help-38

[hallow crane]

yeah and i'm saying u don't need a calculator nor calculus

(i think)

The revenue = (80-2x)(20+x)

(80-2x) is the price of each ticket where x is the extra number of people (from 20)

(20+x) obviously the number of people because 20 + extra = number of people

[loud mica]

But the original 20 people payed full price right?

But that equation doesn’t accommodate for that

[hallow crane]

yes so if you put x = 0, you can see that

x = 0 means 0 people additional from 20

x = 1 means 1 person additional from 20 so 21 people

and so on

[jaunty silo]

I think he means if 1 people comes after 20, then if only that person gets discount or not

[loud mica]

But if I have 21 people, x=1, so 80-2x means everyone gets the discount, rather than just the one person

I could be misinterpreting the question maybe?

[jaunty silo]

I think everyone gets discount for additional

[hallow crane]

it drops for each person

[loud mica]

What a goofy business model what the

[hallow crane]

"drop ... for each person"

[loud mica]

I just assumed it would be a discount for only the people after 20, since that makes more sense imo

[hallow crane]

wait i think you're right lol

[loud mica]

idek

It’s heckin 1:00 am bro

This question seems very ambiguous to me

[hallow crane]

i mean you're right

it'd just be something like: the revenue = 1600 + (x-20)(80-2(x-20) )

[jaunty silo]

Now reading I think you're idea could be also correct

[fading lotus]

I think this is the equation where x+20= number of students

[hallow crane]

yes

but i think we didn't take enough english lessons

so what i wrote prior is probably answering a whole different question lol

[loud mica]

But the way I interpreted it seems like it would make the question way more difficult than it was probably intended to be, I have no idea

[hallow crane]

is one more difficult than the other

i mean arguably

[loud mica]

right?

[hallow crane]

but if you're in a calculus class they're both the same

[hallow crane]

this one is what the questiona ctually meant (what u pointed out)

[hallow crane]

this one is when we give discounts to everyone

yk funny thing is even the first simplistic model still generates revenue

for each additional person

lol

again i think the question is a bit weird

[loud mica]

So moving on, how does each equation have a maximum?

Does one make more sense in that regard, than the other?

[hallow crane]

no actually think about it like this

20 people: 1600
21 people: 1600 + 78 dollar for the additional person
22 people: 1600 + 76*2 dollar for the additional 2 people
.
.
.

but isn't this question contrived?

clearly 28 people is when you get the most money

why does this need calculus

if the bus didn't have a capacity then 40 people actually maximizes the revenue you can obtain

[loud mica]

Is 28 true for both possible equations?

[hallow crane]

yeah

[loud mica]

On the two interpretations

Ok

I’ll write a message to my teacher

[hallow crane]

i might be missing something cuz this question is pretty stupid

lol

anyway do you still want to know how to get the new equation?

[loud mica]

thanks for the help, English is kinda weird sometimes

[loud mica]

Nah I understand it

[hallow crane]

okay then

[loud mica]

I guess I was just confused on how to interpret the question

Ima .close it now

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[gleaming shell]

theres something on my alegbra 2 work ive never seen before and theres no resources that i could find to help me

[dull temple]

is there more to this question?

[gleaming shell]

nope thats all thats given

[dull temple]

Use the table to determine when f(x) = g(x)

[gleaming shell]

do i like multiply f(x) and x together

[vernal warren]

im pretty sure just see and find at what value of x , is f(x) and g(x) equal to each other

e.g when x = 0.5
f(x) = -1.5 , g(x) = -0.75
f(x) isnt equal to g(x) at x=0.5

[gleaming shell]

OHHHH so i just see when they are the same value?

[vernal warren]

yeah , thats what the question wants for now

[gleaming shell]

okay thank you sm

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[wraith hinge]

am i like confusing myself because for a) my book does like

but like

isnt that the case for $\m\P{X \le x}$ not $\m\P{X>x}$?

[dull temple]

no? integral from 200 to inf

[wraith hinge]

yes i misinterperted it with the CDF thanks

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[wraith hinge]

.reopen

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✅

[wraith hinge]

btw like just a question but why dont we consider this a PMF

like its considering the shelf life in days

which is, like, countable

[dull temple]

one assumes a shelf life could be 4.3820 days

[wraith hinge]

fair enough lmao

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[pure isle]

can anyone explain me how does he get t + 2km after ? I mean whats the rule by which he does this

[strange steppe]

$(1 km / 6 min)$ * $(t + 12 min)$ $=>$ $(1 km / 6 min)$ * $t$ + $(1 km / 6 min)$ * $12 min$, where $12 min$ over $6 min$ cancels out and gives $2 km$

[solid kiln]

dusk chancellor

[strange steppe]

you multiply it for each value represented in brackets

[pure isle]

hmmm so lets say there is a fraction 5/4 * (3+2) does that equal to 5/4 * 3 + 5/4 * 2?

[strange steppe]

yesss

[pure isle]

thanks

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[soft grove]

Consider this equation.
$P(x)=x^3+x^2-10x+8$
I want to factor it using the Factor Theorem. Why does dividing the constant by the co-efficient give me the potential factors?

[solid kiln]

soupdog

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[soft grove]

question is above, maybe I posted it too early? ^

[split chasm]

misquoting rational root theorem,
missing many key components

I'd suggest looking up the wording of the theorem and proof

[soft grove]

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[chilly oak]

So I have created a taylor serie up to the second order, as seen in the function T(x). But now, I have to approximate an integral, and for some reason, they do not just pick the function that I already had to come up with. What is going on? Can somebody help me with this?

<@&286206848099549185>

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[wild night]

i got the first part

but the 2nd part i keep getting wrong

for some reason everytime i submit an answer it is wrong i am using the right formula though

arccos(a.b/magnitude of a *b )

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[viral oasis]

Can someone please help

Explain the example I highlighted in purple

I don’t understand how they found x(t)

[bright quarry]

v=u+gt

at max height v=0 because it’s turning around

so t=u/g

plug this in for the ut+1/2gt^2

[viral oasis]

They said to avoid suvat though

[bright quarry]

wdym

[viral oasis]

Look at the remark directly above purple

[bright quarry]

well it’s just a short cut

[viral oasis]

Is there a way to work out x(t) using force

[bright quarry]

h(t)=ut+1/2gt^2

dh/dt=u+gt

[viral oasis]

Or momentum

[bright quarry]

to find a maximum

we do dh/dt=0

u+gt=0

gt=-u

[viral oasis]

I get the second part

[bright quarry]

t=u/g

lol

[viral oasis]

I just don’t know how they did the first part without using suvat

[bright quarry]

is their work on the right

because the solution does what i do lol

i can prove the h(t) formula

if u want

lol

the only force acting on the projectile is mg

which is a constant

this is purely a kinematics problem

a=g no need to use forces here

[viral oasis]

Ok

Yes please

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[marsh forum]

I tried the following

I wrote $u/r + \alpha(u)+\beta(v)/r = v/r$

[solid kiln]

Why am. I here

[marsh forum]

by converting everything to unit vectors

why is that wrong

where r is the radius of the circle

<@&286206848099549185>

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[versed crypt]

hello how do u find a and b?

[blissful bison]

a and b, these are the zeros of a given function, these are the abscissa of the intersection points with the x axis

[versed crypt]

ohhh thank you

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[iron trellis]

Is h(t) here 40?

[dawn ravine]

football is above 40
so we'll take h(t)>= 40
?

h(t) is 40 on some values of time

[iron trellis]

Yeah got it

[dawn ravine]

u can solve quadratic 2 get two values of t where the ball is abv 40m

[iron trellis]

40 = 30t - 5t ^ 2?

[dawn ravine]

30t-5t^2 >= 40

[iron trellis]

Hm

Man, I am sorry idk what I am doing

I cant seem to remember how to isolate t

When I do I keep getting -5t(t-6) and then I get stuck

[dawn ravine]

ok wait im gunna solve and give u a pic

[iron trellis]

Tysm

[dawn ravine]

to find how long it was in air just do , 4-2

[iron trellis]

Okay Ty!

One last thing

The answer is only 2

How would I know which one is right

[dawn ravine]

yea i said here to find how long we have to subtract the roots cuz they are 2 intervals of time

so 4-2=2sec

[iron trellis]

OKAY

[dawn ravine]

...

[iron trellis]

OKAY OKAY Got it!

Tysm!!!

SORRY

I am so lost rn

Tysm

[dawn ravine]

it's oky

[iron trellis]

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[nocturne crane]

is this correct?

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[iron trellis]

Can someone check what I am doing wrong?

[earnest shore]

(a-2b)+(-a-3b) = -2b+-3b = -5b

you didn't distribute your negative properly

@iron trellis

[iron trellis]

Okay

Thank you

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[candid oracle]

Help

[candid oracle]

@everyone

[trim hawk]

,rotate

[trim hawk]

first graph the points you already found (part a)

[candid oracle]

i got no idea how to grapgh it

[trim hawk]

do you remember how function notation works

[candid oracle]

sadly not

[trim hawk]

for a function f(x), the number inside the f(x) is your x-value, and the whole f(x) is your y-coordinate

like for f(x)=x^2, f(2)=4 means you would place a point at (2,4)

try that out with f(0)=2^0

[candid oracle]

alr

is it 0,2?

[trim hawk]

close

2^0 isnt 2

[candid oracle]

0,0?

[trim hawk]

no

whats 2^0

[candid oracle]

2?

[trim hawk]

no

alright so

[candid oracle]

im stupid

[trim hawk]

think of it like this

you can say 2^0 is the same as 2^(1-1)

you can split the exponent and make it 2^1/2^1 or 2/2

whats 2/2 equivalent to

[candid oracle]

1

[trim hawk]

good

works for any number except 0

[candid oracle]

so it was like 2213213123^0

it would be 1?

[trim hawk]

yes

[candid oracle]

aah

so its 0,1

[trim hawk]

any real number at least, i dont recall what you do with complex numbers

[trim hawk]

correct

try the other 3 in part a

[candid oracle]

alr

3,8?

[trim hawk]

yep

[candid oracle]

aight

i did all of them

[trim hawk]

alright

[candid oracle]

0,1 1,2 2,4 3,8

[trim hawk]

those are right

[candid oracle]

YES

[trim hawk]

make sure to write that 2^3 is equivalent to 8 when solving for f(3) to sho work

just 2^3=8 should be enough

[candid oracle]

oh yeah

[solid kiln]

Couldn't find an attached image in the last 10 messages.

Jan 25, 2024, 4:52 AM

[trim hawk]

try the first one for part b by yourself and tell me what you get

[candid oracle]

uhmm

how does negative exponent work

2^-2

thats what I have rn

[trim hawk]

general rule for negative exponents

a^-b=1/a^b

negative exponent, flip from numerator to denominator and vice versa

[candid oracle]

sorry but Im confused

[solid kiln]

Ruby

[trim hawk]

you can use different numbers for a and b

so take like 3^-1 for example

itd become 1 over 3^1
which becomes 1/3

[candid oracle]

hm

[trim hawk]

it works because lowering an exponent by one is the same as dividing by that number

[candid oracle]

does 6^-1 become 1/6?

[trim hawk]

yes

[candid oracle]

ah

[trim hawk]

so 2^1/2 becomes 1 or 2^0

if we divide by 2 again

1/2=2^-1

[candid oracle]

aaah

wait

so how do I find 2^-2

its a -2

[trim hawk]

divide both sides by 2 again to make the 2^-1 into 2^-2

1/2 divided by 2

[candid oracle]

so the answers 1/2?

[trim hawk]

no

its 1/2 divided by 2

[candid oracle]

1/4?

[trim hawk]

yep

[candid oracle]

hm

[trim hawk]

which is the same as 1/(2^2)

[candid oracle]

is 2^-3 1/8?

[trim hawk]

yes

[candid oracle]

alr alr i get it now

[trim hawk]

negative just means you flip from numerator to denominator or the other way around

[candid oracle]

alr

[trim hawk]

after you calculate f(-2), f(-1), and f(-3), tell me what points you get for them

[candid oracle]

uh

im confused

[trim hawk]

so you have 2^-2 as f(-2)

whats the same as 2^-2

[candid oracle]

yea

1/4

[trim hawk]

so the y-value is 1/4

and the x-value is?

[candid oracle]

8?

[trim hawk]

whats inside the f(-2)

what replaces the x in f(x)

[candid oracle]

ohh

-2

[trim hawk]

so its (-2,1/4)

[candid oracle]

oooooh

[candid oracle]

i didnt know farctions could in to that thing

[trim hawk]

yeah, its a bit messy to graph fractions but you definitely can

[candid oracle]

aight

[trim hawk]

plot the points you get from part b then send an image of the points

[candid oracle]

was I supposed to to plot the numbers from part A too>

[trim hawk]

yes, i think you did so thats good

[candid oracle]

yeah

[trim hawk]

you may also want to say (-2,1/4) just to clarify that those are the points you got

[candid oracle]

yeah

uhmm

i never ploted fractions

idk how to do plot fractions

[trim hawk]

so if one box on the grid is one unit tall

[candid oracle]

is it like ploting y-intercept in slope?

[trim hawk]

cut the box in half, the box is 1/2 unit now

[candid oracle]

a

[trim hawk]

you can eyeball it

and dont actually draw the lines

[candid oracle]

was that right>

?

[trim hawk]

remember its negative x-values

[candid oracle]

aaa

[trim hawk]

the heights are right but they have to be to the left of the y-axis

[candid oracle]

alr i jsut fixed it

[trim hawk]

now connect the dots with a curve

[candid oracle]

alr

[trim hawk]

as long as it looks close to the graph, usually teachers are fine w/ it since its just a sketch

[trim hawk]

perfect but remove the line after the point at x=3

[candid oracle]

oh yeah

[trim hawk]

since it says an interval from -3 less or equal to x less or equal to 3

[candid oracle]

yeah

[trim hawk]

heres the full graph for comparison

[candid oracle]

how do I do c?

[trim hawk]

c i would just list all the points you used

so (0,1) (1,2) etc

id recommend stating with (-3,1/8)

since its the leftmost x-value

[candid oracle]

alr

thats it ig im done

ty dude

[trim hawk]

np

[candid oracle]

i wouldnt have been able to finish it withour ur help

i apreciate it

[trim hawk]

cya later

[candid oracle]

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[nocturne crane]

please idk if it's true

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[nocturne crane]

<@&286206848099549185>

[hollow notch]

you needa calculate the area?

Oh nvm

Sso you need to subtract the area of bothe triangles

so I dont know why you were adding the third term
what was your thought process?

And also area of a triangle is half of base times height

[nocturne crane]

i had no idea .. ithought EH(HG)-EK(EJ)+MG(GL)

[true aurora]

the area of a triangle is $\frac{b*h}{2}$ so $(3x+4)*14 -(\frac{x^2}{2}+\frac{(2x)^2}{2})$

[solid kiln]

nico

[hollow notch]

uh why

[nocturne crane]

because they want the shaded area so I minus it

o yea

[hollow notch]

they want the area that is not shaded

[nocturne crane]

i mean the cemented

yey

[true aurora]

A of EKJ=(x^2)/2,
Area of MGL=((2x)^2)/2

Area of rectangle EHGF=14*(3x+4)

[oblique granite]

no 23

how to solve

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[nocturne crane]

oh

[nocturne crane]

ty

[oblique granite]

how to do question 23?

[nocturne crane]

sorry i thought ur helping me💀

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[orchid wagon]

how to reference the x value of the point D?

[knotty locust]

2

[orchid wagon]

sorry?

[knotty locust]

it's 2

[orchid wagon]

no i mean like, how can i reference the x value to plug in the integral

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[frank merlin]

can you switch p and q around with greens theorem?

[high snow]

What p and q?

I don't see anything

[frank merlin]

can i switch them around?

[high snow]

I think no because you are substructing with them

And deviding also

[ionic pendant]

P and Q are not interchangeable, no

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[frank merlin]

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[wraith hinge]

im doing additional maths work today and im at this question,,
i know for the first part im supposed to try and manipulate the figure into a different bunch of triangles or something to use tan cos sin but like

[wraith hinge]

im clueless about where to start 💀

[tepid hamlet]

you can probably make use of this similar triangle here (notice that the green angle is 90 - theta and the blue angle is also theta)

when in doubt in geometry just draw more triangles

[wraith hinge]

!!

thank you!!

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[vernal warren]

everything seems correct

[violet dagger]

oh alr just making sure thanks

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[worldly ferry]

#BACKLIVRSMATTERS

[wraith hinge]

What you yapping about

[terse shore]

Ight

[worldly ferry]

#EQIUALIOTY

[wraith hinge]

Do you want a cup of cyanide?

[terse shore]

That’s not how you spell it

[worldly ferry]

.close

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[wraith hinge]

<@&268886789983436800>

[worldly ferry]

snitch...

[worldly ferry]

ok im sorry

im sorry nothing haappened

[wraith hinge]

You're gonna be clapped

[terse shore]

💀

[wraith hinge]

I recommend reading a history book

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[broken belfry]

I don't understand part b nor its solution

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[teal rampart]

türk müsün

[broken belfry]

no I'm not Turkish

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[fair bison]

(Please don't use help channels for non-help stuff)

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[desert owl]

I need help perfecting the square

[vague citrus]

you have it in the form of (x+ax)^2=b

so, x^2+2ax+a^2=b

notice coefficient of x

match them to solve for a

and then subsequently solve for b

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[oblique meteor]

what would be the integrand for part a?

im not exactly sure where to start as there are multiple possible functions

ln(x)

or e^x

I know that 4/n is the base of each rectangle

or delta x

I dont know how to find the limits of integration

a and b

and then the integrand obviously

would it just be the same thing

but wherever there is an i/n term just replace it with x?

[oblique meteor]

I understand how they are related but im just not sure how to apply it for this partcular problem

[blissful bison]

then choose a and b appropriately in both your cases

i write it:

[oblique meteor]

im not sure how to get a and b from the problem though 😭

[blissful bison]

wait a minute

[oblique meteor]

ah I see

[blissful bison]

when you will have analysed it, then try to apply the analogous technique - method, for the second example of yours

[oblique meteor]

so I guess a would be 0

b would be 4

[blissful bison]

correct

[oblique meteor]

and then we would just replace the i term with x

[blissful bison]

take an exercise book and write in

right

[oblique meteor]

omg thank you so much

i was so confused

[blissful bison]

yvw)

[oblique meteor]

I couldnt find help anywhere else online lmao

appreciate it a lot

[blissful bison]

smiles

[oblique meteor]

do you mind if I dm you I have other questions

u explained it really well

[blissful bison]

sure, you may,m if i have a spaer time, then i may help )

[oblique meteor]

ok thank you so so much

once again

[blissful bison]

yw)

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[astral tangle]

Y=sinx what will be the path of all the tangent over this curve from origin

[austere cedar]

The tangent at any point x = a, is given by:
y = cos(a)(x - a) + sin(a)

I'm not sure what your final answer should look like, though. What is the "path of a tangent"?

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[brave fiber]

How do i get the integral of this function?

[tepid rock]

What's that after e^( ) ...?

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[mossy wagon]

Can someone help 2E pls

[mossy wagon]

Ive already done it but idk

Its weong

[clear saddle]

full circle (28cm since equal) - half circle

[mossy wagon]

I did

Its wrong

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[safe pine]

Could someone help me with where I went wrong with this problem?

[olive horizon]

who told you you were wrong?

[safe pine]

the webwork homework auto marks the answer i put in and its wrong

[olive horizon]

AI is stupid and you are correct

[safe pine]

oh ok thanks

[olive horizon]

you did have some extra steps you could've avoided

[safe pine]

what could i have removed?

[olive horizon]

instead of multiplying $\frac{\sqrt{x}+5}{\sqrt{x}+5}$, you could've factored $x-25 = (\sqrt{x}+5)(\sqrt{x}-5)$ and then cancel out the $\sqrt{x}-5$

[solid kiln]

emphatic_wax

[safe pine]

oh right

thanks

[olive horizon]

but how you did it is perfectly fine. no math errors anywhere. maybe it marked you wrong because you did not write $\lim_{x\rightarrow25}$ in each line

[solid kiln]

emphatic_wax

[safe pine]

i will check again

have a good day!

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[simple jackal]

why does the summation to get to the expectation not converge?

in the highlighted and drawn rv

[zinc ginkgo]

Did you try calculating the sum

[simple jackal]

i obtained cancelling terms on both sides, what am i missing?

[zinc ginkgo]

Your cancellation is unjustified

As a simpler example, try computing

1-1+1-1+1-1+1...

[simple jackal]

ok

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[random vault]

$\frac{x^2y - 4y^2}{2x^4 + 4y^2} + 2x\cos(3y)$ for when (x,y)=!(0,0)
I need help in studying the continuity of this

[solid kiln]

Katalina

[torpid pasture]

when would this not be continuous?

do you see anything that would make it not continuous

[torpid pasture]

remember division by 0 is not possible

[wraith hinge]

help me with that

[tepid hamlet]

!occupied

[trim jolt]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[wraith hinge]

oh

but I need to submit this now

so what am i going to do

[tepid rock]

Start by reading #❓how-to-get-help

[wraith hinge]

I need to submit this in like 5 minutes. i cant do that

which one of those graphs are accurate

[tepid rock]

It's totally a YOU problem, don't bother others in their help channels.

[wraith hinge]

bro

yall just dont like black people

do yall?

i see now

[random vault]

Just help them cause I have no idea

[wraith hinge]

hurry

i have 2 minutes

yall wasted 3 minutes

[tepid hamlet]

kinda sounds like you want test answers which we don't do anyway

[wraith hinge]

i need one answer

[tepid rock]

<@&268886789983436800>

[wraith hinge]

i HAVE A MINUTE LEFT

COME ON

WHICH GRAPH

[wicked drum]

L bozo

[wraith hinge]

BRUH

NOW I HAVE A 69 ON THE TEST BECAUSE YALL WOULDNT HELP ME

OH MY GOD

[random vault]

Well besides 0 , every other value seems fine to me

[tepid hamlet]

yes

so it should be continuous everywhere except (0, 0)

[torpid pasture]

yeah

[tepid hamlet]

rational functions (i think this qualifies?) are in general continuous at all numbers in their domain

[random vault]

the trigonometric function doesn't cause any trouble right?

[tepid hamlet]

lol i only noticed this when i was looking at it and completely missed other term, but no fortunately it doesnt since cos is also continuous everywhere

[random vault]

Okay so the whole function is continuous everywhere besides the origin got it

[torpid pasture]

yeah i dont see any removable discontinuity either

[random vault]

Another question I have about this is finding the direction where the derivative of the function at (0,0) is 1 // sorry for the poor wording

[wraith hinge]

is this in relation to directional derivatives?

[wraith hinge]

.

[random vault]

Yes , now I'm doing the partial derivatives

thank you for the help everyone

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[azure citrus]

is there a reason this isnt 34?

[limber heart]

I think u mightve added wrong

[azure citrus]

shoulda been 14, 7, 6, 5, 2

[vagrant marsh]

14? are you sure

[azure citrus]

oh ok

im jus blind

thank you

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[vagrant marsh]

youre welcome lol

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[severe stump]

Can someone check this rq?

[merry bluff]

Seems good

[severe stump]

Cheers.

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[wide narwhal]

Suppose f and g are inverses and f(8) = 3. Then (g of f)(8) is what?

[zinc ginkgo]

Use the definition of inverse function

[wide narwhal]

Can you just tell me the answer it’s urgent

[zinc ginkgo]

!noans

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The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[zinc ginkgo]

Why is it urgent

[wide narwhal]

I’m tutoring someone

[zinc ginkgo]

Then tell them to join discord

[wide narwhal]

They don’t have it

It’s in person

[wide narwhal]

Hello

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[wintry kettle]

I need help on this question, i have no working im just stuck on what to do

[split chasm]

identify what you have and apply the relevant theorem

note that you have intersecting chords, thus you can apply the intersecting chords theorem
(part of power of a point)

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[sterile fiber]

Hello, im trying to find if two parameterized lines are intersecting and i have a question

why should you replace the t with s in the RHS how does this serve to determine if they intersect or not?

i kinda missed that exact point in lecture, it was something about how the lines could intersect, but not at the same point in time

[sterile fiber]

i just wanna know whats going on in what i wrote down here

wait, nvm im dumb i forgot how you solve for parameterized variables

.close

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[grim summit]

how would u do this problem? how many ways can u get from A to D going through C but not B if u cant cross the same vertice twice

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[grim summit]

<@&286206848099549185>

[sturdy frost]

start finding the cases for going from A to B

then find the cases to go from B to C to D

[sturdy frost]

subtract this from all the cases to go from B to D

[sturdy frost]

and then multiply that number by this above

(A to B)(B to D - B to C to D)

do you understand why this equation works?

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[grim summit]

yes but idk how to do it if u can go in all directions?

[sturdy frost]

uh

if u can go in all directions idt you can use my formula

solution seems nontrivial

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[cunning gate]

Im so clueless on this

Please help

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[cunning gate]

This is what I got..? I don’t know if I did this correctly <@&286206848099549185>

[loud gale]

,rccw

[cunning gate]

Does it seem correct? The only reason I didn’t write in fractional form is cause my calculator gave it to me in decimal

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[final coral]

/help

[final coral]

I have entered the values in my first screenshot but it failed too

Have tried multiple entrees but finally decided to ask for help

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[simple fiber]

let me write it down

wait a minute

hope that will help~

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[astral tangle]

when we derivative of any function then graph of derivative will cut its original function at critical points where the max min exist?

[proper kernel]

no

at critical points, the derivative will cut the x-axis and be 0

because at critical points, the function is flat, which means the derivative there should be 0

that is why by having the derivative be 0, you can find where the function's critical points are

[median torrent]

You can see from your graph

Where f has a max or min, f' has a zero

A slope of zero is a sign that the curve may have a max or min at that point

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@astral tangle Has your question been resolved?

[astral tangle]

without finding the roots of derivative can we assume about max min?

suppose if we are given interval (-1,2)

at 0 derivative is -1 it means f'(x)<0

so it is decreasing

but how we can sure that it will left side decreasingn or right?

[proper kernel]

if you dont know the roots then you dont know where the max and min are

then you have to use alternative methods to find the max and min which arent as good

[astral tangle]

i see

[proper kernel]

most of these methods involve some trickery or involve you guessing at "the max should at least be this"

[astral tangle]

if ann interval is given to us

how can we check whether it is increasing or decreasing in it

[proper kernel]

you find the roots of f'

its between these roots that f' is either positive or negative

find that out

then positive f' means increasing f
negative f' means decreasing f

[astral tangle]

how to check max and min in this function

between [0 to pi]

[proper kernel]

for this particular problem you wont be able to solve for x cos x - sin 2x = 0

what you do instead is (as the question directly asked you) use a calculator

this is part of the "guessing" I said earlier but the guess will be accurate enough

use the calculator to numerically find where f' is 0

then just directly use those values in f to see this max/min

[astral tangle]

but we are not allowed to use a cal in exam

[astral tangle]

so here the question is that in this interval the function will be increasing, decreasing and neighther

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[astral tangle]

.close

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[runic condor]

why doesn't this work with the residue formula? Im getting residue at a: 1/(a-b) and residue at b: 1/(b-a) hence the integral would be zero?

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[runic condor]

oh got it

.close

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[grim estuary]

So my idea is

1. The median of the data
2. The midsection of the data (1+11)/2
3. The mean of the data
4. I dont really understand this question

I just need to know the first 3 question if its right or not. And give me hints for the last question

[grim estuary]

thanks 🙂

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[tepid cobalt]

Can you check if answers 2 and 3 should be switched?

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[tepid cobalt]

About question 4: It is a common problem to be given a set of data points x1, x2, ..., xn and to be asked for a single number that summarizes how these data points are centered.

Perhaps you tell me their mean value, but the previous three problems show that different answers have different properties, and I might have been more interested in the median. Also, a single number to describe the center to data are not very useful on its own.

.reopen

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[thorny ember]

If anyone has some sort of advice on how to solve this question, I would appreciate it. I dont need the answer, just a way to start. I have tried using f=ma and putting it in terms of t, then solving the differential equations but it didnt work. I also tried equating it to the time-dependent distance formula (pictured above), but no dice

[flint sphinx]

sorry if I am not really helping, but how come the force equation doesn't have mass?

[thorny ember]

Just a relationship b/w drag force and velocity. The constant will end up having some sort of mass unit, but not important for this question

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[weary marten]

i need help with some simple functions

[unreal river]

just ask

[weary marten]

well

[bright quarry]

!da2a

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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[weary marten]

the tangent to y=ax^3-x^2-11x in x=3 makes a 45 degree angle with the positive side of the x axis

i need to find the value of a

i got 0.5

what i did

was tan(45) which is 1

so thats m

[final coyote]

what is your question?

[weary marten]

i need to find the value of a

how to solve for a

[final coyote]

you said you got 0.5. whats your question?

[weary marten]

wondering if im right

and if anyone can help me to verify it

[final coyote]

ok, you should say this first.

[unreal river]

Please continue with explaining your solution

[final coyote]

you need f'(3)=1 -> solve for a.

[weary marten]

yeah thats what i did

wait lets solve it again

[unreal river]

Yep, and it gives 2/3

[weary marten]

2/3 meaning a = 2/3

[unreal river]

That's what I got

[weary marten]

f`(x) is 2ax^2-2x-11

so what i do is

1=2ax^2-2x-11 and switch x with 3

[unreal river]

why 2ax^2?

[weary marten]

its ax^3

oh

3ax^2

but same thing applies

1=3ax^2-2x-11 and switch x with 3

[unreal river]

@wraith hinge this channel is occupied

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[unreal river]

yes, substitute x=3 and solve for a

[weary marten]

so

1 = 3a(3)^2-6-11

im pretty slow

or im wrong

[final coyote]

right so far.

[weary marten]

seriously asking

3a(3)^2

equals 9a^2 so 81a or 27a

[final coyote]

a is not squared. 3 is.

[weary marten]

so its

[final coyote]

3 times a times 3 ²

[weary marten]

then its 27a

because 3a times 9

am i right

i guess i am

[unreal river]

you are.

[weary marten]

aight so

1= 27a -6-11

move the numbers to the other side

18 = 27a

a = 2/3

DAMN

i was wrong on my test bro 😢

[unreal river]

Don't worry about it

הדרך יותר חשובה מהפתרון הסופי

[weary marten]

fr

but its 25 points on a test im already failing

[weary portal]

2 birds one stone huh?

[weary marten]

bros everywhere 😭

[weary marten]

yeah i was solving it in both servers

[weary portal]

that's not very nice

solving a math problem requires a time investment

time that could be spent helping someone else if you're already being helped

[weary marten]

multitasking and multiasking

[unreal river]

Shirly, you can close the channel if you are done.

[weary marten]

yeah

thank you guys

i feel smarter lol

.close

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[cobalt sierra]

In a gradient, would the unit vector be the same as dx and dy respectively?

[austere cedar]

No, because dx and dy are infinitesimals, not vectors.

[left oriole]

by unit vectors do you mean i and j as written above?

[cobalt sierra]

Someone explained to me a gradient is involved in getting the second equation in this and I am unsure as to how. I know that the gradient gets the VA, pA, and pV then this is divided by pVA but where do we get the dp, dV, and dA from?

[austere cedar]

Physics equations are always somewhat sketchy

[cobalt sierra]

This is what was said in a thermodynamics textbook I am studying as well.

[austere cedar]

Basically, imagine you're differentiating in terms of t. You'd use the multivariate chain rule to take the complete derivative

[cobalt sierra]

But I am confused as to what one would be differentiating by

Ok

[austere cedar]

Now, instead of differentiating in terms of t, pretend it makes sense to differentiate in terms of nothing. Now you're doing physics.

[cobalt sierra]

See now that's what I thought of initially but that made little sense

[austere cedar]

It can be quickly made sensical if you "divide both sides by dt" or any other infinitesimal

And this is how you'd apply the equation. You'd divide by, for example, dρ, and now you've got regular derivatives

[cobalt sierra]

That makes more sense but a professor of mine said it's improper to apply such arithmetic operations directly to differential like dx, dy, etc but that's not really how it works.

[austere cedar]

Oh yeah you can't divide by infinitesimals at all haha. But, that's how THEY'D think of it

[left oriole]

math professors cringe at this stuff, physics professors think it's perfectly normal

[cobalt sierra]

What does lhs mean?

What is that d() function called? I would like to investigate further into how one can take the derivative of something with respect to nothing.

Oh so the d(pVA) is us saying that we are taking an infitesimally small quantity of pVA as a whole?

Got it. That makes sense. Thank you for your help. I gained more clarity. I appreciate it.

This point is what confused me in the first place. I still don't get where the dV comes from when you do this latter method. I got it when you did d(...). Not now though.

Yes

Oh I was not aware of that form. Do you know of a good resource for me to look into that concept, or do you know the name us that concept? The dF = ∂F/∂X_i dX_i?

Okay thank you

I see. You have been an immense help to me. I truly appreciate your help and kindness. Thank you. No need for further explanation. I don't want to take up too much of your time.

That does indeed make intuitive sense because in the case of, say y = y(x), we can always make the argument that dy/dx = ∂y/∂x.

The partial derivative is the same as the full derivative in the case of monovariable calculus.

I'm glad I ran into you tonight. Once again, thank you. You have gone above and beyond in your assistance.

👏

Okay c ya

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[blazing stirrup]

is this what my professor wants me to do?

[split chasm]

,calc (83+65+91+87+84)/5

[solid kiln]

Result:

82

[split chasm]

your x-bar is off

[blazing stirrup]

damn how the hell did I manage that

ty

.close

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[cold kindle]

Help pls

[trim jolt]

@cold kindle Has your question been resolved?

[cold kindle]

<@&286206848099549185>

[sturdy frost]

when doesn’t y exist

[cold kindle]

?

[sturdy frost]

when is (3x-12)/(2x-6) bad for computation

more specifically when is it in the form of something/0

[cold kindle]

What you mean

[sturdy frost]

take a look at the denominator of the function

if that is 0, it wouldn’t make sense

because you’d be dividing by zero

[cold kindle]

I need help what is vertical asymptote

[sturdy frost]

those dotted lines are asymptotes

[cold kindle]

oh

[sturdy frost]

vertical asymptotes

[cold kindle]

how you find them?

[sturdy frost]

usually you look at the denominator

[cold kindle]

so its 2x-6

in denominator

[sturdy frost]

and it’s when the denominator is zero

[cold kindle]

Can you explain it by desmos

[sturdy frost]

i’ll show you what your graph is

[cold kindle]

ok

[sturdy frost]

you see how at x=3 there’s no value

that’s because 2x-6 is 0 when x=3

you should also see that the values go to positive or negative infinity

[cold kindle]

🗿

how you know x=3

[sturdy frost]

2x-6=0

2x=6

x=3

[cold kindle]

Oh wth

[sturdy frost]

and that’s the denominator

[cold kindle]

You got the answer right

[sturdy frost]

basically when x=3 there’s a division by zero

so that becomes an asymptote (though in certain situations it becomes a hole)

[cold kindle]

let me show you the original question

[cold kindle]

You got the answer right but I am still confused

🗿

[sturdy frost]

try plugging in x=3

[cold kindle]

for denominator ?

[sturdy frost]

no for the whole thing

[cold kindle]

ok

Overflow Error

🗿