help-49

[magic orchid]

no no but if i i wanted to use my formula

why would it be n=11 -1

instead of 10 -1

[midnight plank]

@magic orchid Has your question been resolved?

[ancient plank]

The formula is tn=a r^(n-1)
It'll give nth term of the series.
You need to decide that is the height after bounce considered at 10th or 11th term.

[midnight plank]

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[lofty beacon]

Given natural a1 < a2 < ... < an Prove that: 1/a1 + 1/LCM[a1;a2] + …. + 1/LCM[a1;a2;….;an] <= 2

[lofty beacon]

<@&286206848099549185>

[merry pewter]

i would first strengthen the bound and then use induction

maybe you can show 1/a1 + ... 1/lcm(a1,...an) <= 2-1/a1...an

[lofty beacon]

It's a stronger inequality

[merry pewter]

right

we need to strengthen to apply induction

[lofty beacon]

We need to evaluate from above 1/lcm(a1;a2;...;ak)

[merry pewter]

evaluate how

for induction, all we need to show is that 1/lcm(a1,...,an, a(n+1)) <= 1/a1...an - 1/a1...a(n+1)

actually wait this is probably not true

so maybe we need to strengthen less

[west iron]

seems like it might be <= 2 - 1/an

proving is another matter

[midnight plank]

@lofty beacon Has your question been resolved?

[lofty beacon]

I think that’s true

[merry pewter]

take a_n=2^n, then 1/lcm(a1, a(n+1)) = 1/2^n+1, but 1/2^{a1..an} - 1/2^{a1..a(n+1) is really small

[merry pewter]

this might be enough

let's see

,, 1 \le \frac{lcm(a_1,\dots, a_n, a_{n+1})}{a_n} - \frac{lcm(a_1,\dots, a_{n+1})}{a_{n+1}}

[grand pond]

Bair

[merry pewter]

yeah this works i think

[lofty beacon]

From where u got it?

A I see

So far I don't know how to prove it

[merry pewter]

well you know both fractions are integers

so their difference is at least one

since the one with a_n+1 in the denominator is smaller

[lofty beacon]

Yep

Ohhh

That’s cool

Thx

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[limber acorn]

For this graph, we would have theta = pi/6 and phi = pi/3. Aren't the angles swapped around?

[lilac sage]

depends on your conventions on which is theta and which is phi

[limber acorn]

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[small zenith]

Q39

[small zenith]

(please ignore the pencil marks)

and i just guessed A so it's probably incorrect

[midnight plank]

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[small zenith]

<@&286206848099549185>

[midnight plank]

@small zenith Has your question been resolved?

[patent glen]

Was thinking of moving E such that the line AB is looks somewhat like a basic straight line

Then figure out a line thats parralel to AB, but passes through E, and the line Origo(C1), A

[small zenith]

huh

[patent glen]

I think with this we could figure out the length of AB, and AE

[small zenith]

i don't get your method, but what's the answer u get?

[patent glen]

Havent tried it yet

Something like this

With this, i get AB is 4

weird value ik

maybe we could be able to use some sort of congruence stuff to figure out the sizes of the bigger triangle

Since we have alot of congruent triangles here

[small zenith]

yeah i think that's the way

[patent glen]

yea, but am still thinking about what could we use the sizes for

Oh!

With the sizes we could be able to figure out the angles somehow

Then with the angles, we can figure out AE

I found AE to be 3.58 ish

[midnight plank]

@small zenith Has your question been resolved?

[patent glen]

ABE is also right angled

Got 3.2

So B is correct

a is 4

[midnight plank]

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[small zenith]

ah ok thanks

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[pure wraith]

Two points are selected on a line segment of length L; one before, and one after it's midpoint. Determine the probability that the distance between the two points is greater than L/3

[pure wraith]

Oh wait epiphany

Got it

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[inland patio]

I am stuck trying to verify the proof of Corollary 2.52. If I plug in $f(x)=g(|x|)=|x|^{-a}\chi_B(x)$ in Corollary 2.51, how do I obtain statement a) of Corollary 2.52? That $\chi_B(x)$ doesn't depend on $|x|$ confuses me.

[grand pond]

psie

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[dusky panther]

Prove by means of complete induction: Let A be a statement that can be either true or false. Show that ¬A cannot be expressed using A and the junctors ∨, ∧, ⇒.

[midnight plank]

Please don't occupy multiple help channels.

[dusky panther]

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[lofty beacon]

prove that if a,b,c > 0

[midnight plank]

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[lofty beacon]

<@&286206848099549185>

[last pebble]

I solved it by cancelling the nominator in each fraction, and then substituting x=b/a, y=c/b, z=a/c, and then multiplying everything. After simplifying and using xyz=1, it remains to show xy+yz+xz>=3, if I didn't make any mistake. The substitution is probably optional here, but it made it a bit simpler.

[midnight plank]

@lofty beacon Has your question been resolved?

[lofty beacon]

How do u get xy + yz + xz >= 3?

[last pebble]

how do you get there, or how do you prove it?

to prove it, you can use arithmetic-geometric mean

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[snow iron]

how would I get to 7pi

[charred widget]

ok do u know the formula for a cone's volume

[snow iron]

yeah

pi/3 . r^2 . h

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[crystal field]

Solve for x and y: x^2 + y^2 = 25,

[crystal field]

i just need this quick

lol

[rose trout]

There isn't a unique (x,y) that satisfies this.

[dawn dagger]

There are infinite many solutions, it represents a circle

[crystal field]

i didnt really need this solved i was just trying to see how dumb/smart people really are

i wasnt talking about

math smart

i meant like discord smart

heh

[dawn dagger]

heh you just caused someone to close their help channel because this

[crystal field]

Whoopsie daisies!

[hard shard]

kaue whats with the phlippines flags

[oak slate]

colonization

[crystal field]

i have no idea

but i have a real math question

can someone explain how that one person solved one of the 7 hardest math questons or whatever

i forgot what they were called

so many random signes ive never seen

signs*

[hard shard]

do you even understand the problem to begin with

[oak slate]

it was unsolved for a reason

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@crystal field Has your question been resolved?

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[wise bough]

in a polynomial (suppose Cubic) we consider sum of roots will be -(cofficient of x^2)

I am trying to understand the pattern of sum of cubic roots a^3+b^3+c^3

[wise bough]

I can find it by general expansion (a+b+c)^3=(a^3+b^3+c^3)3(a+b)(b+c)(c+a)

It is lenghty but looking for any method

[midnight plank]

@wise bough Has your question been resolved?

[wise bough]

This is symmetric matrix

[midnight plank]

@wise bough Has your question been resolved?

[midnight plank]

@wise bough Has your question been resolved?

[wise bough]

https://en.wikipedia.org/wiki/Newton's_identities#Formulation_in_terms_of_symmetric_polynomials

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[cinder cosmos]

"Bobby has 4 lamps, 3 of type A and one type B. Type A lamps have an expected lifetime of 100 hours and type B has an expected lifetime of 200 hours. Bob picks a lamp and after 200 hours notices that it still works. What is the probability that Bobby picked a lamp of type A?"

[cinder cosmos]

I tried reasoning the following way: Let $P_L(A) = \frac{3}{4}$, this is the probability that Bobby picked a lamp of type A. The probability that Bobby picked a lamp of type A AND it works after 200 hours can be described with a poisson distribution: $P_W(A) = P(A)200e^{-200} = \frac{3}{4}200e^{-200}$

[grand pond]

Pen

[cinder cosmos]

Then, the probability that Bobby picked a lamp of type A is simply P_w(Aa)/(P_w(A)+P_w(B))

Where P_w(B) is obtained with similiar logic

So, $\frac{3}{4(\frac{3}{4}200e^{-200}+\frac{400}{4}e^{-400})}200e^{-200}$'

[grand pond]

Pen

[cinder cosmos]

Simplifing a bit and plugging into wolfram gives

Th correct answer is 3/(3+e)

which is 0.524

Any tips?

[midnight plank]

@cinder cosmos Has your question been resolved?

[cinder cosmos]

Anyone?

<@&286206848099549185>

[midnight plank]

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[midnight plank]

@cinder cosmos Has your question been resolved?

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[gaunt gust]

how do I start this

[midnight plank]

@gaunt gust Has your question been resolved?

[gaunt gust]

<@&286206848099549185>

[plush palm]

use vectors to find the time it takes for the marble to land and then use this time to describe the distance in x direction

actually its much simpler

keep in mind that both marbles take the same amount of time to reach the ground

[gaunt gust]

I got help from a friend and they told me to use Eo = E -> U = K and find v first with 1/2kx^2=1/2mv^2

[plush palm]

yea

[gaunt gust]

and i think i can find time a kinematics equation

[plush palm]

thats basically it

[gaunt gust]

so I just multiply the 2 to find x?

[plush palm]

just double v and solve for x

[gaunt gust]

wait why do I need to double v

[plush palm]

is d not equal to two times d12?

[gaunt gust]

idk if thats given

[plush palm]

if this isnt the case you have to express it in terms of variables

[gaunt gust]

yeah

thats what I think is assumed

[plush palm]

you definitely need d12 as well though

[gaunt gust]

why do I need d12 if I'm only finding the distance for the 2nd ball

[plush palm]

oh nvm i misread the question entirely

my bad

[gaunt gust]

lol

this is what I have for v and t

which is what I'm told to get

[plush palm]

just plug v into this formula and solve for x

[gaunt gust]

oh wait

[plush palm]

you need to express v in terms of g, H and d though

[gaunt gust]

did i even need time?

[plush palm]

you do

you need t to find v

v = d/t

do you know how to get t?

[gaunt gust]

i thought you were saying to plug in v2 = sqrt(kx^2/m) into 1/2kx^2=1/2mv^2

[plush palm]

nono i misread that

express t in terms of g and H

then use t to get v

[plush palm]

and then plug v into this equation and you got your answer

[gaunt gust]

?

[plush palm]

yes

[gaunt gust]

d/sqrt(2H/g) for v?

[plush palm]

yea

[gaunt gust]

oh and I plug in that v for the energy equation

[plush palm]

yes

[gaunt gust]

ok i'll put that in and see

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[plush palm]

yw

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[gaunt ibex]

Isn’t L4-4L1 a mistake

It’s supposed to be L4-3L1 no?

[runic hamlet]

yes

[gaunt ibex]

Alr I thought I was tripping

What do I do next

L2 swap L4?

To get the 1 above

[runic hamlet]

well you are given the solution...

[gaunt ibex]

Huh

What do you mean

[gaunt ibex]

But if this is a mistake the whole thing is as well no?

[runic hamlet]

they did the correct operation

they just labelled it wrong

[gaunt ibex]

Oh 😂 my bad

Ty

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[gaunt ibex]

.reopen

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✅

[gaunt ibex]

They did another mistake L3-3L2 no?

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[gaunt ibex]

I don’t know which row to deal with next

[hearty rune]

id use the second row to eliminate the 3 and -2

[gaunt ibex]

So 2L2-L1

Wait no

L3-3L2

L4+2L2

[hearty rune]

that works

[gaunt ibex]

Kk lemme try

[gaunt ibex]

I get this

Now L1-2L2

[hearty rune]

can do

[gaunt ibex]

And now I’m stuck

[gaunt ibex]

L2-L3?

[hearty rune]

no that doesnt help anything

deal with the last two rows first

so youre in REF form at least

then you can deal with everything else

[gaunt ibex]

L4+L3

[hearty rune]

that works

[gaunt ibex]

One sec doing it

Then L4/4

L2-L3?

To get rid of the one

[hearty rune]

no

because you would be creating a -1

work from the bottom up

[gaunt ibex]

L3-L1?

[hearty rune]

no

that takes you out of REF entirely

[gaunt ibex]

Oh yea my fault

Hmmm

Wait no

[hearty rune]

(use R4)

[gaunt ibex]

L4-L3

[hearty rune]

no

[gaunt ibex]

Nvm

[hearty rune]

we want to get rid of all the values in the fourth column above the bottom 1

[gaunt ibex]

That just takes out

[hearty rune]

so just use R4 to get rid of them all

[gaunt ibex]

Hmm

L3-L4

[gaunt ibex]

It gets rid of the 1 all the way on the right of R3

Would that work

[hearty rune]

yeah

but do that to all of them

in one go

[gaunt ibex]

Kk

Oh

L2-l4

L1+4L4

Onmgg finally

I get this

[hearty rune]

now you can deal with that remaining 1 on the first row

[gaunt ibex]

Yes

X_1=q

1*

[hearty rune]

?

[gaunt ibex]

Like this

[hearty rune]

ah alright, i meant you could eliminate it if you wanted

but that works

[gaunt ibex]

Ahh

Yes

Ty

Damn it’s a lotta work

😂

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[dense arch]

im working with sets having minumums maximums infimum supremum bounded not bounded. My question is can a set say this set A = { x element N | 1 <= x < 4 } will it have both a minimum and an infimum or just a minimum. It also has a supremum but thats not my issue

[polar mortar]

a minimum is an infimum, so yes.

and infimum is not necessarily a minimum though, so it doesn't work both directions

[dense arch]

minimum is only when the value is included in the set

infimum works when its included and not included in the set

[polar mortar]

yep

[dense arch]

and the same goes for maximums and supremums

[polar mortar]

yes

[dense arch]

okay dope

thank you

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[somber locust]

How does this description of interval work? I know it is talking about radian values.

But if it is describing them as an Interval, would I then view it as the coordinates of a Unit Circle quadrant? Like how I illustrated?

[midnight plank]

@somber locust Has your question been resolved?

[slender walrus]

you'd view it as where the angle of rotation lies

[somber locust]

So does the notation of (x,y) have any merit, or is its resemblance merely incidental without equivocation to (x,y) coordinate syntax?

[midnight plank]

@somber locust Has your question been resolved?

[misty cairn]

@somber locust its not x,y

its (x¹, x²)

[somber locust]

Where is that from?

[misty cairn]

its an interval

like the interval from 0 to 1

(0,1)

[somber locust]

, then how would one determine quadrant 1?

[misty cairn]

quadrant one is when the angle lies between 0 and π/2 no?

[somber locust]

Where did the 0 come from?

I thought we were talking in radian values

[misty cairn]

0 radians is just 0

radian means circumference over radius

so 0 circumference over x radius = 0

π circumference over x radius = π

remember c/d = π

so c = 2πr

[midnight plank]

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[somber locust]

Ah I see thx 👍😎

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• Show your work, and if possible, explain where you are stuck.
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[crimson totem]

h

[crimson totem]

how do i solve for a?

[tawdry laurel]

do you have a calculator

[tacit rose]

SOH CAH TOA

Apply that

[crimson totem]

how would i know which to use in this scenario

[crimson totem]

no

only online calc

lost mine

[tawdry laurel]

but can use calculator for this qn right

[tacit rose]

Use that as a reference

[tawdry laurel]

think of which trigonometric identity to use for a

[tacit rose]

You're looking for the angle, which is theta. Use the image as reference, is 12 Opposite, Adjacent, or Hypotenuse?

[crimson totem]

13/12 ?

[tawdry laurel]

close

also think of applying a trigonometric identity

like sin/cos/tan theta = ?

then we can solve

[tacit rose]

Notice how it's equations, sin theta = Opp/Adj, etc you just presented a fraction

[crimson totem]

wym

[tawdry laurel]

follow this guy

[tacit rose]

You need to form an equation

To solve

[crimson totem]

not sure how to lowkey

new to this

[tacit rose]

.

[crimson totem]

12 is adj

[crimson totem]

sorry for late response

[tacit rose]

What about the 13?

[crimson totem]

opp

[tacit rose]

Look again

[crimson totem]

hyp

[tacit rose]

Do you understand why?

[crimson totem]

this graph

[proper kernel]

@crimson totem you still there?

[crimson totem]

yes sire giga goat

[proper kernel]

You remember me?

I still remember you

[crimson totem]

yes

https://tenor.com/view/biere-faim-mdr-soiree-huugoo-gif-16805976

[proper kernel]

I crashed out when you pulled up “school crash outs 4” 💀

[crimson totem]

lol

[proper kernel]

Outta pocket bro

[crimson totem]

how do i solve for a?

[proper kernel]

Alr let me help

Are you familiar with sin cosine and tangent

[crimson totem]

yea

SOH CAH TOA

note

[proper kernel]

Alright and you’re trying to solve for theta in the question?

Which question do u need help with Blud

[crimson totem]

how to get theta for question A

[proper kernel]

Okay so

What have you tried so far

[crimson totem]

tan0 = 12/13

[proper kernel]

Not quite

We’re given 2 lengths of the triangle

[crimson totem]

yea

[proper kernel]

So which ones are which (hypotenuse, opposite, adjacent?)

[crimson totem]

12 is adj 13 is hyp

[proper kernel]

Yes

So let’s go back to SOH CAH TOA

[crimson totem]

ya

[proper kernel]

We know the adjacent and the hypotenuse

Which are A and H

[crimson totem]

I meant cosine for this btw

[proper kernel]

Which trig function has A and H in it?

Yes

[crimson totem]

Cosine

[proper kernel]

So cos0 = 12/13

[crimson totem]

yes

[proper kernel]

Now we need to isolate theta

What have you tried?

[crimson totem]

0

[proper kernel]

Wdym

[crimson totem]

nothing

[proper kernel]

Do you have any thoughts?

[crimson totem]

not really no

[proper kernel]

Ok

Well what we’re trying to do here is undo the cosine function

So what can we do is use the inverse functions

That is, cos^-1(0)

[crimson totem]

instead we put 12 /13

right

for 0

[proper kernel]

?

[crimson totem]

nvm

[proper kernel]

Wdym

[crimson totem]

sorry go on

i meant this

cos^-1(12 /13)

[proper kernel]

Yes

Cos^-1 undoes the cosine function, so we can combine it with both sides of the equation to isolate theta

In other words, 0 = cos^-1(12/13)

And now you can just calculate it

Is that it?

[crimson totem]

22

how about the question B

[proper kernel]

22 is close

[crimson totem]

cuz its finding sides

[crimson totem]

.6

2

[proper kernel]

It’s 22.62, which rounded is just 23

Make sure you round up not down

[crimson totem]

Ok

how about the question B

its finding sides

[proper kernel]

Try it yourself first

See how you can use the trig functions to solve for the side lengths

[crimson totem]

17.46 for theta or 17

how would i find side

[proper kernel]

Hold up gimme one sec

[livid cedar]

Yeah

He's answering my question rn for some reason

[proper kernel]

No I would never multitask

[crimson totem]

type shi

[proper kernel]

Alright I’m back

What were u asking?

[crimson totem]

how to get side lengthj

[proper kernel]

Alright can u post the picture again

I don’t want to scroll up 💀💀

[proper kernel]

Alright I got it

So

We’re given a side length, an angle, and an unknown hypotenuse.

The given side has a length of 11; is it an opposite, adjacent, or hypotenuse side?

[crimson totem]

adj

[fringe pine]

Just remember your sin, cos, and tan

[proper kernel]

Alright! We’re one the right track! 👍 so now we have an adjacent side with a length of 11, an angle of 37 degrees, and an unknown hypotenuse.

Well, there is no formula for solving for the hypotenuse specifically. But what if we could derive it from a trig function?

[fringe pine]

of the three trig functions, which one do we use?

[proper kernel]

Well, which trig function has an ADJACENT and HYPOTENUSE in it? (SOH, CAH, TOA)

[crimson totem]

Cosine

are we doing adj and hyp cuz were looking for hyp

[proper kernel]

Yes! Cos0 = adj / hyp

[fringe pine]

we’re looking for theta

[proper kernel]

So how can we isolate the hypotenuse, such that the hypotenuse is alone on one side of the equation?

[livid cedar]

Ummm

[proper kernel]

@crimson totem

[livid cedar]

TTicklemypickle, pretty sure we're on question b

[crimson totem]

yae

[fringe pine]

ohhhhh crap

ty

[crimson totem]

put it in opp

[proper kernel]

How can we solve for the hypotenuse in relation to cos0 and the adjacent side?

[fringe pine]

😭

[crimson totem]

wait no

[proper kernel]

Put it in Opp???

[livid cedar]

Yeah, so i didnt think we were trying to find theta...

[fringe pine]

i take that back

[proper kernel]

Blud 😭😭🙏

[crimson totem]

Just tell me

[proper kernel]

Do you want me to “put it in opp”

[livid cedar]

Rayan is challenged by gigaots guidance rn

Gigagoat, u need knief to take over aagain?

[proper kernel]

Hold up I got this

[fringe pine]

OMG I LOVE KNIEF

[livid cedar]

Real

[proper kernel]

@crimson totem where did you go

[crimson totem]

here

[proper kernel]

So basically what I’m saying is

Cos0 = adj / hyp

Right now, we can’t solve for hyp.

[crimson totem]

yae

[proper kernel]

Because it’s not alone in the equation.

[crimson totem]

wym by alone

[proper kernel]

Basically

It’s on the right side of the equation

But it’s also with adj

So hyp and adj are both on the right side of the equation; that is, hyp is not isolated because it is not by itself on that side of the equation.

How can we solve for hyp such that hyp is the only variable on one side of the equation?

Try it

?

[crimson totem]

11/cos

[proper kernel]

Yes!! 👏

Alright, so now we know the hypotenuse is equal to 11/cos0.

Do you remember what theta is? What’s the angle measure of theta?

[crimson totem]

37

[proper kernel]

Right! So the hypotenuse is equal to 11/cos(37), and we can just plug that into a calculator.

[crimson totem]

14

[proper kernel]

Right!

Usually, you don’t want to round to the nearest whole number though, unless the question specifically asks you to.

Personally, I would just write down 13.77, since it is more specific.

[crimson totem]

good point

[fringe pine]

So in summary this is everything we did

[proper kernel]

Thx

[crimson totem]

13/tan(32) = 20.81

i solved the last question

[proper kernel]

Rayan 🍉, you need anymore help, or are you confident with your new skills?

[fringe pine]

(i took a bit too long to post this but it’s a recap now and not a lesson)

[proper kernel]

Thx bro

[fringe pine]

gotchu

[crimson totem]

i got other questions to solve for practice sheet

idk if yall still wanna help

Thank you btw

[proper kernel]

Hold up

I’m checking your answer for the last question

Gimme one minute

[crimson totem]

take ur time

[proper kernel]

Hold up

It might be my issue

But I got 8.59

[crimson totem]

on google calc 13/tan(32) = 19.6

wth

[proper kernel]

Oh I see the issue

you made an error trying to isolate X

But u used the right trig function

Ok so tan0 = opp / adj

[crimson totem]

yea

[proper kernel]

Can you identify the opposite and adjacent sides, as well as theta?

[crimson totem]

yea

[fringe pine]

i’m down to help i love geometry

[crimson totem]

x is op, 13 is adj

[proper kernel]

Right! 👍

[crimson totem]

theta 32

[proper kernel]

So tan 32 = X/13

How can we isolate X?

[proper kernel]

Sure, you wanna take over?

[fringe pine]

yeah sure

[proper kernel]

Alr 👍

[fringe pine]

@crimson totem u know what to do from here or need a hint

[crimson totem]

hint

i saw it on the ss you sent but not sure how we got to the function

[fringe pine]

isolate the x

i can expand it if u want, but i got a bit lazy 😭

[crimson totem]

please

[fringe pine]

so, let’s run back to the other equation

[crimson totem]

ok

[fringe pine]

This bottom part right?

so in this one, i isolated the x by first multiplying it to both sides

lemme show u rq

[fringe pine]

i kinda rushed this one so it’s partially wrong

@crimson totem

that’s what i did for the previous question

after u build ur equation, ur next goal is to isolate the x and solve for it

[midnight plank]

@crimson totem Has your question been resolved?

[midnight plank]

Channel closed

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[midnight plank]

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[dawn prism]

Help, is this a conservative vector field?

[dawn prism]

F is closed

[last slate]

anyone familliar with trading here?

[midnight plank]

@dawn prism Has your question been resolved?

[dawn prism]

.close

[midnight plank]

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[midnight plank]

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[gaunt jetty]

The potential buyer of a particular engine requires (among other things) that the engine start successfully 10 consecutive times. Suppose the probability of a successful start is 0.98. Let us assume that the outcomes of attempted starts are independent. (a) What is the probability that the engine is accepted after only 10 starts? (b) What is the probability that 12 attempted starts are made during the acceptance process?

[gaunt jetty]

For b) I thought this woul be negative binomial distribution

with 12 trials needed and 10 successes

but why am i wrong

[flint rock]

is it because it needs to be consecutive?

[gaunt jetty]

ohhh that makes sense

so we need the last 10 to be successful

2nd should be bad

and 1st could be either?

so 0.98^10 * 0.02 if im not mistaken

is the total probability 0.02 * 0.98^10 (0.02 + 0.98)

[olive matrix]

seeing 0.02 + 0.98 in there makes me suspicious

your words are correct though

[gaunt jetty]

i was thinking we needed to account for both cases of the 1st being either successful or bad

[olive matrix]

oh ok i guess

that's just 1 though :P

[gaunt jetty]

OHH

😭

tysm

.close

[midnight plank]

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[midnight plank]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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[chilly cobalt]

i have no idea how to solve this

[chilly cobalt]

<@&286206848099549185>

uh can someone check my solution

<@&286206848099549185>

[midnight plank]

@chilly cobalt Has your question been resolved?

[chilly cobalt]

<@&286206848099549185>

[static jay]

I gotchu one minute

[chilly cobalt]

whoa

[static jay]

Do you have the original problem?

Wait never mind

[chilly cobalt]

o

[static jay]

sorry man, can’t read handwriting

[chilly cobalt]

sorry man😭

which cant you read

[midnight plank]

@chilly cobalt Has your question been resolved?

[midnight plank]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
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[last slate]

help

[last slate]

i thought when u do this u gotta make 3 in terms of log 7

so like 3= log base 7 343

[plain osprey]

that would kind of not get u anywhere

its also too much work

[last slate]

really?

[plain osprey]

yes

[last slate]

so u can just make everything to the log base 7 without changing anything

if so

then its easy

[plain osprey]

thats a way

[last slate]

so u can just do 7^x x 7^2=3

3/49=7^x

log 7 both sides

x= log base 7 3/49 / log base 7 7

[plain osprey]

x = log_7 (3/49) yes

[plain osprey]

why did u add another log

that seems useless

[last slate]

just for jokes

log 7 to the 7

is just 1

[plain osprey]

ok then

[last slate]

so yh

[plain osprey]

yea

[last slate]

but i swear

in a different scenario

u have to do that

like

3 into log base 7 which is 343

in fact we do it in the next part

[plain osprey]

well in this one, sure

u would have to write both sides in terms of log_2

[last slate]

ok

thanks

.close

[midnight plank]

Channel closed

Closed by @pine willow

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[midnight plank]

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[low garden]

hi

[low garden]

my friend sent his answer for a

but he halved each area value

why?

riemann sum integration

<@&286206848099549185>

[midnight plank]

@low garden Has your question been resolved?

[low garden]

no

mmm im cooked fr

[void lichen]

can you provide a better picture

[low garden]

if its still not clear lmk so i can rewrite it

[void lichen]

whats the question

oop nvm

[dawn dagger]

It should be (b-a)/n = (8-0)/4 = 2

The height is just the function value

[low garden]

oh

[dawn dagger]

R(0), R(2), R(4) and R(6)

[low garden]

yup

[dawn dagger]

Will give you 4 rectangles

[low garden]

yeah

[dawn dagger]

2(R(0)+R(2)+R(4)+R(6))

[low garden]

so where did my friend find 1/2 from

he multiplies it to each rectangle

[dawn dagger]

Unless he did triangular method

1/2 × b × h

But it's usually rectangle

[low garden]

we were never introduced to a triangular concept so idk why he did that

[dawn dagger]

Then 1/2 seems wrong

[low garden]

(60⋅2)+(90⋅2)+(110⋅2)+(120⋅2)

so is it just this

[dawn dagger]

Assuming you did this correctly, yes

[low garden]

lemme double check

[dawn dagger]

Yup

[low garden]

ok wait no idk what im doing

[low garden]

oh its fine?

i end up with

760

total area

so 802.5 is wrong

i see what he did

he did midpoint

thats incorrect tho?

they asked for left end points

not midpoint

ok so just to confirm if 760 is right

[midnight plank]

@low garden Has your question been resolved?

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[dawn dagger]

yes

[low garden]

yuh so i did it i got 760

i told my friend abt it

he did midpoint for no reason

oke tysm

[dawn dagger]

mid

[dawn dagger]

you're welcome

[low garden]

actualy wait

wait nvm

[dawn dagger]

You want me to wait twice

[low garden]

errr

i was abt to ask the follow up question

where i have to do the integration

[sinful trout]

he was kidding lol

[dawn dagger]

of what function

[low garden]

the equation is that 400e thing

[low garden]

ah lmao

we need to use u substitution to integrate that

upper limit 8

lower limit 0

[dawn dagger]

So you wanna integrate D(t) from 0 to 8?

[low garden]

yes

[dawn dagger]

Just use power rule

wait

it's exponential lol

mb

[low garden]

yuh

[dawn dagger]

you can't integrate that lol

[low garden]

lmao

[dawn dagger]

and that's also not what they want

[low garden]

what do i do then

wats it want

[dawn dagger]

e^x^2 something doesn't have an antiderivative in terms of elementary functions

[low garden]

oh i see

[sinful trout]

wdym "something"

xe^x^2 does have an elementary antiderivative

[low garden]

w8 so what do they mean by estimate how do i approach this

[dawn dagger]

bro

[sinful trout]

but yes, what he meant was e^ax^2 doesn't generally have an antiderivative for constants a

(ignoring ofc a = 0)

[hollow oyster]

they are different functions.....

[sinful trout]

"something"

[hollow oyster]

kek

[dawn dagger]

y'all starting a discussion over this here

[low garden]

😭

[hollow oyster]

isnt that what we are supposed to do?

[dawn dagger]

Ok so D(t) gives you the amount of data at a specific hour

[low garden]

Yes

[dawn dagger]

Now I am struggling to understand if "at the end of 8 hours" means from 0 to 8 or at the 8th hour

Using the calculating from a) would suggest from 0 to 8

[hollow oyster]

it is prolly the former

[dawn dagger]

So I would calculate the rieman sum of D

[low garden]

hm

[dawn dagger]

Same idea

2(D(0) + D(2) + D(4) + D(6))

[low garden]

okay so still 4 intervals

[dawn dagger]

And then

You add both

You are uploading data and also removing some

so you wanna figure the difference

[low garden]

Yes also 0 we had 100mb initially

and we removed 760 MB

in part a

[dawn dagger]

This was part a)?

[low garden]

Yes

summed up to 760 MB

[dawn dagger]

Yes you subtract that from the riemann sum with D

Total data uploaded - Total data removed

gives how much data is left

[low garden]

okay let me sub in the values

[dawn dagger]

ok anime girl

[low garden]

wait

whats D(4) and D(6)

[dawn dagger]

Good question

[low garden]

now we use midpt right

[dawn dagger]

I also have a question

[low garden]

hm

[dawn dagger]

How did you get D(2)?

[low garden]

d2 was given no?

[dawn dagger]

Where

[low garden]

90

d0 is 60

wiat

uh

I SUB IT IN

lmao

[grand pond]

bacc (unhelpful)

[low garden]

yes

ok ok i need to sub in all those

[dawn dagger]

We are still estimating it using left point rule, to keep things consistent

[low garden]

yuh

[dawn dagger]

Actually it is [ \text{Total amount of data left} = 100 + \text{Total amount of data uploaded} - \text{Total amount of data removed} ]

[grand pond]

bacc (unhelpful)

[low garden]

mhm

bc we add the

100

[dawn dagger]

looks fabulous, that is the very reason mathematicians use variables

[low garden]

in the beginning

[dawn dagger]

yes

[low garden]

typing things in my calculator rn

[dawn dagger]

wow

[low garden]

d2 is 147.1517765

[low garden]

yes

[dawn dagger]

damns

[low garden]

d4 7.326...

[dawn dagger]

,w 100+Sum[2 * 400e^((-(2k)^2)/4), {k, 0,3}] - 760

[low garden]

haha

[grand pond]

Results provided by WolframAlpha

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

Requested by adoniszgks

[dawn dagger]

the last one laughs the best

[low garden]

i did it in my mind fr

okay 449.055 yes its fine

[dawn dagger]

thanks

[low garden]

wait what

we're at a negative?

[dawn dagger]

explain

[low garden]

100 + removed + gained

wawit

100 + gained - removed

[dawn dagger]

yea

[low garden]

erm

im getting 554.53

for sum of all the Ds

[dawn dagger]

damn

[low garden]

i lied that time

ok

[dawn dagger]

so this lied too

[low garden]

mbb

whos not lying rn.

i mean i got d0 as 400

and d2 as 147.151...

alone

so its above 500

[dawn dagger]

what about d4 and d6

[low garden]

d4 is 7.32..

d6 is 0.04..

[dawn dagger]

,calc 100 + 2(400 + 147.151 + 7.32 + 0.04) - 760

[grand pond]

Result:

449.022

[dawn dagger]

mind blowing

[low garden]

💀

[dawn dagger]

now you dont only keep me waiting

you also lie

[low garden]

WAIT

I FORGOT TO MULTIPLY BY 2

im sorry ok

[dawn dagger]

5th wait

[dawn dagger]

oh no mb

i am just joking lmao

[low garden]

i am takingit seriously and i willc ry rn

[dawn dagger]

it's been a long day for me

oh ok

don't cry

[low garden]

no im kidding

lmao

[dawn dagger]

i am here

[low garden]

449.05

woohoo

[neat cedar]

u sure?

[dawn dagger]

local boss man arrived

[low garden]

yes

[dawn dagger]

watch out

[low garden]

why

[neat cedar]

are you SURE

[dawn dagger]

local boss man

[low garden]

um

maybe?

its just a small decimal diff ok

[neat cedar]

would you bet your life on it?

[low garden]

never

[dawn dagger]

is there a fallacy in the logic

[neat cedar]

so are you really that sure

[low garden]

no im not sure anymore

help me

[dawn dagger]

or what made you come into my channel from league

[neat cedar]

nah I was just gaslighting ur prolly l right

xdddd

[low garden]

wow

smh

bacc person

can we do part c

[dawn dagger]

bro is at the loading screen in lol

[neat cedar]

my bad my bad

[low garden]

thats the last part

we cant do a and b but not c

[neat cedar]

where is c

[low garden]

can not work this way

sending it

[dawn dagger]

yes anime girl

[low garden]

it says b but its c

trust

typo

[neat cedar]

oh yeah should probably turn that off not even in my room

[neat cedar]

so basically u wanna find the derivative then plug in 5

[low garden]

yes

[neat cedar]

🤞🏼

ez done simple

[dawn dagger]

well you are given a table

you can calculate the average rate of change between t = 4 and t = 6

[neat cedar]

then do it

[low garden]

gradient formula?

[neat cedar]

tangent formula?

[low garden]

whahty

yes thuis

this

[neat cedar]

QUADRATIC formula????

[grand pond]

bacc (unhelpful)

[low garden]

why the quadratic

stop lying

[dawn dagger]

bro is just trolling

[low garden]

ur like bacc now

[dawn dagger]

you are making a mistake

[low garden]

ur like me now*

[dawn dagger]

wow

[neat cedar]

yes I saw bacc unhelpful so I decided to join in

[dawn dagger]

now you baccstabbed me

[low garden]

so real

[dawn dagger]

we are no longer friends

[low garden]

im a very good baccstabber

[dawn dagger]

help yourself

[neat cedar]

MACLAURIN EXPANSION???

[low garden]

nuh uh+

where did + come from

see maths is taking over my life

ok let me calc rq

[neat cedar]

guys why do plants hate maths

Because it gives them square roots

[hollow oyster]

MVT reference?

[low garden]

very funny

laughing so hard rnn!

no sarcasm trust

[neat cedar]

I have more