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[molten pivot]

,w int x(1-x^n)/(1-x)

[ocean seal]

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[molten pivot]

Damn nevermind that gets way too complicated haha

It's easier to differentiate, I'm going to see if there's another way

[bright void]

i mean i do understand the procedure tho

[molten pivot]

Its a lot easier to work with infinite sums

Believe it or not

[bright void]

oh

actually it does telescope

.close

[lone heart]

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[silent parcel]

Can you enlarge the image a little?

[mint sparrow]

yes

[silent parcel]

particularly the graph :v ty

[mint sparrow]

is that better?

each grid is .5

[silent parcel]

A little, Im trying to ascertain the information
So is this correct?
The lowest point of the wave is y=-2
And the highest point is y=2
The length of the period is 2 as well?

[mint sparrow]

yes

[silent parcel]

okay - sorry, the graph a little fuzzy :v had to squint

[mint sparrow]

i got y=2sin(2x+.5)

but i think thats wrong

[silent parcel]

So you need an equation of the form y=asin(bx + c)

You know what a regular sine graph looks like?

[mint sparrow]

nope

[silent parcel]

,wolfram sin(x)

search up sin(x) graph on google images (or wolfram alpha), you need to know what this graph looks like

I'm also gonna use a thing called "Radians" have you learned that yet?

[mint sparrow]

no sorry this is the start of this subject

[mint sparrow]

I think i got A and B right i just need help finding c

[silent parcel]

You need to know the following:
Sin(0) = 0
Sin(pi/2) = 1
Sin(pi) = 0
Sin(3pi/2) = -1
Sin(2pi) = 0
And then the wave continues all over again - one period is repeated every 2pi along the x-axis

You using degrees? like 360 degrees=circle?

[mint sparrow]

for?

I dont think so

[silent parcel]

So you got the first bit right, a=2, this implies stretching the function in the y-axis. This is correct.
If you want to "shift" the function along the x-axis, you need to change the value of x, say to (x+c), this will shift the graph left by c amount. BUT, in your case, the function hasn't shifted at all. You can see this arbitrarily since sin(0)=0 and the "shape of the graph" is pretty much the same as if no shift had happened. So c=0
What you do need to find though is the amount the graph has been stretched in the x-direction. So you need to find b (your answer is incorrect I think, but lets work it out).

So you need something of the form:
y=2sin(bx)
Note: there is no c because c is just 0!

[mint sparrow]

ok ok thanks

this is due in 8 minutes btw soo let me speed threw this

[silent parcel]

Now we know that in regular sin functions, the length of a period is 2pi (2 times pi)

BUt in your fiunction the period is length 2

[mint sparrow]

itsnt 2pi/b =period

and period is 2

[silent parcel]

b= 1/pi

the period is usually 2pi, but for you it is 2, so you need to make the sin graph have period 2 instead of 2pi, you can do this by multiplying by pi

its either multiply or divide - sorry, Im not used to rushing

Its multiply

y=2sin(pi x)

make sure you understand why though when you have the time

[mint sparrow]

ok thank you sm

[silent parcel]

also - make note saying "in radians" to the side, in case you havent been taught radians yet, I dont know the answer in degrees, degrees suck

if you are taught radians this should be obvious though

gl

[mint sparrow]

thanks

.close

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[sly wraith]

hello guys can u hel me with thiss???

<@&286206848099549185> for 3d

.close

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[tacit dirge]

Hello

[tacit dirge]

So when conducting a two path test to find if a limit does not exist

How do we have to know if we should use a parabolic test or line test?

[sour lily]

.help

[lone heart]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[tacit dirge]

For lim (x,y)->(0,0) 2x/(x+3y) what should I use?

I used line test but is there a reason why a parabolic test might be incorrect?

[lone heart]

@tacit dirge Has your question been resolved?

[lone heart]

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[drowsy sedge]

Hey everyone, I dont really know how to solve this

[drowsy sedge]

**this is a practice test

[mortal trellis]

well what have you tried

[drowsy sedge]

im just imagining it graphicly

and like

maybe its just

a non continuous function

[ornate condor]

well

it can only be a non cont func

[drowsy sedge]

this is my thing now

idk

i just made that in paint

[ornate condor]

well

[keen plinth]

too complicated

[ornate condor]

u can just pick a

[keen plinth]

pick a simple one you can write down easily

[ornate condor]

like this

[drowsy sedge]

o

[keen plinth]

yeah ig that works

[tacit bobcat]

any function works

[ornate condor]

if u wanna be funny u can use a weird func as well

[keen plinth]

like your example isnt wrong

[ornate condor]

just that uve some weird curves which is bit hard to actually write out

[keen plinth]

but also writing down the formula for it would be a bit pain

[drowsy sedge]

the thing is

i thought the intermediate value theorm

is like

if u got f(x) = negative and for one val and f(x) = pos for another

its gotta like actually cross

[ornate condor]

if its cont itll contain the values inbetween

[drowsy sedge]

this feels like cheating

its teleporting

[ornate condor]

yea

well

they didnt say f is cont

[drowsy sedge]

ok well thats dumb

[ornate condor]

if f is cont u cant do this

[drowsy sedge]

so basically

[ornate condor]

just with ivt

[drowsy sedge]

int value theorm is useless then

it says nothing

[ornate condor]

well

[drowsy sedge]

but the obvious

[ornate condor]

it says

if u have a cont func

...

[drowsy sedge]

it crosses

but if its not

[ornate condor]

all theorems have some conditions

that u cant use if u dont meet them

like

u gotta be at the 13th stage of qi condensation

[keen plinth]

IVT is not really trivial

[ornate condor]

if u wanna join the league of demon sealers

[drowsy sedge]

idk what that is

anyways

[ornate condor]

[drowsy sedge]

im assuming

[keen plinth]

wtf is 13th stage of qi condensation

[drowsy sedge]

there are no conditions on continuity

for IVR

because

[ornate condor]

hahaha

[drowsy sedge]

my teacher

said its ok

[keen plinth]

IVT just needs continuity

[drowsy sedge]

ima close this

what

[ornate condor]

its one that allows u to raise ur innate aptitute by stealing luck from the heavens

[drowsy sedge]

then my thing is wrong

[keen plinth]

what?

[drowsy sedge]

if it needs continuity

then wouldent my thing

[tall topaz]

It doesn’t violate IVT because f is not continuous

[keen plinth]

the assumptions of IVT is continuity

[ornate condor]

well

yea

its like saying pytharawr is useless

[drowsy sedge]

ok but continuity is not a rule of it

[ornate condor]

when u are given some non right angled triangle

[tacit bobcat]

do you think a function that is negative at one side and positive at one side without touching 0 can be continuous?

[drowsy sedge]

I know that

^

[ornate condor]

like again to pyrawr

[drowsy sedge]

but like

[keen plinth]

if a function is continuous then you can apply IVT

[drowsy sedge]

someone said

[keen plinth]

if it is not continuous IVT says nothing

[drowsy sedge]

the rule of IVR is that the function has to be continious

it might of been me

[ornate condor]

a^2+b^2=c^2 when uve right angle etc

[drowsy sedge]

but thats screwing with me

[ornate condor]

but its kinda useless if udh one

[drowsy sedge]

bruh okay this is a bruh momento

im closing this i sorta understand

[ornate condor]

but its still a useful theorem nonetheless

[tacit bobcat]

[ornate condor]

mm

[drowsy sedge]

thanks every1

[ornate condor]

ok

np

[drowsy sedge]

.close

[lone heart]

Channel closed

Closed by @drowsy sedge

Use .reopen if this was a mistake.

[ornate condor]

remember

if u need to rely on someone

u can rely on me

[drowsy sedge]

ill be back asking another question soon

[keen plinth]

[ornate condor]

Patriarch Reliance

[drowsy sedge]

probs like 10 seconds from now

[ornate condor]

yes

[keen plinth]

goddess out here actually trolling

[ornate condor]

wow

kinda mean

[lone heart]

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[bronze grotto]

I have done the first part of this question but I cannot understand where to start in finding the solution for F(r,theta) = F1costheta

It looks like a fourier perhaps but we haven't got to that in my course yet

[lone heart]

@bronze grotto Has your question been resolved?

[mossy laurel]

Yes you know that the radial part is 1 so you just have the order $0$ in the sum (because of the uniqueness of the decomposition in Fourier series)

[ocean seal]

black_couscous

[bronze grotto]

Ah so it is a Fourier series?

[mossy laurel]

When you fix $r$ it is a Fourier series with respect to $\theta$

[ocean seal]

black_couscous

[bronze grotto]

Oh alright I see, I have never solved a Fourier series before so do you have any hints or resources you would recommend to learn how to do so?

[mossy laurel]

You don't really need to solve it

You just know that you can throw everything where $n \ge 1$

[ocean seal]

black_couscous

[bronze grotto]

Oh I think I get what you are saying

And then the first part of the solution becomes just (A+B) multiplied by the other part dependant on $\theta$

[ocean seal]

NightLight

[mossy laurel]

Yes!

Uniqueness comes from the uniqueness of the decomposition in Fourier series

[bronze grotto]

Ah alright thank you

[mossy laurel]

You're welcome

[lone heart]

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[jade oxide]

not sure where to start. take reciprocal? derivative?

[minor needle]

do you know formula for the normal line?

[jade oxide]

no

[minor needle]

where y1 = f(x1)
and m = - 1/f'(x1)

[jade oxide]

ok lemme try

ive not been given a y coordinate

[minor needle]

y1 is f(x1)

and your x1 is -2

[jade oxide]

oh so 5

[minor needle]

yes

[jade oxide]

ok. i have gotten a slope of 1/2 and the coordinate set (-2,5). how do i find the second set of coords?

[minor needle]

slope should be -1/2

then just plug them into equation of the normal line and that's it, you don't need 2nd set

m = -1/2
x1 = -2
y1 = 5
Line:
y - y1 = m(x-x1)

[jade oxide]

my normal line turned out to be 2y=-x+4

[minor needle]

+8*

then it's ok

[jade oxide]

y-5=-0.5(x+2) is what i plugged in, am i missing anything?

[minor needle]

it's correct

[jade oxide]

oh bruh when i multiplied everything by 2 i forgot to make 4 --> 8. my bad its very late where i am

thank you so much for dealing w me

.close

[lone heart]

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[robust oracle]

I have to solve this math problem using factoring - a. The difference between two positive numbers is 5 and the square of their sum is 169. Find the two numbers. However I'm confused on the difference between the square of their sum, and the sum of their square. Overall if you could help me explain that, and how to solve the equation.

[gray isle]

start by introducing two variables to represent your numbers

[robust oracle]

I'm supposed to use one variable

so it would be

x-(x-5)?

[gray isle]

no

if you want to jump straight to using just 1 variable

if one number is x
your other number will be x-5

[robust oracle]

yes so

isnt x-(x-5) correct then

[gray isle]

no

that's just an expression out of context,

x - (x-5) is equal to 5
but that doesn't quite tell me whether you actually know the expressions for your numbers

[robust oracle]

so how should i proceed with it

[gray isle]

if one number is x
your other number will be x-5

now using those expressions,

[robust oracle]

yes

[gray isle]

make the equation that represents the square of their sum is 169.

[robust oracle]

ok so - (x+5)^2+(x^2)=169

[gray isle]

no

that's very wrong

[robust oracle]

uh wait

i mean

[gray isle]

still wrong

that's the sum of their squares

not square of their sum

[robust oracle]

ah ok

[gray isle]

splitting that into smaller parts,
whats the sum of your two numbers, x and x-5

[robust oracle]

2x-5

[gray isle]

yes.

and make the equation that represents the square of that is equal to 169

[robust oracle]

(2x-5)^2=169?

[gray isle]

yes

[robust oracle]

then i expand it?

i assume

[gray isle]

there are more efficient ways to solve

[robust oracle]

yes but my lesson is solving using factoring

so uhh i gotta submit it like that

[gray isle]

what i said doesn't conflict with that

[robust oracle]

ah ok

[gray isle]

you can subtract 169 from both sides

and then factorise as a difference of two squares

[robust oracle]

ok

wait

so

(2x-5)^2 -169=0

then

wdym factorise as a difference of two squares

[gray isle]

(2x-5)^2 -169
is a difference of two squares

there's a factorisation identity for the difference of two squares

apply that

[robust oracle]

does it also work if I expand it, and then factor it from there

[gray isle]

yes

as long as your work is valid

[robust oracle]

is that the 3rd identity

[robust oracle]

aight ill try doing that I'm more comfortable

[gray isle]

i don't know the numbering system of the identities you're looking at

[robust oracle]

ah ok

[gray isle]

is a difference of two squares
there's a factorisation identity for the difference of two squares
you'll like this a lot more once you know it
and you'll pretty much never expand stuff out again if you have stuff in this form

[robust oracle]

yeah true

we also studied identities I just kinda forgot lmao

i can solve from here though

ty

[lone heart]

@robust oracle Has your question been resolved?

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[fallen estuary]

Can someone help me with question 2

[fallen estuary]

<@&286206848099549185>

I’m about to fall asleep so imma just close it if no one replies soon

[sour rock]

<@&286206848099549185> Can someone help me with this problem?

[fallen estuary]

💀

For future use, use the free channels

.close

[lone heart]

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[lone heart]

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[fallen fractal]

hello

[fallen fractal]

okay

so

[somber lantern]

Hello

It's me again

[fallen fractal]

lmao

oh it’s me again

[somber lantern]

What's you problem?

2.12 ?

[fallen fractal]

what does it mean to graphically find a gradient of a curve

[fallen fractal]

lmao

you got it saved?

[somber lantern]

I remember helping on 2.10 or 2.11

[fallen fractal]

hahah

[somber lantern]

Can you send a picture of a specific problem?

[fallen fractal]

sure

[somber lantern]

For a)

[fallen fractal]

idk why it’s so blurry

so on one hand, I could use the calculator for it, however I don’t have the equation for this function

[somber lantern]

You see there is a point at (-1, 1)

And another point at (0, 4)

[fallen fractal]

yes

[somber lantern]

And your formula is Δy / Δx

[fallen fractal]

well

that would work

if it was a straight line

[somber lantern]

Yes

I see it now

Do you know about turning points?

[fallen fractal]

yes

I thought that might be what I need to figure out

but again

I don’t have the equation

[somber lantern]

If you differentiate it graphically the x coordinate of the turning points are now extrem points.

And the x coordinate from the extreme points are intersections with the x-Axis.

So that you know the three blue points for sure.

Are on the differentiated function.

[fallen fractal]

I’m trying to understand what you’re saying

but I’m having a hard time

what are the blue points?

[somber lantern]

They are certainly on the derived function.

And this might be a little bit cheating but we can expect your original function to be a cubic function so that the derived function is a parabola.

[fallen fractal]

how?

[somber lantern]

This?

[fallen fractal]

all of it, I’m not understanding any of it

[fallen fractal]

how do you know this

but also that it’s a cubic function

[somber lantern]

Maybe they aren't extremes.

But then I don't know how you could solve this.

[fallen fractal]

I mean I have the solutions

but only the numbers

not how to solve it

[somber lantern]

If you take the hint it says that the solutions are integers.

If we look at x = 0

[fallen fractal]

what’s an integer

[somber lantern]

Whole numbers

[fallen fractal]

oh

[somber lantern]

... -2, -1, 0, 1, 2 ...

[fallen fractal]

right

[somber lantern]

So if we look at x = 0

The gradient has to be 0.

Because a gradient of 1 would mean that is going to the upper right. And a gradient of -1 would mean that it is going to the upper left.

It is hard to explain this just with words.

[fallen fractal]

there’s no way, otherwise it would have to be a turning point?

[somber lantern]

Yes

Something like this

[fallen fractal]

but the turning point is slightly to the left

[somber lantern]

Yes

I see that.

But how can the gradient be an integer on the point. That's impossible.

[fallen fractal]

ok so the solution for that point is apparently -1

[somber lantern]

No

It is 0

As I said

-1 is on x = 1

[fallen fractal]

it says -1 in the document

[somber lantern]

What?

Sorry but I think it is better if you ask somebody else.

Maybe close this channel and start a new one. Then somebody else can help you.

[fallen fractal]

:/

did I say something wrong?

[somber lantern]

No

[fallen fractal]

oh okay

[somber lantern]

But if -1 is the result the question is to hard for me.

[fallen fractal]

oh okay

.close

[lone heart]

Channel closed

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

.

Can anyone help me with this by using cos

[livid osprey]

Cos and sin but mainly cos

[modest kelp]

Do you know that in a parallelogram, opposite angles complete each other by 180? i.e. $ABC + BCD = 180^\circ$

[ocean seal]

Robin S.

[livid osprey]

Yes but this didn’t really help me

[modest kelp]

Yes, this will probably help you.

Because

[livid osprey]

Can i show what i did

[modest kelp]

You should find $AG$ and $DG$ then you should do Cos Theorem for $AGD$ eventually.

[ocean seal]

Robin S.

[modest kelp]

Yes please?

[livid osprey]

That’s what i did, btw sorry it’s not G it’s E

[modest kelp]

Whatever..

[livid osprey]

See in the end i got this

I assumed the lengths as X

[modest kelp]

Yes but you didn't use angle $BCD$

[ocean seal]

Robin S.

[modest kelp]

did you?

Oh

Yes you did

[livid osprey]

Haha yeah

[modest kelp]

Is it correct, if it is, explain it.

[lone heart]

@livid osprey Has your question been resolved?

[livid osprey]

I am not really sureTT

[livid osprey]

Ok this

[modest kelp]

Well, $\sqrt{3x^2} \neq 3x$ because $\sqrt{3x^2} = \sqrt{3 \cdot x^2} = \sqrt{3} \cdot \sqrt{x^2}$.

So $\sqrt{3x^2} = \sqrt{3} \cdot x$

[ocean seal]

Robin S.

Robin S.

[modest kelp]

Alright, it's more clear now.

[livid osprey]

Oh so what i did is wrong

[modest kelp]

Yes.

[livid osprey]

Ok thank youu for u time

[modest kelp]

It's not wrong, it's wrong in regular math, it may be true in "your" math.

:D

No problem!

[lone heart]

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[fresh hatch]

For given set V place it's elements in a 2d matrix in such a way, that distance between any two nearby elements is minimal possible.
Matrix is big enough to fit all elements.
Distance is determined by function d : V x V -> R

[fresh hatch]

It is like sorting problem for 2 dimensional array

Are there already someone from the past who solved it?

Cannot find anything 😦

[lone heart]

@fresh hatch Has your question been resolved?

[fresh hatch]

I discussing it in math-discussion

[lone heart]

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[subtle pecan]

1. In a restaurant there are 24 square tables with 4 seats each. They can be used separately, or they can be joined in order to have a 6 seat table. If the waiter prepares the same number of 4 seat tables and 6 seat tables, how many customers can he seat?
   (a) 84
   (b) 80
   (c) 76
   (d) 92
   (e) 72

I don't know how to start

[vale wigeon]

you join two "single" tables together to make a 4-seat table

[subtle pecan]

Isn't a single table supposed to have 4 seats?

[vale wigeon]

this is what it looks like

as a top-down view of course

[subtle pecan]

Makes sense

[vale wigeon]

do you understand how to proceed with the problem now?

[subtle pecan]

So there is going to be same amount of 4 seat and 6 seat tables. let's say this amount is x

4x+6x is 10x

No this is wrong

Can you help me further

[alpine sable]

24 = x + 2x

24 = 3x

8 = x

[subtle pecan]

8x10=80

That's correct, thanks for the help

.close

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[pastel aurora]

I got 9 as the answer is it correct?

[idle haven]

yes

correct

[idle haven]

what about the beads tho?

[pastel aurora]

Thank you

[pastel aurora]

lol

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[latent spade]

Hello I have this question I don't get how is it true . The answer should be True

[half belfry]

Hello, I'm stuck on no.10, there was an s present on it and I don't know what to do with it

[pallid scarab]

Sorry already taken

[pallid scarab]

Write f(a) - f(a-2h) = f(a) - f(a-h) + f(a-h) - f(a-2h)

By composition of limits (and using the fact that f is continuous since it's derivable), you'll end up with True

[latent spade]

I don;t what you mean by composition of limits

[pallid scarab]

Like lim[g(f(x)] = g(lim[f(x)]) when g is continuous

[latent spade]

I see but how the composition can be related to this?

[pallid scarab]

Because of the f(a-2h)

Write it as f(a-h - h)

[latent spade]

ah I see

let me try

Oh well I don't why we did this one like how can it be related to f'(a) and how did he get 2f'(a) from it

[pallid scarab]

Ok let's start over and write this in another way

You're looking for lim[(f(a) - f(a-2h))/h]

[latent spade]

right

[pallid scarab]

This is the same as 2 × lim[(f(a) - f(a-2h))/2h]

[latent spade]

but where did the 2h come from

[pallid scarab]

Multiply by 2 on the numerator and denominator

[latent spade]

from the f(a-2h)

like how did it get inside

[pallid scarab]

The f(a-2h) was always there

[latent spade]

shouldn't it be 2f(a+h)

[pallid scarab]

This is what we started with

[latent spade]

but the limits definition says f(x+h) not f(x-2h)

[pallid scarab]

Yes i know

[latent spade]

but then how did he convert it from x+h to x-2h and use it normally? it is okay to change the rule?

[pallid scarab]

But the purpose of composition is to find back something that looks like f(x+h) - f(x)

[latent spade]

so It doesn't have to be simillar to the definition ?

[pallid scarab]

In general, you have f'(x) = lim[(f(x+ah) - f(x))/ah]

This is because ah -> 0 when h-> 0

So you can replace

[latent spade]

but h can't be 0 right?

[pallid scarab]

No, but h can approach 0

[latent spade]

ah i see

[pallid scarab]

If h approaches 0, then a × h approaches 0 too

[latent spade]

but then for this example it says f(a-2h) the a isn't 2

it doesnot have a value

[pallid scarab]

Right it was a bad idea to use "a"

[latent spade]

Oh I am the one mistaken I thought x and a were the same however in the example it says (f(a)-f(a-2h))/h

the h in the denominator doesn't have a 2 as a coefficient

[pallid scarab]

Yep

So we make it appear

By writing 2 × (f(a)-f(a-2h))/2h

The thing on the right will approach f'(a) as h -> 0

So we're left with 2f'(a)

[latent spade]

oh i see what you mean now

I understood

Thanks alot

[cedar pawn]

np

[pallid scarab]

The guy saying np xd

[latent spade]

haha

[pallid scarab]

But yeah you're welcome

[lone heart]

@latent spade Has your question been resolved?

[lone heart]

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[wooden mantle]

We could use integral test for this right?

But is it possible to just cancel out the roots of n

And since 1^n is always just gonna be 1

it becomes insignificant as n approaches infinity

So we are left with 1/2n^3

We take the 1/2 outside the series

And we are left with a p series with the p being 3

So the series converges right?

Is this a viable way to solve it

Or is it better to just use integral test

Apparently via integral series it also converges

[vale wigeon]

if you want to cancel out the root you will be left with a p-series for p=2.5

unless you deliberately intend for algebra to fly out the window

[lone heart]

@wooden mantle Has your question been resolved?

[wooden mantle]

What do you mean

I mean it can be n^1/2

All the same isnt it?

[tacit arch]

one way is a lot easier than the other. try both

[wooden mantle]

Wait gimme a sec

I dont understand isnt

this correct?

[tacit arch]

no, you forgot the n^3 term. but also that's not a p-series yet

[wooden mantle]

Yeah I know, but -1^n is 1

[tacit arch]

,calc (-1)^3

[ocean seal]

Result:

-1

[wooden mantle]

And as n apprcoahes infinity

1 becomes insignificant right?

[tacit arch]

yes

[wooden mantle]

also what do you mean I forgot n^3

What should it look like?

Do you mind showing

[tacit arch]

error in this step

[wooden mantle]

Whats wrong with it?

Oh wait

Do I have to take the 2 out as well?

so its n/2n

or?

[tacit arch]

think about it

try plugging in some values of n like 4

the term in the top formula will be different from the term in the bottom formula

[wooden mantle]

aight lemme try that

one sec

Oh yeah you are correct

So what do I have to do to cancel it out?

[tacit arch]

cancel it out
what do you want to do?

just use distributive property

a(b+c) = ab + ac

[wooden mantle]

with like the (-1)^n*square root or?

actually wait

I dont see where I would have to use it

[tacit arch]

just fix your algebra first. then use comparison test to a p-series test from there.

[wooden mantle]

still dont get it

How does the fact a(b+c)=ab+ac help?

We dont have anything in the form of a(b+c)

[tacit arch]

specifically, the denominator

[wooden mantle]

This part or?

Also its not inside brackets

like the 2n^3 part of it is ouside

<@&286206848099549185>

Could someone just show me what it should be, I really dont get it.

[wooden mantle]

.close

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[proud arch]

Hi, I need help with this question. So far, I've found that the point is not on the curve, and I've found that the tangent line has equation y - 4/a = -4/a^2 (x-a). I'm not really too sure where to proceed from here.

[proud arch]

I also plugged in 1 for y and 3 for x. So the tangent line has equation 1 - 4/a = -4a/a^2 (3-a)?

<@&286206848099549185>

[tacit arch]

nah that doesn't tell you anything about tangent line. you just use that to solve for the value for a

after that algebra, you plug that back in to the initial equation for the line you have.

[tacit arch]

can you show the whole question including part a? i can't tell if what you have is relevant

[eager talon]

Hello @tacit arch

Alright i got your solution

[proud arch]

Part a is a different question.

[eager talon]

Right so first of all xy=4

[proud arch]

Yes.

[eager talon]

X =+-2

Y=+-2

No wait

You do x=4/y

And then you plot it

But what point does the tangent have to be on the graph

[proud arch]

(3,1)?

[eager talon]

3,1 doesn't belong to xy=4

[proud arch]

Sorry, I'm not really understanding the question?

When I solve for a, I get that a = 2, 6?

@eager talon @tacit arch

[eager talon]

a?

Ohh wait

[lone heart]

@proud arch Has your question been resolved?

[lone heart]

@proud arch Has your question been resolved?

[lone heart]

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[tacit flint]

not sure how to do part c ;-;

[alpine sable]

it looks suspiciously similar to the polynomial. try multiplying both sides by 7sec x

[tacit flint]

i multiplied both sides by 7 but idk how to get all the identities the same

[alpine sable]

huh?

multiply everything by sec x

[tacit flint]

i did this

oh by sec?

[alpine sable]

yea

then it should look like your poly

[tacit flint]

ok i’ll try that

OHH WAIT

cosx times secx is 1 right?

[alpine sable]

yes

[tacit flint]

got it

i’m an idiot

thank you

everything is resolved

[alpine sable]

nice

[tacit flint]

WAIT

i’m double stupid

to prove it has no solutions do i just do b^2-4ac

?

[alpine sable]

that only works for quadratics

theres a ^3, so its cubic rn

[tacit flint]

oh yes ofc

[alpine sable]

use your answer to part b to factorise that first

[tacit flint]

how do i show it has no solutions? if i’ve done the working right

ohhhhh snap ok got it

thank you!!

[alpine sable]

yw :)

[tacit flint]

.close

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[idle steppe]

hi

[fallen verge]

which part

[idle steppe]

everything besides the first part

[lone heart]

@idle steppe Has your question been resolved?

[solemn juniper]

The question lays out pretty specifically what it wants you to do

What about it is unclear?

[idle steppe]

i didnt understand his explanation of conditional probability

not quite sure how to use it

[solemn juniper]

Have you heard of the law of total probability?

[idle steppe]

this?

[solemn juniper]

Yes

That is the means by which you condition on all possible throws

[lone heart]

@idle steppe Has your question been resolved?

[idle steppe]

ok im going to watch a video on conditional prob

[lone heart]

@idle steppe Has your question been resolved?

[lone heart]

@idle steppe Has your question been resolved?

[idle steppe]

.close

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[drowsy sedge]

I row reduced and got 1,0,0 0,1,0 and 0,0,1

btw this is homework

so does that mean k can be anything?

[naive valley]

no, what if k=0?

[drowsy sedge]

hmmm

uhh

im not sure @naive valley

[naive valley]

can a set of linearly independent vectors include the zero vector?

[drowsy sedge]

Wouldent it always be there anyways?

wait

I think logically no it cant

@naive valley

monsieur bungo

are u there

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@drowsy sedge Has your question been resolved?

[drowsy sedge]

<@&286206848099549185>

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@drowsy sedge Has your question been resolved?

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[limber nimbus]

how do you intergrate \int \frac{e^{2x+3}}{e^{4x-3}} ?

[limber nimbus]

I've tried to split it up into 2 different ones and then times them together but it doesn't work

[vale wigeon]

isn't this just int e^(-2x+6) dx

which is obvious to integrate

[limber nimbus]

how do you get the +6?

wait

i get it

im stupid

thank you!

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[smoky rampart]

how would i go about solving this?

[ornate condor]

u cant

:O

u need it to = something

[smoky rampart]

oh oops

its derivatives

[ornate condor]

its just some expression

so find the derivative of this eq

ok i hate that

might i introduce u to

derivative calculator

https://www.derivative-calculator.net/

just enter in ur thing n itll show u the ans

with steps

[smoky rampart]

oh alright

thanks

[ornate condor]

n exactly what working is used each time

integral calc exists too

np

come back if u dk still

or dk how to ues it

use

[smoky rampart]

ok that was rlly helpful

all i needed to do was multiply the first term by the numerator then apply quotient rule

i feel dumb

thanks!

[ornate condor]

ayy

np

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[topaz ore]

hello, can anyone check if our group answer here is right? me and my math group are quite confused and we're asking different sections but they all have different answers. thank you!

[runic trench]

its correct tho

[tacit bobcat]

,calc y=-1, sqrt(6y + 7) - sqrt(3y + 3)

Bot is dead, but you can use other calculators

[runic trench]

,calc y=-1, sqrt(6y+7) - sqrt(3y+3)

oof

[topaz ore]

we got ahold of the other section's answer, what about this one though

[runic trench]

the one here is correct

[topaz ore]

thank you!!

.close

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[tacit bobcat]

Not -3

[buoyant storm]

sub z=3y+3, then sqrt(2z+1)-sqrt(z)=1

squaring both sides removes radicals easily

then u solve based on z=4, 0

[buoyant storm]

this solve is correct but unnecessarily long imo

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[lavish oyster]

Is f(x) continuous in x = 1?

[lavish oyster]

i'm confused what to do first

can anyone help?

[ornate condor]

find the left lim

n right lim

if they r the same as f(2) then its cont

[lone heart]

@lavish oyster Has your question been resolved?

[lavish oyster]

but is it the question as x=1 or f(1)?

[ornate condor]

oh wait

oops

ye x=1

[lavish oyster]

okay tyvm

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@spring harbor Has your question been resolved?

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@spring harbor Has your question been resolved?

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✅

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[vapid hollow]

.close

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[alpine sable]

Need to Use Newtons Law of Cooling to solve this

[tacit arch]

and did you?

[alpine sable]

im not sure how to

its a bit confusing

[tacit arch]

https://www.youtube.com/watch?v=ejEXSjdMpck

[alpine sable]

thank you

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[wet beacon]

f(1)=0, f(2)=64, f(-1)=24, f(0)=-20. Which value of x is a factor of the function

[vale wigeon]

is f actually known to be a polynomial function?

if not then the question is meaningless, or you omitted crucial info

[gray isle]

the wording is off as well

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[plucky geyser]

how to find the indefinite integral of a 3 product term expression using integration by parts

[sharp gate]

you need to be more clear about what the actual products are

[plucky geyser]

• Polynomial
• Trigonometric
• Exponential

If there is another integration method to solve this, it's okay.

[sharp gate]

set f = t and g' = e^t sin(2t)

[plucky geyser]

x?

[sharp gate]

you can pull the 5 out

[plucky geyser]

So can we apply uv- integral vdu to anything?

no matter how many terms

[sharp gate]

i mean you just broke it up into 3 products, but you could also write it as

(5t)(sin2t e^t)

which is 2 products

[lone heart]

@plucky geyser Has your question been resolved?

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[agile yacht]

How would I calculate this using an arithmetic series?

[agile yacht]

I’ve done it with a sequence, but the question seems to want me to do it with a series equation

[lone heart]

@agile yacht Has your question been resolved?

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@agile yacht Has your question been resolved?

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[high plume]

Find the value of x?

[ornate condor]

just read the question

lol

whats this

[high plume]

I dont know the language bruh

[ornate condor]

hahaha

[gray isle]

old log notation

$^a\log(b) = \log_a(b)$

[ocean seal]

ℝamonov

[gray isle]

applying change of base laws should get you what you need

[ornate condor]

oh thats cool

[gray isle]

applying change of base laws
...

if you don't know them, its recommended that you try looking it up

[dreamy vector]

Can someone please give the answer if he could.
On the left is the question and on the right is the hint.

[high plume]

$\log_a(b) = \frac{\log_c(b)}{\log_c(a)}$

[ocean seal]

Noone

[high plume]

It can be a b or c

U need try all of them

Did u try it?

[dreamy vector]

Can this question be answered please or you don’t solve words questions?

[high plume]

Use another channel

Wait let me try

[dreamy vector]

Can you tell me which?

Please

[high plume]

#help-2

[gray isle]

combine stuff into a single fraction

common denominators etc

[high plume]

Trying to get the same denominators

$\log_z(a) \cdot \log_z(b) \cdot \log_z(c)$

[ocean seal]

Noone

[high plume]

U know how to make it into 1

I mean like make it into single term

I also stuck at there lol

I just want to mkae it into single term

Make*

[lone heart]

@serene escarp Has your question been resolved?

[next brook]

Do not ping moderators or random users for help.

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[west pebble]

Need help:

3. From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

[river siren]

why it takes minus for invers? why not the plus?

[grave island]

go to an empty help channel

[grave island]

have u draw a diagram

[west pebble]

Yes

[grave island]

show diagram

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@west pebble Has your question been resolved?

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[west pebble]

.reopen

[lone heart]

✅

[last ether]

Did you do this?

@west pebble show the diagram

[west pebble]

I'm getting the pic wait

[last ether]

Yeah, so you can use trigonometric ratios

Since you also found the angle of elevation from the object to the top of the cliff, what ratio represents the ground and the height

[west pebble]

So I'll use tan?

[last ether]

You can

That would put your unknown the denominator though

It would be better to use cot

That way your unknown is in the numerator and it gets rid of the headache of cross multiplying

[west pebble]

So if the equation is correct:

cot 34(deg) = 40/b?

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@west pebble Has your question been resolved?

[west pebble]

.close

[lone heart]

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[short veldt]

For a mile of highway on land, two truckloads of asphalt and one gallon of paint are required.
For a mile of highway on bridges, the city needs one truckload of asphalt and three gallons of paint. The city has 50 truckloads of asphalt and 80 gallons of paint. What should be the variables here (x and y)

[bright delta]

hi

[short veldt]

hi

[lone heart]

@short veldt Has your question been resolved?

[short veldt]

<@&286206848099549185>

[lone heart]

@short veldt Has your question been resolved?

[prime badge]

what's the goal

we're supposed to build bridges over land to conserve asphalt?

[short veldt]

to find the largest total number of miles of highway the city can build

[short veldt]

@prime badge

[prime badge]

i don't know what's the intended solution

[short veldt]

what's the maximum miles of highway that can be built with 50 truckloads of asphalt and 80 gallons of paint

[prime badge]

yeah i don't know how to solve it normally

you can build 25 roads, you;re left with 55 buckets of paint, then you can convert a road to 2 bridges for 5 buckets, so 25+11

[short veldt]

which type of roads

oh

[prime badge]

non bridge

[short veldt]

land

alr

I have to solve it graphically tho

[urban orchid]

this sounds like a linear programming question to me.

[short veldt]

Yea it is

I just don’t know what x and y are

[urban orchid]

Try setting the variables to the kinds of road you are building. Then the requirements will put inequality constraints on the problem

so like x=miles of land highway

and y = miles of bridge highway

[short veldt]

X is less than or equal to 25

[urban orchid]

if you build only on land

[short veldt]

Y is less than it equal to 26?

Yea

Hm

[urban orchid]

think about doing both

how much asphalt will you use if you build x normal miles and y bridge miles?

[short veldt]

Oh

Got it

[urban orchid]

so you have two constraints, and you want to maximize x+y subect to those constraints-- you can expect the maximum to occur at a corner

[short veldt]

Yup

[urban orchid]

great!

[short veldt]

Thank you

.close

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[pseudo notch]

Hi I'm just wondering why this isn't 3pi/4

[pseudo notch]

cuz it would be

pi/2 - (- pi / 4)

[alpine sable]

arctan(0) is?

[ornate condor]

,w arctan0

[ocean seal]

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Requested by Circle#0025

[ornate condor]

,w arctan(-1)

[ocean seal]

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[ornate condor]

wait a sec

thats sus

[pseudo notch]

o wait ignore me

[ornate condor]

oh nvm it has a nice exact val

[pseudo notch]

how do u close it

i just got my unit circle wrong facepalm