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[alpine sable]

i think i remember proving bolzano with lim sup so i used lim sup here

@fiery quest i think youre supposed to close the channel now

[fiery quest]

+close

[alpine sable]

. close

(with no space)

[fiery quest]

.close

[lone heart]

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[wanton valley]

if a function is not continuous in a point is its derivative also not continuous in that point?

[mortal trellis]

if it's not continuous at a point it's also not differentiable at that point

differentiable implies continuous

[wanton valley]

okay thanks

.close

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[wanton valley]

wait no

.open

does it work like that?

[slender marten]

.reopen

[wanton valley]

.reopen

[lone heart]

✅

[wanton valley]

okay I need to figure out if a partial derivatives are not continuous in a point

does it suffice to prove that the function itself not continous in the point?

[mortal trellis]

I doubt it

just show that the partial derivative is not continuous?

[wanton valley]

my bad partial derivatives

[mortal trellis]

actually partial derivatives can exist even though the function is not continuous

[wanton valley]

okay thank you

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[mortal trellis]

consider the function on R^2 which is 1 everywhere except on the axes

[lone heart]

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[ornate condor]

can someone explain root test

i feel the 2nd one is totally different but anyway how do i intuitively understand it

also in the first image where does the z^j go

@keen plinth

[native granite]

On the root test, the $z^j$ does not appear\
L is the limit of n-th root of $|a_n|$, not $|a_nz^n|$

[ocean seal]

Twenty

[ornate condor]

$\sum_f(n) z^{n} = z^{n}sum_f(n)$ ?

[ocean seal]

Circle

[ornate condor]

nvm anw

isnt z^j part of the series

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[hot storm]

There's an inverse function of it right?

[vocal hawk]

,w solve x=y/(xy-1) for x

[ocean seal]

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[lilac nest]

If you want to find the inverse function of a function like this one it has to be in the form y=f(x) or x=f(y), but it's not in this case.

[vocal hawk]

assuming y=y(x)

[hot storm]

I forgot what it's called but I have to change its form into another one so it can have an inverse function?

Right?

[lilac nest]

You need to isolate the Ys on one side and the Xs on the other

[hot storm]

Could you show me?

[lilac nest]

Try to multiply both sides by the denominator to get rid of it

[lone heart]

@hot storm Has your question been resolved?

[hot storm]

Yes

[lone heart]

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[alpine sable]

Is there a way to quickly calculate cosx and sinx where x is not in [0, 2π[ ?

[molten pivot]

Yeah

Take x mod 2pi

[alpine sable]

How can i do that ?

[keen pasture]

Like cos (2πn+a) = cos a

[alpine sable]

so n is ?

[keen pasture]

Any natural number

[alpine sable]

Yeah, i mean n is number of courses in the circle. how can i know the number of courses ?

like 49π/4

It's π/4 but i don't know n to know that it's π/4.

[keen pasture]

(48+1,25)π

[alpine sable]

maybe n = cos a/2π - a

[keen pasture]

Pretty sure this formula is wrong

[alpine sable]

ah

[mortal trellis]

just subtract 2pi over and over again until you are in the correct interval

[alpine sable]

yeah, for that reason i asked is there a quick way to do that

[mortal trellis]

in this case 2pi=8pi/4, so subtract 8 from the numerator repeatedly

[alpine sable]

Uh i can see that

[mortal trellis]

well I mean this is super fast. clearly if you subtract it often enough you reach 1pi/4, cause 49 = 48+1 and 48 is divisible by 8

[alpine sable]

yeah true

[mortal trellis]

or convert 49/4 to 12.25 and subtract 2 repeatedly until you are left with 0.25=1/4

[alpine sable]

yeah i will do that one

thank you

it's much easier for me

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[hardy tiger]

I need help calculating the critical points in "f(x) = (3 x^2 - 12) / (x + 4)" because I forgot how to do that...

[hardy tiger]

I do have the first derivative already

[rose gate]

Find the first derivative and set it equal to zero

Here though I believe you can simplify the original function -> factor out a 3 in the numerator and you’ll end up with 3(x^2 -4)

[hardy tiger]

What would mean that x IS -4 right?

[rose gate]

you can then factor via the difference of two squares the (x^2-4) into (x+4)(x-4) and then cancel out the x+4 in the numerator and denominator

[rose gate]

Yeah this function is undefined at x = -4 but you can do this algebra to make your life a little easier

oh actually maybe you can’t since you end up with a straight line

[hardy tiger]

And to find the critical point I have to put the -4 into the original function?

[rose gate]

yeah just differentiate via the quotient rule and then set the numerator equal to zero

ignore what I said about simplifying

[rose gate]

Is -4 what you get from setting the first derivative = to 0 and solving?

[hardy tiger]

Yes

[rose gate]

If so then yes but that would be problematic since it’s undefined at x = -4

So check your working again maybe or ask someone else

[hardy tiger]

But it's undefined for the derivative of the function

not for the original function right?

[rose gate]

It’s undefined for the original function I think you mean

Since the original function has (x + 4) in the numerator

So x = -4 leads to division by zero

[hardy tiger]

oh yeah...

[rose gate]

But it would also be undefined for the derivative yes

[hardy tiger]

So the critical point is -4?

[rose gate]

so yeah I’d say check your differentiation again

[rose gate]

probably not since it’s not a valid x value for this function

[hardy tiger]

Hmm

let me see

[rose gate]

It’s asymptotic at -4

[hardy tiger]

yeah

Got the x values of the critical points I think

-0,54 and -7,46

And now to find the Y value just insert them into the functions right?

Yeah I think so lmao

thx though

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[alpine sable]

Can somebody help me with this

[stark plover]

Okay so

[void solar]

a few icecreams

[stark plover]

The right most box in the bottom expression looks like an eight

Let’s say big box = x

Bottom expression becomes 4(x + x/2 + x/8) = 13x/2

[alpine sable]

Okay

[stark plover]

Let’s call each batch of ice cream y

y^3 = x

So bottom expression equals:

,tex \frac{13}{2} \times y^{3}

Oops

6.5 * y^3

Where y is a batch of four differently colored ice creams

[alpine sable]

Ok

[alpine sable]

@long delta Help please

I need the exact answer because im too stupid to do math right now

[long delta]

Trying to comprehend

One sec..

[alpine sable]

Ok

@long delta Please are you there

[alpine sable]

@frigid stream can you help

Please 🥺

[alpine sable]

<@&286206848099549185> PLEASE GUYS

[copper stone]

the question is weird but 5.5 * the big box

the big box being (ice cream)³

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

So is that the final answer

Sorry im just in a rush

[copper stone]

i guess

[alpine sable]

Hmm

[lone heart]

@alpine sable Has your question been resolved?

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[lament sail]

Anyone knows how to do it?

Thought about using am gm but didn't do much

Apparently you are supposed to use cauchy schwarz

[lone heart]

@lament sail Has your question been resolved?

[lament sail]

<@&286206848099549185>

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@lament sail Has your question been resolved?

[lone heart]

@lament sail Has your question been resolved?

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[slow hound]

bro reopen it

i got it @lament sail

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[lament basalt]

@trim wagon
Hello, remember the question
sin (-105)?

[lament basalt]

Is this now correct? Thanks

[tall hearth]

,ask sin(-105°)

[ocean seal]

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[lament basalt]

[tall hearth]

thats not the formula for sum of angles

[lament basalt]

Oh yeah nvm

[lament basalt]

It's sin a times cos b + cos a times sin b, right?

[tall hearth]

yea

[lament basalt]

Ohkay I'm gonna close this thanks

.close

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[tranquil oak]

how would I go about solving this?

[tranquil oak]

do I replace the sin's for a?

[echo socket]

Yeah you can introduce a new variable a = sinx

Although it is not that necessary

Technically speaking

I'd go with just factoring the LHS

[small fog]

replace for sin(x) for a, solve quadratic, reverse substitute a, reverse find sin(x)?

[tranquil oak]

I get (2sin(x) + 1) and (sin(x) +1)

[tranquil oak]

what would I do with that?

[gilded citrus]

(2sin(x) + 1)(sin(x) +1) = 0 => 2sin x + 1 = 0 or sin x + 1 = 0
ie sin x = -1/2 or -1

[tranquil oak]

oh solve

[gilded citrus]

now check which of these is possible for the allowed range of x

[tranquil oak]

-1/2?

[echo socket]

2sinx + 1 = 0
2sinx = -1
sinx = -1/2

[tranquil oak]

oh do I look for sin of -1/2 on the unit circle?

[echo socket]

No, you look for an angle sine of which is -1/2

And don't forget that the angle should be between -pi/4 and 0 as well

[tranquil oak]

-15?

[echo socket]

-15 is definitely not in the interval

[tranquil oak]

im confused

[echo socket]

You have solved trigonometric equations before, right?

[tranquil oak]

yeah I just forgot

sin of -1/2 is pi/3 right

[small fog]

what

[echo socket]

Sine of -pi/6 is -1/2*

[small fog]

we don't need sin(-1/2)

we need arcsin(-1/2)

[tranquil oak]

which is -60 degrees correct?

[echo socket]

Yes

[tranquil oak]

but that wouldnt be the answer

[small fog]

yea

you need -60 degrees in radians

if it is in the range, then you are done

if not, find arcsin(-1)

[tranquil oak]

-1.0472

[small fog]

now actually find arcsin(-1) without using a calculator

[tranquil oak]

how

[small fog]

since you need it in a multiple of pi

[tranquil oak]

I need it in the form of a decimal

thats why I was using the claculator

[small fog]

you can use calculators, just get it in the form of pi

[small fog]

why?

[tranquil oak]

thats what the assignment requires

[small fog]

send the screenshot of where it says thAT IT Needs a decimal

since working with trig functions without pi is like trying to work on exponential function without e

[small fog]

oh

then just do the decimal

to first 3 digits

[tranquil oak]

-1 is pi right

so it would be 3.14?

[small fog]

arcsin(-1) is not pi

it's like -pi/2

[tranquil oak]

oh so -45 degrees

[small fog]

no

approximate -pi/2

pi is 3.1415

find -pi/2

[tranquil oak]

-1.570?

[small fog]

yes

[tranquil oak]

thats not the answer though right

?? @small fog

thats not it

[small fog]

yea

it is not in the range

[tranquil oak]

so -1/2 and -1 are both not in the range

what do I do next

[small fog]

are you sure -1/2 is not in the range?

[tranquil oak]

-1.0472 isnt the answer either

[small fog]

arcsin(-1/2) is about -0.523

[tranquil oak]

how do u get the arcsin

[small fog]

formally, find the inverse of sin

practically, use a calculator

[tranquil oak]

Got you

[tranquil oak]

Thank you

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[coarse wedge]

https://www.symbolab.com/solver/triple-integrals-calculator/\int_{0}^{\frac{pi}{4}} \int_{0}^{\frac{\pi}{2}}\int_{0}^{2} ^{ }\rho^{2\sqrt{2}}sin\left(\phi\right)d\rho d\theta d\phi?or=input

Is this the correct setup?

[lone heart]

@coarse wedge Has your question been resolved?

[heady pollen]

why does your integral go from 0 to 2?

also, if i understand the integral correctly, it describes a perfectly round sphere with radius 6
so should you go from 0 to pi and then from 0 to 2 pi?

[lone heart]

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[hardy tiger]

I have no clue how to solve this:
"The line t passes through the points D(2,-9), and E(3,4). The point F is not on the line t.

1. Prove that the triangle DEF has an angle of 90° in F.

2. determine the point G that lies on the line t, so that the triangle DFG is isosceles with F as apex."

(Sorry if the terms are not correct, I translated from Dutch)

Could someone help me?

[hardy tiger]

The problem is that I don't know where to start or what to do to solve this

<@&286206848099549185>

No, no one?

.close

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[viscid tulip]

Need help with this related rates question

[viscid tulip]

<@&286206848099549185>

anyone free to help

<@&286206848099549185>

[iron mulch]

Alright so your first step is to read the rules

ONCE

[viscid tulip]

ah my bad

.close

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[winged crag]

I'd like to know what are the pros and cons of the Newton Raphson method.
And are there more requirements?

What I know is that you have to be able to derive the function. However, this is more a requirement than an advantage or disadvantage. Also that it's necessary that the intermediate value theorem is between a positive and negative number of the interval.

[worn fox]

It can fail for some initial values, especially when you have derivative zero at a point

[winged crag]

Would you say, that if you choose a good initial value near 0 so the calculation can be done very quickly.
Would you count that as a pro?

[worn fox]

Sounds like a pro to me, but I'm not familiar with how efficient Newton raphson is with good initial values in comparison to other methods

[winged crag]

Because i need to compare the newton raphson method with the bisection method and regula falsi method.

To find the commonalities and differences

[winged crag]

But since you're smart and i'm not i'm also going to count it as a pro 🙂

[worn fox]

Maybe take your favourite graph with some roots and use those methods on it and compare them

[winged crag]

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[foggy parrot]

Im confused about the 3rd one

[limpid spade]

Note r=h

So u can write it as pir^2r or pih^2h

[foggy parrot]

oh

alright

[limpid spade]

Dont forget to Simplify afterwards

[foggy parrot]

ok

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[lone heart]

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[buoyant tulip]

How do I solve this

[turbid violet]

Hmmm not sure if it's the right track but you could treat ADC as an equilateral triangle

and you know OA is = 10 cm

since OABC is a square OA = AB = BC = CO = 10cm

you can calculate the diagonals AC and BO using Pythagoras's theorem

[buoyant tulip]

So 10 squares plus 10 squared divided by 2

Sorry 10 squared plus 10 squared and then square root it

[turbid violet]

yep

[buoyant tulip]

But you don’t know the height form the middle to D

[turbid violet]

so the midpoint of one of the diagonals should give you the point straight below D down to the XY plane

[buoyant tulip]

But how would you know the z distance from the XY Mid point To D

[turbid violet]

the height is given in the question looks like

10 cm

so that's your z distance

[buoyant tulip]

I need to get better at reading the question I was so clueless to how you would find the hight and it’s been there the whole time 😭

[turbid violet]

no worries lol, I spent quite a bit of time figuring out how you could calculate from all the other sides but then re-read the question and saw it 😛

[buoyant tulip]

Thanks for the help

.close

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[finite trail]

Y=4^X

[finite trail]

It says to sketch that graph

I have no idea how to

[finite trail]

This one I mean

[tacit arch]

plot points for a few numbers x

[finite trail]

Brb in 2 mins

[tacit arch]

like x = -2,-1,0,1,2

[finite trail]

But wait

4^(-1) is .25 correct?

[heady pollen]

correct

[finite trail]

Oh wait it just clicked for me. Very simple. Sorry idk why it took so long.

Thanks

Jesus Bless!

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[agile salmon]

whats the range of this, and when does function increase?

[naive valley]

the question is technically ambiguous since we don't know what the function does beyond the left and right side of the screenshot

[limpid spade]

Yes

[naive valley]

but if you assume they go on forever at those slopes then what does that tell you?

[agile salmon]

they do go on forever

and wdym those slopes

[naive valley]

whatever the slopes of those lines are

i.e. if they continue linearly forever in each direction

[agile salmon]

1/6 and 1/10?

or is it 1/8 im not sure

[naive valley]

well one of them has a negative slope

the actual numerical values don't matter, the point is, does the graph extend arbitrarily far downward

if so then that tells you that the range is (-infinity, something] or (-infinity, something)

[agile salmon]

is the "something" 8?

[naive valley]

range = the values on the y axis

what's the largest y value that the function reaches?

[agile salmon]

oh im dumb

1

[naive valley]

yep

[agile salmon]

what about when function increases

[naive valley]

any thoughts about that?

[agile salmon]

i think it increases until it hits 8,1

[naive valley]

right, so it's increasing for what set of x values?

[agile salmon]

wym what set

[naive valley]

well what's the expected form of answer you're supposed to provide?

[agile salmon]

x<(a)

a is your answer

[naive valley]

ok

so the function is increasing for x < what?

[agile salmon]

8

[naive valley]

yes

[agile salmon]

oh okay thank you

[lone heart]

@agile salmon Has your question been resolved?

[agile salmon]

hey could you help me with something else

and yes it does go on forever

[alpine sable]

why does this look like a test

what is that 💀

[agile salmon]

idk they just do that

its homework not a test

[lone heart]

@agile salmon Has your question been resolved?

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[boreal stag]

Asking for questtion biii

[pale thistle]

do we know how many shirts they each make in a 1 hour time period?

[boreal stag]

Yes

[pale thistle]

ok so im assuming somewhere your algebra got mixed up because your initial steps are right yet your final answer is off by a lot

imma work through it rq lemme see what i come up with

[pale thistle]

this is where i think you messed up

i dont see the next steps clearly as how you got 7020x^2 and other terms

[boreal stag]

I am not sure what to do

[pale thistle]

did everything right up to the step where you first crossed it out

we do multiply the bottom of the fraction over

do you have a calculator with you?

[boreal stag]

Yep

[pale thistle]

ok so yeah just expand the right hand side of 117(x^2+3x)

[boreal stag]

What abt the left side

[pale thistle]

we can leave that until we expand the right side

after we do that we can move it all over to the right side and combine like terms

[boreal stag]

I think i got it

I did a calcution error

[pale thistle]

ahh ok yeah happens to the best of us

[boreal stag]

Thanks

[pale thistle]

of course

.close

[lone heart]

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[vagrant marsh]

How do i get help <@&286206848099549185> the rules are a bit confusing

[vagrant marsh]

oh

I jus need help confirming that this is 126 degrees or not

Thecontext behind the question is: The figure below shows a map of five streets that meet at Concord Circle. The measure of the angle formed by Melville Road and Emerson Avenue is 118°. The measure of the angle formed by Emerson Avenue and Thoreau Street is 134°. Hawthorne Lane bisects the angle formed by Melville Road and Emerson Avenue. Dickinson Drive bisects the angle formed by Emerson Avenue and Thoreau Street. What is the measure of the angle formed by Hawthorne Lane and Dickinson Drive?

anyone here?

[wary stream]

Please read #❓how-to-get-help

[wary stream]

!15m

[lone heart]

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.

[vagrant marsh]

.close

[lone heart]

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[unreal cloud]

I was taking a Practice Test for my Calculus 2 Course, and it's been quite a while since I've been in Calculus 1, so there are many fuzzy parts of the subject for me but my professor placed a good amount of focus on Integration and Derivatives, I'm unsure of how to approach this question though

I tried plugging in 0 for the equation on the right but that doesn't give me any answer close to the options

<@&286206848099549185>

[small fog]

first find the average rate of change in that interval

very simple dy/dx

[small fog]

a

[unreal cloud]

What would be the process of finding the derivative?

[small fog]

no

you just need the average rate of change

delta y over delta x

and delta x is 2

and y goes from -4 to 2sqrt(2)-4

[unreal cloud]

Ah then I actually had no clue how to answer this question, I've never heard of Delta Y or Delta X

[small fog]

what

delta is "change in"

it's just change in y / change in x

[unreal cloud]

Lol! I've seen dy/dx but never understood what it meant

Ohhh

that makes sense

[small fog]

so the change in x is from 0 to 2

that is 2

[unreal cloud]

so in the interval 0,2 it changes by 2

[small fog]

change is y is from -4 to 2sqrt(2)-4

aka 2sqrt(2)+-4

[unreal cloud]

and I plug in 2 in the place of X in that function?

Gotcha

[small fog]

aka -4+2sqrt(2)

[small fog]

no

actually

yeah

yes

yes

do that

[unreal cloud]

LOL!

Yeah, I see that now

Thank you!!

You completely turned my head in the right direction once you said Delta is "change in"

[small fog]

np

[unreal cloud]

Now I'm trying to figure out how to properly solve 2 times the sqrt of 2 -4, I know that the square root of 2 can be simplified to 2^1/2

[small fog]

it's much more simple

here's a hint: think of subtracting by 4 as adding -4

and think of the fact that addition is communative

[unreal cloud]

meaning?

[small fog]

remember how f(0)=-4?

and you want to find the CHANGE in y

maybe you could add 4 on both of the values to make it a bit easier

[unreal cloud]

Let me try it out

[small fog]

if you did it right, then the change in y should be ||2sqrt(2)||

and the overall average rate of change should be ||sqrt(2)||

[unreal cloud]

Damn, I'm just hardheaded, I can't really figure out the change in Y

from -4 to -4+2sqrt(2)

the difference is mainly the 2sqrt(2)

so if that is the change in y then using dy/dx

2sqrt(2)/2

the 2's cancel out

and we're left with sqrt(2)

wait

i popped off there

sqrt(2) can be simplified into 2^1/2

[small fog]

yes

[unreal cloud]

if we find the derivative

[small fog]

for the mvt don't you need to find the anti derivative?

wait nvm

[unreal cloud]

it would be 1/2*2^-3/2

actually

that makes things worse i think

let me get my rules chart for derivatives

sqrt(2) is a constant so it wouldn't change much as an answer that is acceptable

so with the overall average roc being sqrt(2), what do I do with now?

[small fog]

do you know antiderivatives

[unreal cloud]

Yes

Would I use the reverse power rule?

[small fog]

yeah

[unreal cloud]

which would result in

2^(3/2) over 3/2

[small fog]

aka 2/3(2^3/2)

now subtract -4x because of the -4

then multiply it by 2

because of the 2 you should have took out of the integral earlier

so you get $\frac{4}{3}x^{\frac{3}{2}}-4x$

[ocean seal]

hired

[unreal cloud]

Okay, let me try to process the -4 and 2 being introduced, I'm sorry for this taking a bit of time for me to get

This is what I had before the -4x and 2

[small fog]

no

it was (2/3)2^3/2

[small fog]

yeah

[unreal cloud]

I forgot how to handle fractions within a fraction

[small fog]

that simplifies to (2/3)2^3/2

[small fog]

dividing by x is the same as multiplying by 1/x

[unreal cloud]

like this?

[small fog]

yes

so you have that

then you subtract 4x

because of the -4

[unreal cloud]

the -4 from the y interval correct?

from when it said -4 2 sqrt(2)

[small fog]

now you multiply it by 2

since you took out the 2 at the start

[small fog]

now you can put the *2 into the 2/3

so you get 4/3

[unreal cloud]

like that?

[small fog]

yeah and now you put it in the 2/3 so you get 4/3

[small fog]

yeah

so now you have the antiderivative

of $\frac{4}{3}x^{\frac{3}{2}}-4x$

[ocean seal]

hired

[unreal cloud]

and with that,

[small fog]

now try out the values in the original question

that are in the interval [0,2]

[unreal cloud]

the 0 & 2?

oh okay

0 - 2 not only 0 and 2

[small fog]

yeah

but NOT [0, -2]

[unreal cloud]

so 0 would give me 0

[small fog]

only [0, 2]

[unreal cloud]

hmm

[small fog]

yes

which is not sqrt(2)

[unreal cloud]

when I plug in 1

I dont even know how to evaluate that

1^3/2. ?

[small fog]

that is 1

[unreal cloud]

oh

actually

that was a brain dead moment from me

1 to the power of anything

is 1

anyways

1 x 4/3

i could change 1 into 3/3

and multiply

which would be 12/9

omg im dumb

4/3 x 1 is just 4/3

so 4/3 - 4(1)

4/3 - 12/3

which would equal -8/3

which is still not sqrt(2)

now to plug in 2

[small fog]

wait

ignore everything i said

i am stupod

[unreal cloud]

oh noo lol

[native granite]

So what is the question ? 🧐

Did you manage to find c ?

[unreal cloud]

I did not manage to find c

[small fog]

ok apparently it's 1/2

[unreal cloud]

In this case, what would c be?

[small fog]

idk how my mvt calculator got to that

[native granite]

Yep that's what I found too

Okay so mean value theorem states

In our case

There exist c in $[0,2]$ such that [\frac{g(2)-g(0)}{2-0} = g'(c)]

[small fog]

yes

[native granite]

(I don't know how much you explained so I'm starting from here ^^)

[small fog]

we got to this point

[native granite]

Okay, you got the expression of g' too ?

[ocean seal]

Twenty

[small fog]

it should be there exists a c where g'(c)= sqrt(2)

[native granite]

Okay

So yeah basically it's solving this for c

[small fog]

my idea was to take the integral of both sides

[unreal cloud]

Okay so @small fog at what point should I erase from my mind

[native granite]

Oh no you don't need that actually. In fact, I don't really know what you could conclude with this ?

[small fog]

but for some reason this calculator says we need to find the derivative g'(c)=1/sqrt(c) for some reason

[native granite]

Yeah

[small fog]

why tho

[native granite]

$(\sqrt(x))' = \frac{1}{2\sqrt{x}}$

[ocean seal]

Twenty

[native granite]

So $g'(x) = \frac{1}{\sqrt{x}}$

[ocean seal]

Twenty

[native granite]

You can also see that as a power rule, depending on which one you prefer : $\sqrt$ is basically power $1/2$ so the derivative would be $\frac{1}{2}x^{1/2-1} = \frac{1}{2}x^{-1/2}$

[ocean seal]

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

[small fog]

yeah

[native granite]

Okay

[small fog]

but how do we get this now

nvm it's because you multiply it by 2

[native granite]

Well $g(x) = 2\sqrt{x} - 4$ so we just have to apply this formula I gave for root derivative

[ocean seal]

Twenty

[native granite]

Yes

The 2/2 cancels out so we get 1/sqrt x

@unreal cloud You fine ?

[unreal cloud]

I'm a little lost but I felt that hired is digesting it so they can give me the run down

[small fog]

so erase everything i said about integrals

you need to find the derivative

and the derivative of this function is 1/sqrt(x)

[unreal cloud]

Okay so we have a value of c in the interval (0,2)

we found the dy/dx

is that still relevant?

[small fog]

yes

[unreal cloud]

the dy being 2sqrt(2) and the x being 2

[small fog]

yes

[unreal cloud]

the 2's cancel, leaving us with sqrt(2)

[small fog]

because now we need dy/dx to be sqrt(2)

so 1/sqrt(c)=sqrt(2)

and 1/sqrt(x)=sqrt(1/x)

[unreal cloud]

where does the 1/sqrt(c) come from?

[small fog]

1/sqrt(c) is the derivative of your fucntion

[unreal cloud]

oh of the 2sqrt(x) -4

[small fog]

we need f'(c)=sqrt(2)

f'(c)= 1/sqrt(c)

[unreal cloud]

sorry, im trying to find the derivative of the function to get that 1/sqrt(x)

derivative of -4 is 0

[small fog]

yes

derivative of sqrt(x)?

[unreal cloud]

sqrt(x)

like that correct?

[small fog]

yes

[unreal cloud]

Okay and then

[small fog]

you need to find 1/sqrt(x)=sqrt(2)

and you can find that simply by just knowing that sqrt(x)^n is equal to sqrt(x^n)

in this case, n=-1

[unreal cloud]

so where would the -1 come from?

[small fog]

1/x = x^-1

so you just need to find 1/x=2

and then you are done and that is your answr

[unreal cloud]

Phew well that was a lot

I'll definitely have to practice that question and speed up the process

What would I search up to tackle problems like these?

.close

[lone heart]

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[gray isle]

prod to sum law for logs

[lone heart]

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[pine cliff]

wait is 78.65 rounded to 3 sig figs 78.6 or 78.7?

[pine cliff]

my textbook says 78.6 while the calculators on the internet say 78.7

[alpine sable]

78.7 if your textbook says that its either wrong or you got somewhat off in some part of your equation

or, more than likely, it rounded earlier in the equation

[pine cliff]

alright i think the textbook is around 10 years old

[alpine sable]

or rounded each time thru the steps

[pine cliff]

i see

[alpine sable]

i mean the rule in math has always been round up but couldve been just a simple mistake by some guy making it that didnt get realized

yea 5 and higher rounds up

[pine cliff]

yea i was questioning myself cuz the textbook said that

[alpine sable]

ask your teacher tho maybe the textbooks wrong or you're a bit off

[pine cliff]

i think the question didn't hve any equation

it was just round 78.65 to 3 sig figs

[alpine sable]

does the question directly ask to round "78.65" to three sigfigs

[pine cliff]

yup

[alpine sable]

yea then that is a mistake

[pine cliff]

alr

thanks for the help

.close

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[pine cliff]

uh

[pine cliff]

one of my friend is saying that

if ur rounding with sig figs

and the number before the number ot be rounded is even

and if its odd

its different

ex.

78.65

he says that it rounds to 78.6

and for 78.55

it rounds to 78.6

is that really how it works?

[wide raven]

yes sir i can confirm that it is true

the thing is it is equidistant from both 78.5 and 78.6

so idk why but we keep the the last sig fig even

[alpine sable]

oh Nightshade my apologies I gave you an incorrect answer earlier I was misunderstanding

[pine cliff]

o ok

[alpine sable]

yes its a weird rule tbh but when the number held right after is exactly 5

you round to the closest even whether up or down

[pine cliff]

ok i get it

[lone heart]

@pine cliff Has your question been resolved?

[lone heart]

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[narrow portal]

I’m not sure at all on what I have to do here.

[alpine sable]

recall the distributive property

what does it say?

[narrow portal]

Write an equivalent expression?

I think

[alpine sable]

don't focus on that part yet

what is the distributive property first

[narrow portal]

Combine like terms?

[fair osprey]

No?

Do you know how to solve like.3(x+y)?

Or stuff like 3(5+x)

[narrow portal]

No 💀

[alpine sable]

grab the definition your class has

if they gave you one

if not ill send it right now

[narrow portal]

that’s what he’s been telling us 😂

[alpine sable]

bruh

are u fr?

[narrow portal]

All he says distribution property is combining like terms

yes

[alpine sable]

heres the distributive property, for any $a, b, c\in\mathbb{R}$ we have $a(b+c)=ab+ac$

[ocean seal]

jswatj

[narrow portal]

hm alright

[fair osprey]

Let’s try something simpler then. Try 3(1+7) but don’t add the 1+7 first

Or 3(x+y) is you want

[narrow portal]

Is this 24

[alpine sable]

yes

[fair osprey]

Yeah, but can you show the steps? That probably wasn’t the best example, how about 4(5-v)?

[narrow portal]

Alr I’ll try

So I gotta expand by distributing terms.

4x5+4x -v

Simplify 4x5 to 20

20+4x -v

Regroup terms

20-4v

Is that right?

[fair osprey]

Yeah

Now try solving your problem from earlier

[narrow portal]

Alr I’ll try but Idk how since it has 2 variables

[fair osprey]

Just keep them separate

Like what about 5(c-h+j)?

[alpine sable]

write it as $4((10q+4r)-1)$ then its two things instead of 3

[ocean seal]

jswatj

[narrow portal]

Alright

So I gotta expand by distributing terms.

4x10q+4x4r-4

Simplify 4x10q to 40q

40q+4x4r-4

Simplify 4x4r to 16r

40q+16r-4

is that right?

[alpine sable]

yes!!

good job

[narrow portal]

😂

Thanks for making the problem sound a lot simpler

[alpine sable]

np

[narrow portal]

I thought it was some giant problem 💀

[fair osprey]

Oh that’s when they make it look simple /hj

[narrow portal]

Alright well I’m full on lost now he never taught us this

[alpine sable]

does the line cover any number greater than 9

[narrow portal]

no

[alpine sable]

okay

does it cover 9?

[narrow portal]

yes

[alpine sable]

does it cover numbers less than 9?

[narrow portal]

yes

[alpine sable]

then it must be x<=9

since <= means "less than or equal to"

[fair osprey]

Which ones are greater than 9, less than 9, and which ones are on 9 and which ones aren’t?

[narrow portal]

Is this the one with the line under the <

or the one without it

[alpine sable]

with the line under

[fair osprey]

Try solving it yourself

[alpine sable]

^

[fair osprey]

Or just narrate how to solve it here

[narrow portal]

it’s a timed thing 💀

i can’t type back fast enough and answer

[alpine sable]

is it a test?

[narrow portal]

nah

[fair osprey]

We can’t help on tests

[narrow portal]

delta math timed assignment

Timed grade

[fair osprey]

Well what if you were on a test? What don’t you understand?

First, what’s the main number we’re looking at?

[narrow portal]

I don’t understand what it means by inquality and what I’m meant to be looking for

[narrow portal]

0 I think

Or -1

[fair osprey]

Yeah. -1

Which way does the line point?

Left or right

[narrow portal]

right

[fair osprey]

So does that mean it covers number greater than or smaller than -1

[narrow portal]

Greater

[fair osprey]

So that eliminates half the options. Which ones are left?

[narrow portal]

X <-1 and then the same thing but with a line underneath the greater sign

[fair osprey]

No, it goes to the right so it’s greater. That’d mean the remaining options are x>-1 and x>=-1

[narrow portal]

Ohh

[fair osprey]

Do you know the difference between them in what they mean in math?

[narrow portal]

Nope not at all

I was absent this whole week so I didn’t get to hear anything abt it

[fair osprey]

Ohh alright. Well the one without the line you know means greater or less than right?

[narrow portal]

Yeah

[fair osprey]

Do you notice anything different between them? Aside from the way they point and numbers

[narrow portal]

Only thing I notice is the smaller arrows on one side

[fair osprey]

Anything else about the large arrows?

What about the circles?

[narrow portal]

Some of the circles aren’t filled in

and some are

[fair osprey]

Yeah! That’d the main thing. < and > are the empty ones. The ones with the underline mean “greater or equal to” and “less than or equal to”

The filled in ones are >= and <=

[narrow portal]

Ohhh

So since the dot is filled in

it would be the answer with the line?

[fair osprey]

Yep

X>=-1

[narrow portal]

Alright

I think I got it from here

Thanks for the help!

.close

[lone heart]

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[alpine sable]

send an example

break it up

[ornate condor]

u can first do prime factorisation

[lilac nest]

Try to find the prime factors of 136 and see whether there are any squares in it

[wide raven]

factorising

the same, prime factorisation

[ornate condor]

sqrt 8=sqrt(2*2 2) =sqrt 2 * sqrt(22) = 2 sqrt2

[lilac nest]

√48=√(2⁴×3)=2²√3=4√3

The only faster way is calculator

We already sent 2

[lilac nest]

It's written down

[lilac nest]

This one too.

[wide raven]

there is a square root before that

[ocean seal]

Andrea276

[wide raven]

136=2^3*17

[ornate condor]

wasnt my example of 8 pretty simple tho

[wide raven]

we can take only even powers out

[wide raven]

it was fine, it told us what we ought to do

[ornate condor]

did u understand the example with 8?

[wide raven]

i never came up with 17

i just divided by 2

[lilac nest]

You just start by dividing by 2, then 2 again, then 2 again then you get to 17, which I'm sure you can divide by 17. Of course if you get a big prime number is going to be harder, but they won't put them in your test

That's the procedure to find the prime factors of a number

Always divide for the smallest prime number that gives remainder 0

[wide raven]

and because it is even

[lilac nest]

Until you get to 1

[lone heart]

@trail terrace Has your question been resolved?

[lone heart]

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[rocky tendon]

**Sherry is the sole proprietor of a successful flower shop. In Sherry’s flower shop the ratio of roses to lilies is 4 to 3. The ratio of Lilies to peonies is 4 to 1. What is the ratio of roses to peonies?
**

[rocky tendon]

how would i find this?

do i divide? multiply? add? subtract?

im super confused

[vale wigeon]

roses : lilies = 4 : 3
lilies : peonies = 4 : 1

[rocky tendon]

i still dont really get it

would i multiply?

<@&286206848099549185>

[iron mulch]

Okay so your first step is to read the rules

!15min

[lone heart]

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.

[chrome plank]

Here's a consideration, but I'm not sure if it's the right tip
For every 4 roses, there are 3 lilies
For every 4 lilies there's 1 peony

That's what those proportions are trying to say

[rocky tendon]

ohhhh

that helps alot

**For every 4 roses, there are 3 lilies
For every 4 lilies there's 1 peony
What is the ratio of roses to peonies?
**

i dont get it

idk what to do

i fuckin give up

fuck this

😔

[void solar]

How can you relate them

What do the two have in common

[rocky tendon]

for each 4 roses = 3 lillies
for each 4 lilies = 1 penoies

[void solar]

For every 4 roses, there are 3 lilies
For every 4 lilies there's 1 peony
What is the one thing that both lines have

[rocky tendon]

but still, im just repeating my self

[chrome plank]

Big tip here, ||how many roses are needed to have 4 lilies?||

[void solar]

They both involve lillies right?

So thats how you can link the two things

[rocky tendon]

to have 4 lilies, you need 4 and a half i guess ?

[rocky tendon]

ohhh

thats true but

do i multiply ?

[void solar]

So to relate roses to peony. You can do it striaght away right.

You have to go through lillies

So if you can find how many roses are 4 lillies

and you know 4 lillies are 1 penoies

x roses = 4 lillies
4 lillies = 1 penoies

x roses = 4 lillies = 1 penoies

[rocky tendon]

5 roses to equal 4 lillies?

because if 8 roses equal 6 lillies

then 7 roses would equal 5

and 6 would equal 4?

[void solar]

No

you cant just plus one on both sides

[rocky tendon]

ohh

[void solar]

When you increase on side and increase the other side. Its not by a flat amount but rather stuff like double or half the value

[rocky tendon]

ohhhhh

4/3 is 75% tho, how would i be able to make 4 lillies?

[void solar]

yes so 3 x 4/3 will give you 4 lillies

[rocky tendon]

ohhhh

yeah

[void solar]

but to keep the ratio the same

you have to do it to the other side right

so 4 x 4/3 roses = 3x 4/3 lillies = 4 lillies = 1 penony

So then you can just cut out the middle man (lillies)

and equate roses to peony

[rocky tendon]

ohhh

so 4/3 would equal 1 peony

so the answer is 4/3 : 1 ?

[void solar]

yes

wait

[void solar]

4 x 4/3

not just 4/3

[void solar]

4x4/3 roses= 4x4/3 lillies = 4 lillies = 1 peony

[rocky tendon]

OHH

the answers on my practice test are
**
25:2
18:1
7:1
16:3**

[void solar]

So to solve questions like this.
First find out how you can link the two
Then modify the ratio so you can equate the two lines

[void agate]

Here's how I solved it

[void solar]

well whats 4x 4/3

[void solar]

yeah it might be easier that way cause your working with whole numbers

[void agate]

Yep and its the same steps you mentioned

@rocky tendon First we link the common variables between them

[rocky tendon]

so i would do 4 x 3 and get 12

or would i do 4x4 first

[void solar]

Do you know how to multiply fractions?

[rocky tendon]

im trying to learn

[void solar]

Turn the number 4 into a fraction first. Which is 4/1 right

[void agate]

The thinking process here is: "How many roses give me the same amount of lilies as peonies?"

[rocky tendon]

yeah

[void solar]

Then times the top numbers and the bottom numbers

[rocky tendon]

4/1

OHHH

so lemme do that on paper

4/1 x 4/3 right ?

[void solar]

$\frac{4}{1} × \frac{4}{3}$

[rocky tendon]

thanks man

[void solar]

thats not a multiply sign....

its a big x

oh well

[rocky tendon]

it still works

[ocean seal]

Xiszt

[rocky tendon]

since these arent the same

[void solar]

Doesnt matter if they are the same or not

That only matters in addition or subtraction

In multiplication you just times the top by the top. and bottom by the bottom

[rocky tendon]

OHHH

YOOOO

[void solar]

[rocky tendon]

16/3

YOOOO

[void solar]

Do you know how to divide fractions?

You flip the back one. then just multiply it

[rocky tendon]

ohhh

canu show me ?

like

[void solar]

$\frac{1}{2} / \frac{1}{3} = \frac{1}{2} × \frac{3}{1}$

[ocean seal]

Xiszt

[void solar]

Then you just multiply it

[void agate]

Yo @void solar could you help me out in #help-7｜zen1thxyz

[rocky tendon]

OHHHH

thanks so much bro, i was so close to giving up

you are a life saver my g

is there a way i can save this channel ?

so i can study off of it?

[void solar]

screenshot it lol