devout mauve]

just requires finding the integral of r

[fathom ridge]

yup

[lucid fossil]

The what of r? Should I just integrate r(x)?

[devout mauve]

well but then you only have w which is u' so you have to integrate again. which by that point is probably painful

yes. integrate r(x)

[devout mauve]

from here. w'(x)/w(x)=-r(x), integrate both sides with respect to x

[lucid fossil]

Alright, currently working my way through this ^^

Ended up with this expression 🤔

Feels like a kinda wonky solution tbh

[lucid fossil]

Thoughts?

[devout mauve]

that's correct

[lucid fossil]

Nice! Thank you so much!

Does this type of differential equation have a name?

I see that it's second order, but is there more to it?

[marsh citrus]

@lucid fossil Has your question been resolved?

[marsh citrus]

@lucid fossil Has your question been resolved?

[marsh citrus]

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[primal trench]

A 9 cm high pyramid has an equilateral triangle as its base, whose incircle has a radius of 2.5 cm. Find the surface area of the pyramid.

[primal trench]

Base sketch

[marsh citrus]

@primal trench Has your question been resolved?

[primal trench]

<@&286206848099549185>

[marsh citrus]

@primal trench Has your question been resolved?

[marsh citrus]

@primal trench Has your question been resolved?

[unborn condor]

that sketch is pretty bad tbh.
The incircle should be touching all three sides, and yours is not touching any.
It should also be tangent to each side, so the radius is perpendicular to the tangency point

This would be a better drawing. I added the bisector

now, you know it's an equilateral triangle, and you know that the circle has radius 2.5cm.
Which means that AB=2.5cm.
Since you know ABC is a right triangle, and the angle on the left is 30º, you can get both CB and CA with the trig functions.
Having CA gives you the side of the triangle, since it's twice that.
Having the side of the triangle you can calculate the height with pythagoras.
With that, you got the area of the base.
Since you got the height of the pyramid, you can compute now the volume

[marsh citrus]

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[hot mantle]

I don’t understand how my answer is wrong for question d

Apparently it’s sqrt(3+x)

It should be sqrt(4-|1-x|)

Right?

[bright jay]

$(1 - x)^{\frac{1}{2} \cdot 2} = (1 - x)^{\frac{2}{2}} = (1 - x)$

[elfin berry]

dldh06

[hot mantle]

What about this tho

@bright jay

[bright jay]

This is true, yes but you can do what I presented above

And get the correct answer

[hot mantle]

But if x is greater than one, then the final value is a negative number

[hot mantle]

Which is inconsistent with this

[late geode]

$(\sqrt{x})^2$ isn't the same as $\sqrt{x^2}$

[hot mantle]

Ahhhh ok

[elfin berry]

ℝam()n()v

[hot mantle]

That’s what I was thinking

Thank you

.close

[marsh citrus]

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[digital otter]

need help combining this transformation

here is the graph in the textbook

but how?

my immediate instinct is take multiply all the y values by 1/2

Can someone please explain?

hello

@fluid mica

<@&286206848099549185>

[trim quest]

yeah that graph doesn't match that definition for g

are you sure you're looking at the right solution?

you posted question number 35 but under your graph it looks like the next question is 42

[hot mantle]

Ye that doesn’t look right

[trim quest]

your instinct is right (for the first step)

[digital otter]

this text book fucking sucks

it shows answers for every odd question and because I libgenned it im pretty sure the questions cut off

I just want to know if what im doing is right

I multiply each y value by 1/2 then shift down one

if thats the case how in the every living fuck am I taking a y value of one to a y value of 3

i got a test tmrw this shit pisisng me off

[trim quest]

yeah, that's right

what's wrong with 1 and 3?

[digital otter]

no im just saying the graph

jumps to a y value of 3 which is in no way possible if im multiplying 1 by 1/2

sorry this question has been sending me through a loop

[trim quest]

oh yeah that graph is wrong

[trim quest]

this

[trim quest]

does not match this

[digital otter]

well

the graph i sent was the transformation applied to the one i sent

are you saying that 1/2f(x)-1 isnt that

[trim quest]

it is a transformation of the one you sent

but it's not 1/2 f(x) - 1, no

[digital otter]

https://cdn.discordapp.com/attachments/907022703230345237/1157110460663992360/image.png?ex=65176a97&is=65161917&hm=bc57389e0521b8dfa97f64c3b4532d6e387ad913ae7466acafb9cba2e30ef07a&

this right

[trim quest]

yes. that is not 1/2 f(x) - 1

[digital otter]

in the context of this

https://cdn.discordapp.com/attachments/907022703230345237/1157110460663992360/image.png?ex=65176a97&is=65161917&hm=bc57389e0521b8dfa97f64c3b4532d6e387ad913ae7466acafb9cba2e30ef07a&

no

https://cdn.discordapp.com/attachments/907022703230345237/1157110460663992360/image.png?ex=65176a97&is=65161917&hm=bc57389e0521b8dfa97f64c3b4532d6e387ad913ae7466acafb9cba2e30ef07a&

the original one i sent

[trim quest]

bro lol

[digital otter]

I mean

[trim quest]

yeah, I know what you mean lol

[digital otter]

okok sorry thanks a bunch bro

I really appreciate it

[trim quest]

What you said was right about squishing the graph vertically by 1/2 and shifting it down 1

no problem 👍

[digital otter]

just

wait

1 more if u can

if i had

[trim quest]

sure

[digital otter]

lets say

g=(2x)

f(2x)*

i would divide by 1/2 right

[trim quest]

you'd divide the x values by 2

that would make it 2 times skinnier

[digital otter]

and if I had 2f(x)

I would multiple my y values?

[trim quest]

yes

[digital otter]

ahhhhhhhh okay you have given me the moses brain split moment

real goat

thanks a bunch

.close

[trim quest]

No problem glad it helped

[marsh citrus]

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[cosmic mantle]

hello can someone please explain why y diffrentiates to e^t(1+t) and not just te^t

[desert dirge]

product rule

[cosmic mantle]

ohhh ok it makes sense now thanks, i dont know why but using product rule never comes to my mind lol

.close

[marsh citrus]

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[still temple]

i dont understand this part

how do we know that

[marsh citrus]

@still temple Has your question been resolved?

[floral linden]

chain rule

[still temple]

wouldnt it just then be d^2z/dx^2 * dx/dt?

oh

thats equivalent

isnt it

wow

ok

.close

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[thorny coral]

help

[terse turtle]

!status

[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[thorny coral]

1

[marsh citrus]

@thorny coral Has your question been resolved?

[terse turtle]

do you know implicit diff?

[terse turtle]

it might be more convenient to bring all y's to one side

[thorny coral]

kinda - still getting the hang of it

[thorny coral]

so have it be 0 = (x-2)/(y+3) - y ?

[terse turtle]

i was thinking $y(y+3)=x-2$

[elfin berry]

chlamydia

[thorny coral]

oh

and then do I derive both sides?

[terse turtle]

so the general idea is if you want dy/dx, you can differentiate all your x normally, but when differentiating y, there's an extra *dy/dx

yeah go ahead

[thorny coral]

so it's gonna be dy/dx ( dy/dx ) = 1?

[terse turtle]

huh

where'd you get that

[thorny coral]

ok well thats where im stuck

what am I deriving from the left side?

[terse turtle]

differentiate with respect to y and then multiply by dy/dx

[thorny coral]

oh

I see it now

I got it

[terse turtle]

cool

[thorny coral]

.close

[marsh citrus]

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[proud hemlock]

How do i find the coordinates for the point where the side of AB intersect with the line perpendicular to it? So far i know that the gradient of that line is the negative reciprocal of AB

[marsh citrus]

@proud hemlock Has your question been resolved?

[marsh citrus]

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[compact flower]

how

genuinely just don't know what i can even do here

i've tried (1(-4))+4(7)

[terse turtle]

what have you got for h'(x)

[compact flower]

h'x=f'x+g'x right?

[terse turtle]

$(x,f(x))'\neq f '(x)$

[compact flower]

and i thought that xfx would translate over to x

[elfin berry]

chlamydia

[terse turtle]

you need product rule here

[compact flower]

i thought it would be

xf'x

how would i use product rule here lol

[terse turtle]

two functions x and f(x) multiplied together warrants product rule

just that f(x) isn't specified

[compact flower]

oh so it'd be like

(1)(-4)+(x')(5)

i just dont get how i take the derivative of x on its own when it's just... 1?

[terse turtle]

yes

then it's 1

[compact flower]

so is it just

1

+28

ah

i didn't know that a coefficient variable needs to still be treated as such even if its already given a value, thanks

.close

[marsh citrus]

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[merry yarrow]

can anyone help me explain this

[marsh citrus]

@merry yarrow Has your question been resolved?

[static quarry]

!status

[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[merry yarrow]

1 and 2 ish

ive done alot of research about this question online and everywhere is different

[static quarry]

have you tried computing P(not A and not B) and comparing it with P(not A)P(not B)?

[merry yarrow]

like this?

[static quarry]

right, see if that's also true if you replace $A$ with $\overline{A}$ and $B$ with $\overline{B}$

[elfin berry]

Bungo

[merry yarrow]

it isn

i thought that isnt true?

how would i like check whether thats true for A and B compliment

[static quarry]

well you know that
$$P(A \cap B) + P(A \cap \overline{B}) + P(\overline{A} \cap B) + P(\overline{A} \cap \overline{B}) = 1$$
and you have enough information to calculate the first three terms on the left side

[elfin berry]

Bungo

[static quarry]

that will allow you to find $P(\overline{A} \cap \overline{B})$

[elfin berry]

Bungo

[static quarry]

then compare that with $P(\overline{A})P(\overline{B})$ and see if they are equal

[elfin berry]

Bungo

[merry yarrow]

hold on

i think i have a way

nvm

i dont

@static quarry i have this, now what?

[static quarry]

you know P(A and B) = P(A)P(B) since A and B are independent

[merry yarrow]

so is it 1 - P(A)P(B)?

[static quarry]

can you compute P(A' and B) given P(B) and P(A and B)?

[static quarry]

is what that

[merry yarrow]

P(A and B) = P(A)P(B) so in the thing wouldnt i replace P(A and B) with P(A)P(B)

how am i suppose to compute P(A' and B) im lost

[young owl]

https://cdn.discordapp.com/attachments/907022703230345237/1157155069360345138/image.png?ex=65179423&is=651642a3&hm=e90692fc07c98e59e5623d1aab2a76767564bfabd1d4b66c770b35d6124e0342&

the answer is yes

[merry yarrow]

why though?

[young owl]

I'm trying to think of a good example

[merry yarrow]

ok

but does this not work?

[young owl]

it does

I misread sorry

your proof is correct the ans is yes

[merry yarrow]

okok thank you

[marsh citrus]

@merry yarrow Has your question been resolved?

[marsh citrus]

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[proud hemlock]

.reopen

.reopen

[still temple]

Hey @terse turtle, you helped me in another channel, sorry I was AFK

[still temple]

Can you help me with this formula please?

[elfin berry]

?

[still temple]

What does X^2 mean

You square the random variable?

When computing E(X)?

And is there not a formula for the standard deviation?

I feel like I haven't seen the one above in class before

[marsh citrus]

@still temple Has your question been resolved?

[young owl]

X² means you square the values that X can take

[stoic saddle]

yes

[stoic saddle]

there is, it's sqrt(variance)

[young owl]

for example if your variable is 0 with proba 1/2 and 2 with proba 1/2
E(X) = 1/2 * 0 + 1/2 * 2 = 1
and E(X²) = 1/2 * 0² + 1/2 * 2² = 2

[still temple]

Oh, okay

Let me try this

Is this fine?

Especially last question

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

Can anyone please help me

[terse turtle]

3rd page, end of third line:

$E^2(X)=(2)^2$

[elfin berry]

chlamydia

[terse turtle]

rest looks fine

[terse turtle]

$\sigma=\sqrt{0.9}\approx0.948$

[elfin berry]

chlamydia

[terse turtle]

i'm still concerned about this

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[tender mantle]

,rotate

[tender mantle]

I got by solving

[acoustic field]

the answer is 3

[still temple]

@terse turtle thanks a lot for helping out, really appreciate it

[tender mantle]

<@&286206848099549185>

[marsh citrus]

@tender mantle Has your question been resolved?

[marsh citrus]

@tender mantle Has your question been resolved?

[marsh citrus]

@tender mantle Has your question been resolved?

[tender mantle]

.close

[marsh citrus]

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[boreal aurora]

Hi

[boreal aurora]

Hold on

[waxen dust]

,rccw

[marsh citrus]

@boreal aurora Has your question been resolved?

[boreal aurora]

.close

[marsh citrus]

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[echo folio]

∃y ∈ R such that ∀x ∈ R we have y^4= 4x

[echo folio]

We have to determine if this is true or false

Justify to be exact

I don't know how to approach this

[stoic saddle]

do you think it's true or false

[echo folio]

I think its false

[stoic saddle]

then prove its negation

[echo folio]

hmm

The negation is

∀y ∈ R , ∃x ∈ R such that y^4 = 4x

Right?

[stoic saddle]

no

one small detail

[echo folio]

hmmmmmmmmmmmmmmmmm....

What did I miss

hmm..

oh

y^4 is not equal to 4x

[stoic saddle]

right

$(\forall y \in \bR)(\exists x \in \bR)(4x \neq y^4)$

[elfin berry]

Ann

[mystic gust]

the negation is true because if we take x = y^4 we get 4y^4 not equal to y^4 which is true

which implies that the original proposition is false

[marsh citrus]

@echo folio Has your question been resolved?

[stoic saddle]

4y^4 isn't always unequal to y^4.

[marsh citrus]

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[modern belfry]

How do I get symbols like the element symbol, rational numbers, and integers on latex overleaf?
and the implies symbol for like p implies q
can I just do => or is there a specific way to get a symbol?

[dire spire]

$\implies$

[elfin berry]

saad

[marsh peak]

[ \in ]
[ \mathbb{Q} ]
[ \mathbb{Z} ]

[dire spire]

$\in$

[elfin berry]

A Lonely Bean

saad

[devout mauve]

if you dont know the command of a symbol you can look it up on detexify

[stoic saddle]

#latex-help btw

[devout mauve]

or google

[stoic saddle]

also amssymb package

i think?

for the mathbb letters

[dire spire]

https://tug.ctan.org/info/symbols/comprehensive/symbols-a4.pdf

[marsh citrus]

@modern belfry Has your question been resolved?

[marsh citrus]

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[celest folio]

so do i do 5-5(Sqrt x - 4) + 5x^3 - 20?

for a

[pastel leaf]

(f+g)(5) =f(5)+g(5)

plug in 5 in f

plug in 5 in g

add the results

@celest folio

[celest folio]

thx

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[winter flicker]

a(n) = 4*a(n-1) - a(n-2), with a(0) = 1. Help me find the explicit formula/closed form formula for this

[marsh citrus]

@winter flicker Has your question been resolved?

[pastel leaf]

can u use generating functions?

[winter flicker]

idk what that is, havent learnt in my cs class

also its 1,3,11,41,153... for values of n that are 0,3,6,9,12...

[pastel leaf]

i think we need two initial values

like whats a(1)=?

[winter flicker]

there is no 1

its 0,3,6,9...

n = 0 would the inital value in this case

[pastel leaf]

a(1) = 4*a(0) -a(-1)

a(2) = 4*a(1)-a(0)

[winter flicker]

a(n) = 4*a(n-3) - a(n-6) this should be written as this ig

[pastel leaf]

okay i plug in n=0
whats a(-3)?

[winter flicker]

Nothing

[pastel leaf]

a(0) = 4*Nothing - a(n-6)

need more context here

[winter flicker]

4*(n-3)

[pastel leaf]

u have a there >_<

so this is the formula?
a(n) = 4*(n-3) - a(n-6)

[winter flicker]

It’s a(n) = 4*a(n-3) - a(n - 6)

[marsh citrus]

@winter flicker Has your question been resolved?

[marsh citrus]

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[tardy summit]

i was doing this question and was stuck midway

[marsh citrus]

@tardy summit Has your question been resolved?

[marsh citrus]

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[quick moth]

I’m confused on where to start

I made the denominator

1-cos^2x

But now I’m lost

I assume I have to factor the numerator but I don’t really know how

Can I factor the same as -4x^2-3x+1?

[open flame]

im struggling

[pliant hedge]

#❓how-to-get-help

[pliant hedge]

You're aware of trig Identities correct?

[quick moth]

Yes

I know my trig identities for the most part

[open flame]

i did

[quick moth]

[-2, 2]

Lowest point is -2. Highest is 2

[pliant hedge]

you're posting in someone elses channel just fyi

okay dont worry about the right side you should be able just to manipulate the left side into being the right side using those identities

[quick moth]

Ye

[pliant hedge]

You're going to have to be a little more specific if you need anything else

[quick moth]

I was posting on doing the left

Planning

How

What

How is the numerator an identity

[open flame]

oh

[quick moth]

I have a little hint sheet for a guidance on how to start

And it says

“Factor the numerator, look for Pythagorean identities”

[terse turtle]

you can do this

[quick moth]

oh ok let me try it

[terse turtle]

and pythagorean means $\sin^2x+\cos^2x=1$

[elfin berry]

chlamydia

[quick moth]

Ok so I got here

Now whar should I do?

Oh wait i can separate the bottom into (1-cosx) (1+cosx) right ?

And cancel some things out

[terse turtle]

yes

[quick moth]

Oh I’m done

Ty

Honestly I can’t thank you enough for your help these past days

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[quaint arrow]

So i see that to find the cross product of 2 vectors in R3, you can take the determinant of the vectors

[quaint arrow]

like this:

is it possible to calculate the cross product with vectors in R2, or Rn?

using the determinant formula

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[tough ridge]

help

[tough ridge]

i dont understand this

where do u get 5/6 from?

its about percentages we are learning

?

[proper zodiac]

,calc 5/6

[elfin berry]

Result:

0.83333333333333

[tough ridge]

yeah but that doesnt answer my question lol

how do u get 5/6

above its 83 1/3 percent

how do convert that over to 5/6

[proper zodiac]

Convert 83 1/3 to an improper fraction, divide by 100 and simplify

[tough ridge]

wut....

so first u make 83 a fraction over 100

so it becomes 100/83

rite?

[marsh citrus]

@tough ridge Has your question been resolved?

[late geode]

no

first

convert 83 1/3
to an improper fraction

[marsh citrus]

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[tropic igloo]

How to know if the mapping is function or not?

[wise lance]

So you understand the mapping already right?

@tropic igloo ?

[tropic igloo]

Yess

A mapping diagram represents a function if each input value is paired with one output value

am i correct?

[wise lance]

So the first thing is to check if the function can get two Ys(the thing after arrow) value

For the same x value

One to one
Means that there is only one function value for each x value

meaning any horizontal or vertical line drawn in the graph should not intersect more than 1 point

One to many (not function)
For each x value there are multiple function values

Many to one
For func value there could be multiplie x values that can achieve the same value

[wise lance]

By the way what did you try to do

!status

[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[tropic igloo]

Thanks

but i think A mapping diagram represents a function if each input value is paired with one output value

'will tell u if its a function or not

[marsh citrus]

@tropic igloo Has your question been resolved?

[lofty gyro]

yea, each input paired with on output
but there can be many inputs link to the same output and it still a fuction

[marsh citrus]

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[brave spear]

uh

[brave spear]

.

[marsh citrus]

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[whole minnow]

p

[whole minnow]

subject: Functions

find its domain

so I know that the points that are in its domain are those where the funciton inside of the root are positive

so It should be this

but I don't think i'm supposed to use a graph calculator and I don't know what to do then

[drifting trout]

You're right on the money with how to go about finding the domain. To find this algebraically, it's much easier to factor the polynomial under the square root

That's a very intimidating polynomial, but if you try to divide out something common, such as (x + 1), you might find it looks familiar

[whole minnow]

ok

I think that helps

I managed to factorize something

(-3x^2+3)(x-1)

oh i messed up somewhere

let me check

(-x^2+1)(x-3)

this one is better

(x-1)(x+1)(-x+3) thats a complete factoring

[drifting trout]

Yes that's right

So now we know the domain is everywhere where the product -(x + 1)(x - 1)(x - 3) is non-negative

[whole minnow]

ok

I have to analyze values between these right

yeah that worked

thanks so much friend

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[keen ocean]

7.26 Refer to Exercise 7.11. Suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that P[g1 ≤ (Y − μ) ≤ g2] = .90.

[keen ocean]

i need to provide a formula for g1 and g2 but since they are not necessarily equal on teh bell curve

[marsh citrus]

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[marsh citrus]

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[arctic swallow]

Yo

[arctic swallow]

42 875 is a product of 3 factors in which all r same

[lofty gyro]

do you mean like 125 is made up of 5×5×5
and what 42875 is made up of ?×?×?
like that?

[lofty gyro]

like it like that? @arctic swallow

[arctic swallow]

Yeah

[lofty gyro]

oh okay

[arctic swallow]

That what it says in my book

But

It will take long time to guess

I mean you can't just loop and test going from 0 until u find

[lofty gyro]

so first thing do you notice it can be divided by 5?

[arctic swallow]

Yeah

Its a long ass number so yeah

Sure

There has to be an answer

[lofty gyro]

then since there are 3 same numbers

[dawn gate]

just take the cube root ?

[lofty gyro]

that 42875 can be divided by 5 , three times

[arctic swallow]

How

[lofty gyro]

try do this first and see what you got

[lofty gyro]

i bet lolk means to use a calculator

[arctic swallow]

Its ok i think

[lofty gyro]

well, even with that, would still recommend this method

[arctic swallow]

35 it is

42875^(1/3)

[lofty gyro]

yes

35 is the answer

[arctic swallow]

Thanks for help y'all @lofty gyro @dawn gate

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[rancid storm]

@arctic hare

[still temple]

is this a test

[inland cape]

Where are you stuck

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[rough fulcrum]

I don’t get slops

Slopes

[inland cape]

ok so

do you know the relationship between x and y

in terms of slope?

[marsh citrus]

@rough fulcrum Has your question been resolved?

[rough fulcrum]

uhh slope = y/x I think?

[inland cape]

yeah so

find the amount y changes

and the amount x changes

and then do y/x for each

[rough fulcrum]

y = 2 and x =7

sp 2/7?

*so

[inland cape]

for AF yes

[rough fulcrum]

so thats AF slope?

[inland cape]

yes

[rough fulcrum]

oh wait what

do i just leace lke 2/7

[inland cape]

yeah depends how your teacher wants it

could be a decimal approximation or just 2/7 is fine

[rough fulcrum]

what abt AE

is it 1/7?

@inland cape sorry for tagging

how do u do AD?

its just a line

[inland cape]

so what is 0/7

for ad

and ae is 1/7 yeah

[rough fulcrum]

oh ok ty

so AD is 0/7?

[inland cape]

well what is the value of 0/7

[rough fulcrum]

0

could u help me with one more

i just need osmone to double check it for me

wth this question

[rough fulcrum]

<@&286206848099549185>

[still temple]

it's your math teachers who give you these exercie

[rough fulcrum]

??

[inland cape]

what are you doing here

labeling the segments

or drawing from scratch

and either way i think u have ur negatives wrong

negative slope should be down and to the right, not just a segment that starts in the negative

[rough fulcrum]

huh

could u do one of the negatives for me

so i could see

an example

[inland cape]

\ line will look like this

[rough fulcrum]

for a negative?

[inland cape]

yes

[rough fulcrum]

wait rlly?

[inland cape]

positive is like this /

[rough fulcrum]

isnt it suppose to be positive

oh

huh

i need a visual 😭

[inland cape]

sorry im a bit busy atm trying to multitask

so its hard

[rough fulcrum]

oh

[inland cape]

can u send a pic of the graph without any lines

so i know the boundaries

and ill draw you a negative line

[rough fulcrum]

just a 8x8

[inland cape]

so -8 and +8 are the bounds for both x and y axis?

[rough fulcrum]

huh

i mean this

[inland cape]

ok

gimme a sec

[rough fulcrum]

so all my slopes arent right?

[inland cape]

yes

you had them wrong

[rough fulcrum]

oh

but y is the vertical one

so why isnt it right

[inland cape]

because y is decreasing by 4

so -4/1

=-4 for the slope

[rough fulcrum]

im doing 4

not -4

4/1

[inland cape]

that line has a slope of -4

the one you drew

list the coordinates for the start and end point of that line segment

and tell me the differnce between them

[rough fulcrum]

0,4 and 0,1

i think

idk

[inland cape]

no

so its x,y for coordinates

[rough fulcrum]

yea

[inland cape]

so 0,4 is right

[rough fulcrum]

im so confused

[inland cape]

the other coordinate is 1.0

1,0

so (0,4) and (1,0)

how does x change

and how does y change

from (0,4) to (1,0)

[marsh citrus]

@rough fulcrum Has your question been resolved?

[marsh citrus]

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[fallen stump]

I dont understand the answer

Why did they use hte power rule and do that

[devout mauve]

do you understand why the limit is equal to f'(1)?

[fallen stump]

yes

[devout mauve]

ok

then they decided to compute the derivative in another way

aka power rule

cause that is easier

[fallen stump]

wait

[fallen stump]

actually no, sorry

[devout mauve]

do you know the limit definition of derivative

[fallen stump]

first principles? @devout mauve

[devout mauve]

if you want to call it that

[open kayak]

Let me show another way, though the derivative one is probably faster. \ We have that $a^n - b^n = (a-b)(a^{n-1} + a^{n-2}b + \dots + ab^{n-2} + b^{n-1})$. Thus, [\frac{x^{1000} - 1}{x - 1} = \frac{(x-1)(x^{999} + 1 \cdot x^{998} + \dots + 1^{999})}{x - 1},] which is equal to [x^{999} + 1 \cdot x^{998} + \dots + 1^{999},] which has $1000$ terms and so evaluates to $1000$ for $x \to 1$.

This is how you derive the power rule anyways

(for natural n, that is)

[open kayak]

If you call the limit definition that, yes

[marsh citrus]

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[wooden grotto]

Could someone help me understand why I'm getting c and d wrong?

[spark otter]

when you compute the maximum rate of change (or directional derivative), you have to compute it with a unit vector

<-1600/49,-1600/49> is the correct direction, but not a unit vector

[wooden grotto]

so its 1600/49 for c and -1600/49 for d?

Or am I not thinking about this properly?

<@&286206848099549185>

[spark otter]

nono, as I said the direction is good

however, if you compute $|<-1600/49,-1600/49>| = 1600/49 \neq 1$

[elfin berry]

rafilou2003

[spark otter]

the norm of the chosen vector is not 1, therefore the directional derivative cannot be computed

so you have to... normalize your vector

[wooden grotto]

Once I normalize it, what then?

After normalizing this vector: <-1600/49, -1600/49>, I got: (-1/sqrt(2), -1/sqrt(2))...

[spark otter]

yep

and then compute the directional derivative with this vector

[wooden grotto]

I still get it wrong somehow. After computing the directional derivative of the vector, I get (3200sqrt(2))/98

[spark otter]

can you show your work?

[wooden grotto]

We do (-1600/49,-1600/49) *(-1/sqrt(2),-1/sqrt(2)), right? Dot product

[spark otter]

i mean show your work for the directional derivative of T

[wooden grotto]

This is my entire work on the problem: For the function T(x,y)=200/x^2+y^2+3 the partial derivatives are:
∂T∂x=−400x/(x^2+y^2+3)^2
∂T∂y=−400y(x^2+y%2+3)^2

At the point (2,2)(2,2), the partial derivatives are:
∂T∂x(2,2)=−400(2)(2^2+2^2+3)^2=−1600/49
∂T∂y(2,2)=−400(2)(2^2+2^2+3)^2=−1600/49

So, the gradient of T at (2,2) is:
(-1600/49, -1600/49)

The unit vector u in the direction of the gradient is:
∇T(2,2)=(−1/sqrt(2),-1/sqrt(2))

The unit vector uu in the direction of the gradient is:
u=(−12,−12)u=(−2
​1​,−2

Computation of the dot product of ∇T(2,2) and u to find the directional derivative:
DuT=∇T(2,2)⋅u
DuT=(−1600/49,−1600/49)⋅(−1/sqrt(2),−1/sqrt(2))
Du​T=(-1600/49​*-1/sqrt(2)​)⋅(-1600/49*-1/sqrt(2))
DuT=2*(1600/49sqrt(2))
DuT=3200/49sqrt(2)

[marsh citrus]

@wooden grotto Has your question been resolved?

[marsh citrus]

@wooden grotto Has your question been resolved?

[marsh citrus]

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[lunar abyss]

how would i calculate normal force

[fallen stump]

Do you know what an FBD is? @lunar abyss

[lunar abyss]

yes

[fallen stump]

Ok draw it

[lunar abyss]

i did

[fallen stump]

lemme see

[lunar abyss]

naw

[fallen stump]

ok start with that

[lunar abyss]

i did

[fallen stump]

show it then

[lunar abyss]

thats too much work

[fallen stump]

..

[lunar abyss]

is it just mg?

[fallen stump]

not really

it’s at an angle

[lunar abyss]

mg(cos 36)

??

[wise jackal]

what forces do you have in the y direction?

[lunar abyss]

ohhh shit

my b

36 sin (36) + mg?

[wise jackal]

close

how did you find it?

[lunar abyss]

cos

?

my head

[wise jackal]

no it’s still sine

[lunar abyss]

oh?

[wise jackal]

you’re using the angled force in the y direction

[lunar abyss]

yes

and then mg?

[wise jackal]

which is 36 sin(36), yes?

[wise jackal]

yeah that’s the gravitational force

[lunar abyss]

yeah

what am i missing then

[wise jackal]

oh wait

ok yea

[wise jackal]

it is this

[lunar abyss]

thanks boo

.close

[marsh citrus]

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[lament scarab]

how to solve cubes?

[lament scarab]

<@&286206848099549185>

do you put the exponent first and devide before turning it into cube?

[dapper heart]

What do these =? So far these look like simplified expressions, not things you can solve

[lament scarab]

its supossed to be the sum/difference of the question

(a format/example)

[dapper heart]

Oh jeez so the cube of x^6 is x^2 and then 8y^3 is 2y

ThT doesn’t matter maybe

Uhmm

[lament scarab]

ah so you have to find the cube of the exponent?

[dapper heart]

Yea and exponents like divide by the power of the radical

So cube root of x ^12 is 12/3 x^4

[lament scarab]

what if it was a factor how do you find its cube root?

in the first exponent you have to find its square? is that what you did at x^6

@zenith crystal

how?

[marsh citrus]

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[upbeat dagger]

Suppose we want to negate a statement such as this:

[elfin berry]

tejveer

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[white lantern]

im not sure if i understood the pull-back correctly
is it only the use of grams determinant on a vector field?

[marsh citrus]

@white lantern Has your question been resolved?

[white lantern]

<@&286206848099549185>

[marsh citrus]

@white lantern Has your question been resolved?

[marsh citrus]

@white lantern Has your question been resolved?

[marsh citrus]

@white lantern Has your question been resolved?

[sly zephyr]

can you elaborate on the question for the others ?

[white lantern]

If a task is stating to specifically only execute the pull-back
Does that only include grams determinant?
Or is there a number of other things that need to be executed as well, besides the calculation of the derivatives of the vector field into a matrix system to determine the eigenvalue?

[marsh citrus]

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[idle stirrup]

I am stuck on this question

What I did is finding the gradient first

then calculate the poiI got point (2,1/2, 9/2)

But this point does not belong on the surface apparently

[marsh citrus]

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[keen wyvern]

do i multiply the (5x+6)(6x-1)

and then equal it out to 48x-8

to solve

[thin bison]

Yes...

Or even better

Is to just equate it

You can factor a 8 out of the left expression

[elfin berry]

_basudev

[marsh citrus]

@keen wyvern Has your question been resolved?

[keen wyvern]

i need help finding H

[marsh citrus]

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[candid pebble]

Can someone explain this to me? I got a=8 but it says its wrong and I don't know why.

[marsh citrus]

Show your work, and if possible, explain where you are stuck.

[candid pebble]

nvm i solved it, sorry!

.close

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[ionic stirrup]

hi

[ionic stirrup]

need help with a linear algebra problem please

Let V be a vector space, and let S be a finite subset of V. Then, prove that $dim(Span(S \cup { x})) \leq dim(Span(S))+1$

[elfin berry]

jriver

[ionic stirrup]

thanks in advance for the help

for what its worth, ive proven that the statement is true when S is linearly independent, but not for when its linearly dependent

but im not sure if thats even the right strategy, so if someone could let me know that would be great

[restive sun]

if you broke it into cases where x is in the span of S or not, I think that should still similarly apply to the non linearly independent case

either x is in the span already, in which case the dim is unchanged, or it isn't, so it adds an extra degree of freedom, or dimension

[ionic stirrup]

hm how would i formalize this

thats the part im having trouble with

(specifically the case where x is not in the span of S --> adds another dimension)

[restive sun]

if it's not in the span of S, then it's linearly independent from the vectors in S (by definition)

so it must contribute +1 to the dimension of the maximal independent subset of S U {x}

span(S) is the set of linear combinations of vectors in S; if x isn't in there, it's linearly independent from S

[ionic stirrup]

oh ok wait thats so true

let me digest this

wait ok i dont quite follow what you have after you note that x is linearly independet from vecs of S

[restive sun]

the dimension of a set of vectors is the number of vectors in a maximal linearly independent subset

or rather, the dimension of some space spanned by that set of vectors

but anyway, dim(span(S)) is the number of vectors in the biggest linearly independent subset of S possible

if x lies in span(S), then this biggest subset is unchanged

because you can't add it to the subset; it's linearly dependent

otherwise, you can add it to this subset to get a larger one, so the biggest subset possible is now the previous biggest subset, plus an extra vector, x, so the dimension has increased by 1

[ionic stirrup]

ok like this makes sense intuitively

as in i am following what you are saying

but its not rigorous right

[restive sun]

I think this should be sufficiently rigourous?

it's just expanding definitions

and case analysis

you cover all cases so it's fine

[ionic stirrup]

hm

so essentially ur two cases are that x in span(S), or x not in span(S)

[restive sun]

yeah

and it can't be the case that both hold, or neither hold

(excluded middle and whatnot)

[ionic stirrup]

right

[restive sun]

so those are the only two cases

[ionic stirrup]

wait actually im still confused about the x not in span(S) case

[restive sun]

if it's not in the span we can add it to a maximal LI spanning subset of S to obtain a maximal LI spanning subset of S U {x}

and because we've added an extra vector, the dimension has increased by 1

just picture the case for like, 2 to 3 dimensions

say S is a set of vectors that span a plane

great, we can find two LI vectors in S that span the plane, so span(S) has dimension 2

if x lies in this plane, we don't get anything new

the same subset still spans

if x doesn't lie in this plane, then we can reach all of 3d space

by using x to access the 3rd dimension

by adding x to whatever set of 2 vectors we spanned the plane with, we get a set of 3 vectors that span 3d space

so the dimension is now 3

[ionic stirrup]

ok right this makes sense

i think i get it now

thank you!

[marsh citrus]

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[fierce dove]

question 80

[fierce dove]

not sure where to start for this one

[whole sleet]

Let's look at 77. What's the lowest power?

[fierce dove]

1/2

[whole sleet]

We should factor x^(1/2) out

[fierce dove]

i need help with question 80 specifically

[whole sleet]

Same deal. Don't let the x-1's throw you off

Lowest power, factor that out

[fierce dove]

oh ic

.close

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[gloomy salmon]

im not sure about my answer for part B

[gloomy salmon]

it feels wrong? idk

oh i can simplify it

wait no

.close

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[coral lagoon]

Discrete Math: Can anyone explain to me what the difference between consistent systems specifications and proporisitional satisfiability is?

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[rocky pilot]

can someone tell me how 7/3 was obtained?

[elfin berry]

riemann

[hazy lion]

plug in 1 for x

you will see

@rocky pilot

[rocky pilot]

Yea I saw it...

Im so slow..

[hazy lion]

youre good

[rocky pilot]

.close

[marsh citrus]

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[still temple]

ftc2