help-10

[tidal hawk]

it’s 4

[swift pagoda]

[tidal hawk]

HAHAHAHA

I made the same mistake when checking 🤩

[swift pagoda]

Alr that’s all I needed

[obtuse pebble]

@swift pagoda Has your question been resolved?

[obtuse pebble]

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[quaint roost]

I am not sure how to set up an equation to figure this out

[zenith void]

$a(t)=60t+650$

$c(t)=90t$

[warm shale]

Acrol

Acrol

[zenith void]

So if you equal that

$90t-60t=650$

[warm shale]

Acrol

[zenith void]

You get

$x=21.\bar{6}$

[warm shale]

Acrol

[zenith void]

And if we need x < 20, then it is safe

[quaint roost]

Thank you! I think I got the answer earlier, but I didn’t have the line over when submitting.

[zenith void]

np

remember to close

if you feel it's clear, ofc

[quaint roost]

.close

[obtuse pebble]

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[green sinew]

how do i start

[mint tendon]

you with me so far gojo?

[green sinew]

yes

@mint tendon

[mint tendon]

reciprocate now

[green sinew]

ok how does the 100 matter

@mint tendon

[mint tendon]

glad you asked satoru

[green sinew]

ohh

i see

i got it

0.2

thanks

[obtuse pebble]

@green sinew Has your question been resolved?

[thin wyvern]

Star A has a magnitude of 2.5; star B, 5.5; and star C, 9.5. Which is brightest? Which are visible to the unaided eye? Which pair of stars has a flux ratio of 16?
<@&286206848099549185>

[obtuse pebble]

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[balmy badger]

help

[balmy badger]

this question

<@&286206848099549185>

[cedar lichen]

!15m

[obtuse pebble]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[nocturne minnow]

!15m

[obtuse pebble]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[high lily]

!15m

[obtuse pebble]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[balmy badger]

ok i will waity

15 mits

[merry peak]

no

now you lost your only ping

[balmy badger]

i donot know what that mean

s

so i make a quesiotn and like if 15 mits pass then i use it?

[cedar lichen]

If nobody has answered, yes

But you only ping ONCE

I'm pretty sure it says that in #❓how-to-get-help

[balmy badger]

ok so will my question never be anwerd now?

.close

[obtuse pebble]

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[merry peak]

.reopen

[obtuse pebble]

✅

[merry peak]

so

no

i will be answered

it

just because helpers aren't pinged doesn't mean it wn't be answered

[balmy badger]

ok

then

[obtuse pebble]

@balmy badger Has your question been resolved?

[obtuse pebble]

@balmy badger Has your question been resolved?

[obtuse pebble]

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[timid silo]

I was getting help with this question earlier but had to leave for school

We had gotten this far along and he was trying to explain to me how to do the second party but I didn’t understand what he meant when he said multiple the fraction

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

;-;

[timid silo]

.close

[obtuse pebble]

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[frigid glade]

I’m probably approaching this wrong

[desert sinew]

Hint: You probably want a 0/0 limit, or else your limit on LHS won’t be well-defined.

[frigid glade]

Thats why I set the numerator = x

So that when I plug in 0 it becomes 0/0, which means i can use L’hopitals rule

But now idk how to solve for b

[desert sinew]

That is not exactly what I say…
Even when you get an integer as limit value, it does not mean numerator and denominator is in direct equality or one-multiply-another relationship.

e.g. $\lim_{x \to 0} \frac{\sin x}{x} = 1$

[warm shale]

jimmy1234

[frigid glade]

Oh I see so should I try making numerator = sinx?

[desert sinew]

Thats also not what I am saying 🙂

[frigid glade]

😭 how should i approach it then

[desert sinew]

What other means you can think of for obtaining some zeros? You may want to have another thought about it 🙂

[frigid glade]

Make root(ax+b) = 3?

That would make the limit = 0

<@&286206848099549185>

[desert sinew]

More accurately, you may want to make this happen.

$\lim_{x\to 0} \sqrt{ax + b} - 3 = 0$

[frigid glade]

The bot didnt work

[desert sinew]

No idea why. But I guess you get the idea 🙂

[frigid glade]

I dont understand

<@&286206848099549185>

[slate zephyr]

!15m

[obtuse pebble]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[frigid glade]

I asked 40 minutes ago 🙂

[slate zephyr]

once

😉

[frigid glade]

😅 but then nobody is helping me

.close

[obtuse pebble]

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[strong copper]

solve for D 9w=6/7d

[jaunty jewel]

What is w?

[strong copper]

pretend its just a random unit

basically i need d=.....

just need to isolate it

[jaunty jewel]

Well, what have you tried

It's pretty simple, so I imagine you tried before coming here

[strong copper]

yeah for some reaosn i cant get it

d=6-9w

is what i got

[jaunty jewel]

No, that it's not close

Is that d in the denominator?

[strong copper]

yes

Is that the answer?

[jaunty jewel]

Yes, but you need to simplify that fraction

[strong copper]

So this?

[jaunty jewel]

Still needs to be simplified further

Make sure that's there's a single numerator and a single denominator

[strong copper]

i have no idea how to do that

[jaunty jewel]

Do you know how to divide fractions?

[strong copper]

i dont remember

all need same demoniator?

[granite crag]

2/3w/7 can be seen as (2/3w)*(1/7)

[strong copper]

so 2/14w

[granite crag]

well 3*7 isn’t 14

[strong copper]

oh wattt mb

2/21w

[granite crag]

yes sir

[strong copper]

i feel like thats the wrong answer though

[granite crag]

whatt

[strong copper]

nvm

thx

.close

[obtuse pebble]

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[fading birch]

Let there be 10 balls randomly distributed into 12 baskets of unlimited capacity
(1) what is the chance the number of empty baskets is exactly 2?
(2) what is the chance the number of empty baskets is exactly 10?

[river kindle]

I actually don’t know how to solve but what class is this it seems interesting

Is it just probability

[fading birch]

Probability and statistics

[river kindle]

Ahh it’s my first day today

[fading birch]

I'm looking it up and it's a popular question called Balls and Bins which has applications on Computer Science Load Balancing

Still can't make sense out of it though

[river kindle]

Seems like a counting problem

[zenith raft]

exactly 2 empty baskets means 10 baskets got exactly 1 ball and 2 baskets got no balls

and there are 12 choose 10 ways for that to happen

@fading birch does that help?

[fading birch]

Oh

Lemme grab a pen real quick

Hmm I may need more explanation for this one chief

[zenith raft]

ok let's ignore this then

we can find the probability of distributing balls randomly into the baskets and distributing to an empty one all 10 times

that will 1 for the first ball, 11/12 for the second ball (11 empty baskets left), 10/12 for the third ball, etc.

[fading birch]

One question here: it states that basket has unlimited capacity

So shouldn't I factor in the chance that 2, 3, 4 balls fall into the same basket and then subtract it?

[zenith raft]

if 2 balls fall into the same basket, there can't be exactly 2 empty baskets

because there would only be 8 left to distribute into the remaining 11 baskets

[fading birch]

Ah so I can assume those baskets are going to be unique then!

[zenith raft]

leaving 3 or more empty ones

assume? not sure what that means, I'd just say you can reformulate the question

[fading birch]

I had initially thought since the events were mutually exclusive, I would need to leave the denominator as 12 every time

So it wasn't clicking for me just yet

For the second one I guess I could do it like this then?

[zenith raft]

what makes you think you shouldn't do that?

[fading birch]

I second guessed and doubted myself

[zenith raft]

do you get it now?

[fading birch]

Yep

In retrospect this topic is much more intuitive than the calculus courses

I don't think I'll get far from just looking at the teacher's examples

[zenith raft]

yasss I agree haha

[fading birch]

And with that homework done!

I can finally start this week's class

.close

[obtuse pebble]

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[zenith raft]

what about part 2?

[fading birch]

I can use the 2/12 and scale it to the power of 11, no?

[obtuse pebble]

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[runic thunder]

(Find the derivative of the function)

[grave ember]

What’s wrong with that answer?

[timid silo]

yeah your answer is correct

[runic thunder]

Can i not simplify it more

Oh

Cuz like with this one

Oh wait i can combine these?

[grave ember]

All I would do is get rid of the negative power maybe

[runic thunder]

I think

[timid silo]

simplify it's quite vague here but i guess you can either get rid of the negative exponent or do common denominator

[runic thunder]

So would that be 4/(3 cuberoot(t)) - 8/(3 cuberoot(t))?

[grave ember]

Yeah

[timid silo]

missing the ² on the last term

[runic thunder]

Oh

Where would the 2 go?

[timid silo]

$x^{-\frac{2}{3}}=\frac{1}{\sqrt[3]{x²}}$

[warm shale]

Al3dium

[runic thunder]

Okay ty

[obtuse pebble]

@runic thunder Has your question been resolved?

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[runic thunder]

Hmm i dont know where i went wrong

I tried 2x but that was wrong

Then i treid 2x+0 cuz maybe it didn’t want us to simplify

Then i tried 2x+2 in case it just wanted the derivative of the 1st equation so far

[obtuse pebble]

@runic thunder Has your question been resolved?

[devout sable]

Look closely

[runic thunder]

<@&286206848099549185>

[devout sable]

What is it asking for

,texsp $\dv{f(x)}{x}$

[runic thunder]

Would that just be x^2+2?

Wait nevermind

[frigid glade]

Yes because its just asking you to rewrite it

[obtuse pebble]

@runic thunder Has your question been resolved?

[obtuse pebble]

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[limber sinew]

Did I do this right?

[tidal geode]

it seems correct to me

[royal basin]

checks out

[limber sinew]

okie thank you!

.close

[obtuse pebble]

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[obtuse pebble]

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[solid vortex]

do I use rise/run here

[royal basin]

that won't do much good to you

you want the distance from A to B

[obtuse pebble]

@solid vortex Has your question been resolved?

[solid vortex]

so pythagorean theorem?

[royal basin]

that might help you more, yes.

[solid vortex]

i c

[obtuse pebble]

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[edgy void]

I have been debating over two paths that I can't seem to wrap my head around. Either I can multiply the left terms by x (not sure how that works since x may be positive or negative which changes the inequalities arrows direction). I’ve also been considering a character table but I don’t feel confident in how I would go about using it. (I know the answer is x>=1 or x<0 but I don’t know how to arrive at that conclusion without a calculator/computer)

[royal basin]

multiply the left terms by x (not sure how that works since x may be positive or negative which changes the inequalities arrows direction).
good on you for recognizing the exact reason why you can't do that.

you can write the whole thing as a single fraction though

and then factor the top

and you will have a sign table with 4 breaking points

[obtuse pebble]

@edgy void Has your question been resolved?

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[edgy void]

Thanks for the help 🙂

[obtuse pebble]

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[marble crystal]

what does integral meann

[devout sable]

Antiderivative

[tidal hawk]

yepp just the opposite of differentiation

[marble crystal]

ok

.close

[obtuse pebble]

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[cursive zinc]

help

[cursive zinc]

confused on what it wants in 2nd and 3rd part

[obtuse pebble]

@cursive zinc Has your question been resolved?

[devout sable]

It wants you to eliminate z

By doing this

$z= \frac b{3y} \implies y^3 + \qty (\frac b{3y} )^3 =c$

[devout sable]

Solve this

It will be quadratic in y^3

[obtuse pebble]

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[mystic scroll]

How would i go about proving this, I could imagine i wouldnt need much math

but only make a few assumptions

[kind hawk]

if you can show that something is always less than 5, can you then also show it's always less than 17?

[vast wren]

that’s the definition of limit, right?

[mystic scroll]

i dont get it

I get that 5 is less than 17, but how can i prove that there always exist a larger epsilon

if i am understanding the question right

[kind hawk]

if for some epsilon_0 we can find a delta such that this equation is true, then we can also find such a delta for a different epsilon > epsilon_0

[obtuse pebble]

@mystic scroll Has your question been resolved?

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[leaden shoal]

,rotate

[leaden shoal]

i think its 12

[sullen widget]

Yeah, that looks right

Maybe show the intermediate work using the 2pir formula

[leaden shoal]

ok

[obtuse pebble]

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[drifting igloo]

Hello

[drifting igloo]

I need help with a triangle

https://cdn.discordapp.com/emojis/716088203039473685.png?quality=lossless&size=48

[high lily]

a dog isnt a triangle

[drifting igloo]

Need to search the area

[knotty crow]

,rccw

[modern solstice]

,rotate

[devout sable]

,rotate

Lmao

[drifting igloo]

Don't mind the double x there

Anyways i need help with this thing that been giving me headaches

[knotty crow]

what is it

[drifting igloo]

45°

[knotty crow]

and x (not base) is an altitude?

[drifting igloo]

Lemme send a better pic

Need to find the angle of triangle

[knotty crow]

you said area

[drifting igloo]

Yes

[knotty crow]

to find area u can use law of sines if you know

[drifting igloo]

Calc

Sorry

Nsosmf

Calculate the area of 🔺

[knotty crow]

ok so let

this point be D

[drifting igloo]

Oki

[knotty crow]

since angle B is 45 you've marked AD as x

yes?

[drifting igloo]

Correct

[knotty crow]

you know AD is an altitude, so angle ADC is a right angle

[drifting igloo]

Ok

[knotty crow]

what is angle CAD then?

[drifting igloo]

Uhh

75?

Wait no k3kdked

60

[knotty crow]

closer, but it's 30

180 - (90 + 60)

[drifting igloo]

I see

So 30

[knotty crow]

I wanted to show that triangle ACD is a special type of a triangle (30, 60, 90), do you know its properties?

[drifting igloo]

Oh yeahv

I tried using this formula

Hold up

[knotty crow]

so now try to express CD in terms of x

[drifting igloo]

This one works no?

[knotty crow]

be careful, because triangle in your query is rotated (according to your pic)

yes

[drifting igloo]

You mean it's different for the 45?

How would it be for it then

[knotty crow]

I mean angles are in other places

30 is up

and 60 is down

[drifting igloo]

Do you have a pic that express it pls?

So I can take note about it

[knotty crow]

your picture is good, you can use it

[drifting igloo]

Oh ok

So it only swaps 60 for 30?

[knotty crow]

I meant this is a position of your triangle

[drifting igloo]

Ty

Ok so let's keep going

[knotty crow]

I've mentioned it because a lot of people have problems

[knotty crow]

Try to solve for CD in terms of x

[drifting igloo]

x√3?

Using that?

[knotty crow]

look, we can say AD is a√3

we also know AD is just x

[drifting igloo]

So x then

Ok

[knotty crow]

so x = a√3
what is 'a'?

because CD is 'a'

[drifting igloo]

Ohh

Uhh

CD is x?

[knotty crow]

no

x = a√3
divide both sides by √3
then x/√3 = a

[drifting igloo]

Ohhh

So it was like I said then?

Ok so

I change the x for...

60?

[knotty crow]

x/√3 no x√3, there is a difference

[drifting igloo]

Ahh

[knotty crow]

now you know that BD = x and CD = x/√3
you also know that BC = BD + CD = x + x/√3 = 60

Can you solve for x

[drifting igloo]

Ok so

The 60 is from the B to C correct?

[knotty crow]

yes

[drifting igloo]

60m no?

[knotty crow]

60 meters, exactly

[drifting igloo]

Ok

So what I do with the 60 now

[knotty crow]

read what I've sent once again and try to understand

[drifting igloo]

Sorry aaa it's kind hard to understand from only text without like a pic

So

[knotty crow]

so put information we've achieved so far in your picture

then it will be easier

[drifting igloo]

I

I'm doing a knot in my brain wait wait

So

The angle between cad is 30

Now i have to Express it to x

No?

[knotty crow]

not angle, it's about segment CD

strategy is to find 'x' because then we'll be able to find the area (cause height is x)

[drifting igloo]

Ok

So we find X

Using

x√3?

It's 60√3?

Or 30√3

https://cdn.discordapp.com/emojis/877367841739902977.png?quality=lossless&size=48

Hello? 😭

[obtuse pebble]

@drifting igloo Has your question been resolved?

[drifting igloo]

https://cdn.discordapp.com/emojis/665670287664087041.png?quality=lossless&size=48

[obtuse pebble]

@drifting igloo Has your question been resolved?

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[timid silo]

show your working

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

I just need to understand how to start

[high lily]

consider formula for circumference

[timid silo]

so apply the formula?

[high lily]

do you know the formula for the circumference?

yes/no

[timid silo]

can you refresh my memory please

i know screenshots im sorry

[high lily]

so no?

[devout sable]

For god sake please take screenshots, also is this some kinda academic test?

[timid silo]

not a test dw

[devout sable]

Hmm

#help-25 message it says final exam tho

[timid silo]

had a test yesterday

[devout sable]

Wym it says 9/13/2022 7 am

Date

[timid silo]

i had a test yesterday and i couldnt get help

fuck it

.close

[obtuse pebble]

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[devout sable]

And current time in kiribati is 4:00 am 9/14/2022

[stable rain]

LES GOOO

DISCORD DETECTIVES

[devout sable]

(Which is the first time zone)

[random depot]

[devout sable]

<@&268886789983436800>

Guy couldn’t lie properly

[obtuse pebble]

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[latent panther]

Anyone able to help me solve this?

[latent panther]

Sorry its kindve small but if you click on it it will be easier to read

[mint tendon]

split up the integral first

[latent panther]

Like this right?

Heres a better picture

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[obtuse pebble]

@forest crag Has your question been resolved?

[slim cove]

are we assuming x_n converges?

oh wait yeah the first sentence

okay

so you already found L

and we just need to show that the sequence is decreasing

that's correct

do we know what x_0 is?

[slim cove]

you also need to consider what happens if x0 = 12 but yep that's correct!

[obtuse pebble]

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[white summit]

Hello

I am a bit stuck on this problem. I believe it is an optimization problem, however I am not quite sure since my attempts have been futile

Q: A and B are the intersection points of the curve and the coordinate axes. The point P lies between A and B on the curve. The area of the triangle APB should be as large as possible. Find the coordinate of P and the area of the triangle

I have tried to create a function A(x) for the area that encompasses A(x)=0.5bh=0.5xy=0.5x(sqrt(4-x))

However when using it and its respective derivative A'(x)=0 to find an x-value, I get the wrong answer, since I get an Area of 1.5396 (instead of the answer A=1). Therefore, has anybody any idea of what my mistake/error could be approaching this problem

Answer to the problem P(3,1) and Area = 1

[white summit]

Sketch I made to the problem

and of course the corresponding function of the green line

ah and I used the derivative A'(x)=(0.5x(sqrt(4-x)))' which yielded

[mint tendon]

you can do this with multivariable calculus

woah

but im sure that just finding the point where $\c o P'(x) = \tu{slope of $\c l \overline{AB}}$ should be enough

[warm shale]

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

[mint tendon]

the base is going to be AB

therefore you want to maximize the height

which is perpendicular to AB

[white summit]

right, makes sense

but

P'(x) is a slope on my function f right?

[mint tendon]

yep

the tangent line

[white summit]

and if my slopes of P'(x)=AB I get the largest distance between AB and my point P

[mint tendon]

yeah

[white summit]

ahhh that is genius

[white summit]

alright, then I'll try to solve it. Thank you so much!

.close

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[humble coyote]

how am i supposed to show that a column without a pivot depends on one with a pivot?

[humble coyote]

i'm not sure i even understand the wording of that question

<@&286206848099549185>

[merry peak]

i have no clue

[humble coyote]

should i write that

[mint tendon]

LOL

the question is weird, can you elaborate a bit more on it

[humble coyote]

this is rref of A

and this is A

[obtuse pebble]

@humble coyote Has your question been resolved?

[obtuse pebble]

@humble coyote Has your question been resolved?

[humble coyote]

.close

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[exotic palm]

i dont understand what they meant by substitution to get to the final answer

[hardy widget]

Where does it say substitution?

[exotic palm]

the video, i was watching for an example problem like this one

[hardy widget]

Where does it say substitution?

As in what part of the solution, since it doesn't explicitly state 'substitute' anywhere

[whole spindle]

Is it asking you to substitute the x value into the derivative to find the equation

Or are you just finding the slope

[exotic palm]

he just says which by substitution to get to the final answer, which is 8a-6a^2

[whole spindle]

Oh so do you need help finding the derivative

[exotic palm]

oh

[hardy widget]

It's prolly this then

set h=0

[exotic palm]

so just plug in the zero into the h

[hardy widget]

yeah, it's just solving the final limit by direct substitution

[whole spindle]

Once you plug in 0 as h it should clear away the h’s and leave you with the answer you got from your teacher

[exotic palm]

right, i forgot about this step

thank you !

[whole spindle]

of course!

[exotic palm]

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[sullen raptor]

Can I get a step by step process how to do this question?

[obtuse pebble]

@sullen raptor Has your question been resolved?

[sullen raptor]

<@&286206848099549185>

[obtuse pebble]

@sullen raptor Has your question been resolved?

[primal wedge]

do you know how to find partial derivatives?

[sullen raptor]

Yes. I do

The partial derivative for x is 10x/7 and the partial derivative for y is -2y/7

[primal wedge]

ok, do you know general equation of a plane ?

[sullen raptor]

ax + by + cz + d = 0

[primal wedge]

good, in scalar form?

[sullen raptor]

a(x-x1) + b(y-y1) + c(z-z1) = 0?

[primal wedge]

cool

now what are a, b, c for tangent plane?

[sullen raptor]

Im not sure

[primal wedge]

well A(x-x1) + B(y-y1) + (z-z1) = 0 A=a/c, B=b/c

what are A and B ?

[sullen raptor]

6 and -3?

[primal wedge]

i mean in general?

the formula of a tangent plane?

[sullen raptor]

A is the derivative of x and B is the derivative of y?

[primal wedge]

yes (the value in the point)

[sullen raptor]

the 6.1 and -3.1?

[primal wedge]

no, no - the initial

this one you plug in the equation of the plane - and get the approx

is it ok to you?

[sullen raptor]

I'm still confused on what I have to do. I just know the derivatives.

[sullen raptor]

Still unsure

[primal wedge]

1 - find dz/dx, dz/dy ✓
1.1 - find z1
2 - find the equation of tangent plane in point (6, -3)
3 - plug the value (6.1, -3.1) in this equation

so we have A(x-x1) + B(y-y1) + (z-z1) = 0

what are x1, y1?

[sullen raptor]

x1 is 51/7 and y1 is 186/7

[primal wedge]

not realy , x1, y1, z1 are the coordinates of a point where the plane touches the surface

[sullen raptor]

x1 is 6 and y1 is -3

[primal wedge]

good can you find z1?

[sullen raptor]

-6

[primal wedge]

good

now can we find A and B?

do you see how to find them?

[sullen raptor]

A is 51/7 and B is 186/7

[primal wedge]

hmm..
Gene — Today at 00:15
Yes. I do
The partial derivative for x is 10x/7 and the partial derivative for y is -2y/7

[sullen raptor]

is the work correct?

[primal wedge]

this is not what I have

we need to plug x1, y1 to the partial derivatives

[sullen raptor]

i did, that is under the box labeled 1

[primal wedge]

but the derivatives are not the same as you mentioned

do you see?

[sullen raptor]

ignore the previous work, based off the picture alone, is the work correct? and if not where was the mistake made?

[primal wedge]

well, I think there is a problem with the derivatives

[sullen raptor]

for partial derivative of x, we leave the y component alone since we are deriving in respect to x, so the only information being changed is the x component and the constant

is that information wrong?

nvm, checked the book and realized my mistake

[primal wedge]

ok

but you get the idea

is it ok to you?

[sullen raptor]

Yea. Got it

[primal wedge]

great!

[sullen raptor]

Thanks i guess.

.close

[obtuse pebble]

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[misty temple]

It is not true that if it’s raining, I have my unbrella

[misty temple]

I’m not sure how to make this a proposition with variables

I tried doing !(r -> u) but I’m not sure if it’s that or (!r -> u)

How can I tell whether I would convert that sentence to one or the other?

The English feels ambiguous

[obtuse pebble]

@misty temple Has your question been resolved?

[obtuse pebble]

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[vernal linden]

Jim buys 7 apples and 4 pears for $7.25. At the same prices, Hanna buys 5 apples and 9 pears for $10.40. What is the price of one pear?

[vernal linden]

they asked me to use cramer's rule

I don't quite get how i should use cramers rule with this question

[junior flame]

well if you let a be the number of apples and p be the number of pears for convenience

you get 7a + 4p = 7.25

and 5a+9p=10.40

you then can substitute those values into cramers rule

[vernal linden]

oh

let me try it out

[junior flame]

good luck!

[vernal linden]

will it be (0.55, 0.87)

but it asked me for the price of one pear?

[junior flame]

which is the y coordinate?

0.87

id need to double check

[vernal linden]

0.87 is the y coordinate i got

[junior flame]

the answer i received was

0.55, 0.85

maybe double check your math?

that should give p=0.85

[vernal linden]

oh yead did something wrong

got the right answer now thank you very much

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[hardy coral]

The height (in meters) that a ball reaches after being thrown from the ground is given by h = -2t^2 + 4t, where t represents time in seconds. What's the max height the ball reaches?

[clear fog]

If you differntiate it, you will get the velocity, and differentiate again, you will get acceleration. Then you can input values and get the time where velocotiy reaches 0

[hardy coral]

oh it's not actually physics

it's just quadratic function

that's what i'm trying to figure out

farthest i've reached in this question is rewriting the equation and then doing the vertex formula. I need y only so...

rewritten eq: -t^2 + 2t

4ac - b2 divided by 4a translates to...
4(-1)(0) - 4 | -4
0 - 4 | -4
-4/-4
1

but that doesn't really seem to make sense to me

[clear fog]

ohhk

[hardy coral]

thanks for the help though!

[clear fog]

np

isn't the x axis -b/2a?

and when u input that value, you will get y right?

[hardy coral]

yea

ohh

let me check real quick then

gives me

-3

as y

Done. I'm not supposed to rewrite the equation.

-b/2a = -4 / 2(-2) = 1

x = 1

4(-2)(0) - 16 / 4(-2)
0 - 16 / -8
2

as simple as that

0,2

the max height the ball takes after being launched is 2 meters.

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[ornate pasture]

HELP ME AMEN

[obtuse pebble]

@ornate pasture Has your question been resolved?

[distant moth]

👿

[obtuse pebble]

@ornate pasture Has your question been resolved?

[obtuse pebble]

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[timid silo]

Two objects are moving in the same direction along a straight path at a constand speed, one at 0.9 m/s and the other at 1.9m/s.

How far would the objects have to travel so that the faster object arrives 5.5 minutes before the slower object?

[timid silo]

I can't figure out a way to write the equation in a way to isolate it to one variable, I always end up with a time variable and a distance variable. Completely lost :/

<@&286206848099549185> 🙏

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

have been looking all over google for a formula and cant find anything in the right format

[random depot]

use distance-speed-time relation

[timid silo]

Can I get a little more help on how I make that work with this specific problem? I have:

330sec = x/0.9 - x/1.9

would x = the answer, how much time they need to travel to fill the requirement?

[random depot]

ur on the right track

[timid silo]

I've got an answer but I can't comprehend how that works

is this just something where I should just trust the formula

[random depot]

What’s ur ans

[timid silo]

564.3 meters

[random depot]

Yeah shld be aight
I got the same thing

[random depot]

Read up on dis

[timid silo]

Can you link it? looking up distance speed time relation only comes up with speed = distance/time with no mention of that formula ever

[timid silo]

could you just shoot a link over so I don't have to bother you anymore? thanks for the help btw

[random depot]

This formula is to investigate specific differences

[timid silo]

I don't know how to search that on google

[timid silo]

What is the page where you found this pic?

.close

[obtuse pebble]

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[sand light]

Need some help with this problem

[sand light]

Top part is my work

Ignore the simplify portion

I dont know if the sqrtx^6 is added on accident? I dont know what to do with that piece but I know the x^3 is written as a proper piecewise function

or is it that the sqrtx^6 is equivalent to absolute value of x^3

Never mind, after putting some test numbers into my calculator I found that sqrtx^6 is equivalent to absolute value of x^3. I dont need help anymore but do feel free to let me know if my work is correct or not

.close

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[exotic escarp]

where do I begin

[obtuse pebble]

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[exotic escarp]

this is just hard af

[obtuse pebble]

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[zinc torrent]

How do I solve this

[royal basin]

what's zeta

[stable rain]

woah whys there a what

D:

[royal basin]

is this some kind of troll? this feels like a troll.

[obtuse pebble]

@zinc torrent Has your question been resolved?

[obtuse pebble]

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[timid silo]

hello

[timid silo]

Does anyone know anyways i can improve my algerbra so that calculus is easier for me

[random depot]

do more practice qns

[timid silo]

idk where to find them

or what site

[thick oracle]

You need algebra for calculus?

[cloud dove]

khanacademy

[thick oracle]

Lol

Aint that the least of your problems

[bold bane]

@languid oxide You can find Algebra textbooks using Google --> algebra filetype:pdf

[timid silo]

what do you mean ?

thx ill check out khan .close

.close

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[bleak eagle]

How to prove sqrt(3) is irrational through contradiction? I know the proof for sqrt(2) being irrational and I figure they are related, but I can’t fully figure it out

[obtuse pebble]

@bleak eagle Has your question been resolved?

[royal basin]

it is a good exercise to take the proof of the irrationality of sqrt(2) and try to reproduce it for sqrt(3)

[bleak eagle]

Thank you! I figured it out I think

.close

[obtuse pebble]

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[lethal grail]

I set the equation x^2 -4 / x- 2 = to ax^2... and plug in 2

and do the same w 8x-a+b = ax^2... and plug in 3

and subtract the system of equations and find a and plug in a to find b, and get 7, 9 but its still incorrect

[bright lava]

How did you plug in 2 when denominator is x-2?

[lethal grail]

it was basically 0 = ax^2...

was that incorrect

oh wait ur right

i couldnt have plugged in 2, what could I have done

[bright lava]

So instead, you need to take the limit as it approaches 2.

Actually, you can consider doing a difference of two squares.

$x^2-4=(x+2)(x-2)$

[warm shale]

Phoenix Wright

[bright lava]

Try continuing from here.

[obtuse pebble]

@lethal grail Has your question been resolved?

[obtuse pebble]

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[devout sable]

,rotate

[tall flint]

How I do b

[royal basin]

congratulations you clowned yourself

you've managed to crop this in a way that makes two different problems appear under letter b

and we cannot tell which one you were talking about

[tall flint]

This is simultaneous equation

[royal basin]

ok, so it's the lower b.

$\begin{cases} 4^x = 2^y \ 3 \log_{10}(y) = \log_{10}(x) + \log_{10}(2) \end{cases}$

[warm shale]

Ann

[royal basin]

this one, yes?

[tall flint]

Yes

[royal basin]

ok

[tall flint]

Only that

[royal basin]

have you made any progress so far or are you stuck not knowing how to begin?

[tall flint]

Yes

I tried making the right hand side to fraction

But don't know how to solver for the left hand side

So like 3log 10 (y) = log 10 (x/2)

[royal basin]

this is illegal already

log(a) + log(b) ≠ log(a/b) in general

also may i suggest doing a little work on the first equation?

[tall flint]

How exactly?

[royal basin]

well for example you could write 4^x as 2^(2x)...

[tall flint]

,rotate

[royal basin]

sure you could do that

i would've stopped at y = 2x

but if you have a fetish for fractions then you can also go with x = y/2. doesnt really make a big difference.

anyway now you have y = 2x

[tall flint]

I insert for y

So the x I substitute with y/2

@royal basin done finding the answer

Thanks

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

y'' + y = sinx , how do I solve a diff. eq. when resonance appears for a trig. function?

[timid silo]

which is?

nothing

its doenst exist

ye they're cringe

do you know?

he was just waisting ur time

i have not looked at your question

let me see

maybe you could look at mine

yea nice inspect element

if ur not gonna help go away

@timid silo could you look at mine please

i dont know vectors XD

[timid silo]

mine is channel 6

its not vecotrs

also do u have a specific question

because its hard to see what you mean

like when you say resonance do you mean resonance forcing?

term

@timid silo

im gonna take a random case for u then

wtf

[warm canopy]

Oh my god what

[timid silo]

nah just how do i solve that diff equ

[warm canopy]

Lol

[timid silo]

for the particular solution, do i assume y = Asinx + Bcosx?

[warm canopy]

Viking your trial solution should be Asin(x)+Bcos(x)

Yes

[timid silo]

but then it cancels

yea thats waht i was thinking

when u try to calc A and B

[short zodiac]

Yes

That'll work

[timid silo]

so whats the step after?

[rigid pine]

The forcing function f(t) is said to be in resonance with the system is the frequency of the forcing function is the same as the natural frequency, i.e., the frequency if f(t) = 0.

[timid silo]

nah it dosent work

[short zodiac]

Did you try?

[timid silo]

yes

[short zodiac]

Can you post it here?

[timid silo]

you get -Asinx -Bcosx + Asinx + Bcosx = sinx

so 0 = sinx

which is fcked

[short zodiac]

I see

[rigid pine]

You've not followed the method of undetermined coefficients correctly.

[timid silo]

what do you mean ?

[rigid pine]

You appear to have used the trial solution y_p(x) = A sin(x) + B cos(x).

[timid silo]

usually i just multiply my assumed function with x

[timid silo]

what do i use instead?

[warm canopy]

Go away

[short zodiac]

This guy needs to be reported

If you don't have anything to contribute don't stay here man

[rigid pine]

My help is turning into a word salad. :/

[warm canopy]

This is not useful information

Now***

Ugh

[timid silo]

what so x(Asinx+Bcosx) ?

[rigid pine]

Yes.

[timid silo]

ye but i tried this

before

i can try again i guess

[warm canopy]

Try harder

[timid silo]

or i guess

[warm canopy]

[timid silo]

before i did Axsinx + BxCosx

maybe thats wrong

[warm canopy]

It's right you just need to be careful

[rigid pine]

Q(x) in this problem is sin(x) and our terms in u(x) are sin(x) and cos(x) so we need to multiply by x.
The guess should work with correct workings.

[timid silo]

ye im on it

but i felt like i did this

before

and it didnt work

[warm canopy]

Basically when your initial trial function appears in your solution to ODE=0, it's a good idea to try it multiplied by x

[timid silo]

ye mb

i did one mistake before

but glad everything makes sense now

[rigid pine]

Awesome.

[timid silo]

ty!

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[cosmic badge]

I can't figure out how to do the last part , any help would be great , thanks

[inland solar]

So you want r of the smaller ball.

Ratio give you radius of the big sphere, it is 2r.

You calculated already Vc the cone volume. Half Vc is the sum of Vs and Vb, where Vs is volume of small sphere and Vb for the big one.

Can you get the answer from here!

[cosmic badge]

Nope 🤧 could you maybe write it down if possible?

[inland solar]

Not now, I'm cooking dinner.

[cosmic badge]

Oh okay , whenever you've got time then

[obtuse pebble]

@cosmic badge Has your question been resolved?

[inland solar]

I did that fast, please check it back.

[cosmic badge]

Is 3√500 the final answer?

It's supposed to be 3.68 though

[inland solar]

Check back.

3.68 is the cubic root of 50, look if I add a 0 somewhere.

The h, i put 360 instead of 36. Here is my mistake.

So cubic root of 50 is your radius.

Do you understand my demonstration?

[cosmic badge]

What does the = with the ~ mean?

[inland solar]

In general, it means approximately ,around ...

If you mean, the equal with the weavy top bar.

3.68 is approximately, cubic root of 50 is exact.

[cosmic badge]

No I meant the one you wrote that looks like an upright = with the ~

[inland solar]

You mean pi?

[obtuse pebble]

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[cosmic badge]

Ohh

Okay thanks for the help

[obtuse pebble]

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[inland solar]

Is how I write it!

[inland solar]

.closed.

.close

[obtuse pebble]

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[dreamy jackal]

can someone explain this step by step? and whats the general steps for simplifying radicals??

[small thicket]

rewrite the numbers as powers of something

like the 81 can be rewritten as something ^ something

same for 16

we also know that $\sqrt{x}$= x^\frac{1}{2}

[warm shale]

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

[dreamy jackal]

does it need to be perfect 6 exponents?? or any exponent? to like simplify it

[small thicket]

not necessarily

factor of 6 will also help with simplifying

[dreamy jackal]

wait you wil find a number that is like m^n = 81 ? did i understand it correctly?

[small thicket]

mhm

[dreamy jackal]

what do you do with the variables?

[small thicket]

what did u end up putting 81 as

[dreamy jackal]

9^2

and for 16 is 4^2

[small thicket]

it would be better to put it as a power of 4

bc x is also to power of 4

[dreamy jackal]

oh wait so u follow the variable's exponent for the power of 81?

[small thicket]

if u can yes

[dreamy jackal]

ohhh

[small thicket]

it would help u simplify easier

[dreamy jackal]

if i cant find the ^ of 16, can it just stay as 16 then right?

[small thicket]

sure

btw its 2^4

notice

4 can be split up into

2*2

which is just 2^2

$(2^2)^2 = 2^4$

[warm shale]

Mothy

[dreamy jackal]

oh so if you cant find the ^ with the same as the exponent variable, you could just do any ^ that is equal to 16?

[small thicket]

u could always do that

but its best to find something with the same exponent variable

if u cant then well there isnt anything u can do about it

[dreamy jackal]

oooo okok that became much clearer but what about the variables ?

[small thicket]

rewrite then as fractional indices probably

same with the coefficients

[dreamy jackal]

whats fractional indices

[small thicket]

have u not learnt yet?

[dreamy jackal]

not that i remember