help-0

[light mango]

probably more suited for engeneering discord ig

[tough hatch]

,, u_x(y) = \frac{\partial}{\partial x} u(y)

[light mango]

uhhh

[tough hatch]

is u(y) constant?

[light mango]

these calculations add c to the equation which im supposed to solve

thats not intergate?

[light mango]

no

[tough hatch]

what is u(y) though

or u(x,y) rather

[light mango]

the velocity of the fluid

[tough hatch]

so no equation for it

[light mango]

yea thats what im supposed to do

[tidal bay]

u2-u1=u3-u2....?

[light mango]

huh

yea so i definitely integrate in this problem

thats how it works

so i find it weird that you guys find that weird

[dull onyx]

mental illness

[thorn tapir]

.....wat

[woeful pulsar]

please only post about help for math in the #questions channels

[royal drift]

Hi, i really want to study english math but dont know where to start can someone help me pls?

[woeful pulsar]

what do you mean by "english math", like "math in english"?

[royal drift]

Yes correct, i really want to study abroad

[woeful pulsar]

hmm Khanacademy is a pretty good resource for studying math in english

[royal drift]

Do they charge money tho?

[dusk canyon]

Khan Academy is free

[west hearth]

Got a question, why do we write dy/dx when it’s actually delta x that tends to 0 and not delta y

Because doesn’t “d” imply some very very small quantity

[tough hatch]

(d/dx) y

[west hearth]

Oh

What’s the d doing alone in the numerator

Or is that just notation

For taking the derivative of y = f(x)

[tough hatch]

well\
we also have integrals of functions of x like $\\int x\diff x$

[west hearth]

Yeah

[tough hatch]

dy and dx are also called differentials

[west hearth]

Yes

[tough hatch]

you can integrate a derivative, both with respect to x

[west hearth]

Yeah

[west hearth]

I also wanted to ask uhh when we limit delta x to 0

Why doesn’t delta y also tend to 0

It’s hard to grasp this

Also is it possible to have an infinitely large change in y when dx tends to 0?

[tough hatch]

e.g. $\int x\left(\frac{\diff}{\diff x}\right)\diff x = x$

[west hearth]

Well delta x limiting to 0 would mean that there is a very very very small change in x

So shouldn’t that cause a very very very small change in y

Ah

Makes sense

Wdym

If you are far along a vertical asymptote then the y values are increasing rapidly wrt to x right

[tough hatch]

dx tends to 0 doesn't mean x approaches a value where the function is asymptotic

[tough hatch]

yes

[west hearth]

Yeah so how do we show that delta y also doesn’t tend to 0

If the change is very very small

[tough hatch]

why shouldn't it?

[tough hatch]

if there is a very small change in y then that means delta y is very small, i.e. close to 0

[tough hatch]

everything is sus

existence is sus

[rocky fossil]

thanks

[tough hatch]

ez answers

[rocky fossil]

lol

wait

is that a property

is log_9(m) = log(m)/log(9) a property

wait

oh nvm

i got it

[flat pecan]

are you guys finished?

[tough hatch]

seems like they are.

mb for the unnecessary ping

[flat pecan]

Given a deck of 40 cards of 4 seeds with 10 cards each of values:2,3,4,5,6,7, J, Q, K, A, what is the chance of drawing 5 cards of distinct values?

[old cobalt]

What is the difference between rearranging and quadratic formula?

[shell widget]

@old cobalt What they mean by rearranging is that u isolate "x" by algebraic operations

quadratic formula is the same thing but the rearranging is already done

[tough hatch]

answered on #help-1 lol

[old cobalt]

Thank you 🙏

[flat pecan]

anyone?

<@&286206848099549185>

[noble sinew]

So 1st draw doesn’t matter, then 2nd draw has prob (39-3)/39, 3rd draw has prob (38-3-3)/38 and so on

Multiply the probabilities together and you get the answer

[flat pecan]

I did try something like that but doesn't appear to be working

[noble sinew]

It does

[flat pecan]

Ok, what if I wanted to find the number of combinations which satisfy what is being asked?

[vale wigeon]

4 seeds? did you mean suits?

[flat pecan]

How would I go about that?

[flat pecan]

Idk how its called in English, but its the 4 common types

[vale wigeon]

yeah suits

the number of hands with all cards having distinct values is 10C5 * 4^5

divide that by 40C5 to get your probability

[flat pecan]

Why 4^5?

[vale wigeon]

10C5 = number of ways to choose which 5 ranks you get
and 4 ways to choose the suit for each rank

[noble sinew]

,w (39-3)/39*(38-3-3)/38*(37-3-3-3)/37*(36-3-3-3-3)/36

works fine?

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[vale wigeon]

,w (10C5 * 4^5)/(40C5)

[flat pecan]

Xd

[vale wigeon]

,w (C(10,5) * 4^5)/C(40,5)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ann#0413

[vale wigeon]

there we go

[flat pecan]

I see thanks

[flat pecan]

Yeah yeah I was just thinking in terms of combinations

Thanks a lot both of you

[fossil tree]

can someone explain to me what a norm of a vector is in english, i look it up and have no clue what it means still

[true crystal]

It is kinda its length

[fossil tree]

ok? wdym kinda

[true crystal]

A length means that you have a notion of distance which is not unique in all context

but it is a way to understand it

[fossil tree]

so whats the difference between a norm and its magnitude then

wouldnt that be the same

[true crystal]

If I have to go from point a to b I can represent a vector that goes from a to b and its norm would give me the distance between the points

[vale wigeon]

none

[fossil tree]

would finding its absolute value i.e its magnitude be the same

[vale wigeon]

except 'magnitude' typically refers only to euclidean norm

[fossil tree]

huh

[vale wigeon]

while 'norm' can be more general

[true crystal]

In vector context it means basically the same

its more of terminology

[vale wigeon]

there are ways of assigning a length to every vector in your space that aren't the same as the euclidean norm you're used to but which are still consistent

there are certain rules an assignment of lengths must obey in order to be called a norm

[fossil tree]

so to find the norm id do the sqrt of ux^2+uy^2+uz^2?

[vale wigeon]

"the norm" requires context

[fossil tree]

the question has no context

[vale wigeon]

can you show the question

maybe it's a devil-in-the-details thing

as it so commonly is with math

[true crystal]

That is the Euclidian norm

[fossil tree]

If u = (−1, 2, 2) is a vector in R3

, find the following:

a) ||u || (the norm of u)

well it wouldnt send the symbol

but thats legit it

[vale wigeon]

okay

so they probably want the euclidean norm

since it sounds like youre not quite at the level where you would give 'exotic' norms any consideration

[fossil tree]

nope

im just starting vectors

so is the norm just 3?

[true crystal]

yes

[vale wigeon]

yes

[fossil tree]

math complicated, thanks my guys

[true crystal]

but at a higher lever you should be more specific

[vale wigeon]

in math sometimes it makes sense to measure distance in ways other than the euclidean norm

[fossil tree]

isnt that the same thing tho

[true crystal]

Yeah there is some distance that are easier to deal with depending on the context

[alpine sable]

Other than Euclidean norms?

What can be the other ways?

In algebraic forms or smth?

[fossil tree]

ok this is all going way over my head

i slept through every class so idk whats going on

[alpine sable]

@true crystal sorry for pinging but like I would really want to know what is meant by what Ann said

Some examples that is

[true crystal]

There are a lot of other vectorial spaces than Euclidian space

[alpine sable]

Interesting

Any references from where I can learn about them

Or smth

[true crystal]

Which one

[alpine sable]

This one

[true crystal]

Probably vector space

[alpine sable]

Vector Space

Okay.. I haven't even done Vectors by now, just know the basics

[true crystal]

Here is another notion of norm :

$||f||=\sqrt{\int_0^1 f^2(x)dx}$

[vale wigeon]

you forgot the square root

as written this is not a norm

[true crystal]

Yes

[alpine sable]

sorry this is beyond me

[true crystal]

You are like really quick I was going to change it xD

[alpine sable]

Guess this isn't for me

[ocean seal]

King1219

[true crystal]

Why didn't you ping Ann then ?

[alpine sable]

Because

I am afraid

Is there some quick way of finding this?

For three degree things I would just check it manually but for 4 I just checked whether the things in the options make the thing 0

[oak chasm]

Yes. You can either plug in each pair and see if it produces zero or you can divide the polynomial by (x - (-1))(x - 2) and factor it.

[alpine sable]

Factor the remainder?

[oak chasm]

You need to be careful of multiplicities, though.

[alpine sable]

Or quotient

Yes

Oh I am so dumb

Nvm

[oak chasm]

If they're zeroes, there will be no remainder.

[alpine sable]

Yeah that's why quotient

[oak chasm]

(x - zero) evenly divides a polynomial.

[alpine sable]

I don't get what is meant by this

Nvm

I am so dumb

Sorry

I got it

[oak chasm]

There will be a real number x that produces a higher value when filled into that polynomial than other reals.

[alpine sable]

Just put it as 1

Cause for any other thing

Or 2 actualy

But for any other thing it becomes minus

2 is small too

One returns 12

Bro

Why didn't I think of this

Ok now this is the one I couldn't solve after 15 minutes

Ugh

Shouldn't I put the value as 2

And then find the root of one equation or something

Lemme try

No

Doesn't make sense

Probably divide the 2 expressions

No still I will have 2 things remainder and quotient

Ugh

[oak chasm]

One must be (x - 2)(x - m) and the other must be (x - 2)(x - n).

[true crystal]

If (x - 2) is a factor of x^2 + ax + b what does that mean ?

[alpine sable]

This

[oak chasm]

For some m and n.

[alpine sable]

I know that but I don't know how to proceed after it

[true crystal]

Yeah is means that 2 is a root

[oak chasm]

OK, so expand the two things.

[alpine sable]

Okay

But

No clue what comes in the place of m and n

[oak chasm]

Expand (x - 2)(x - m). Expand (x - 2)(x - n).

[alpine sable]

Ok

[true crystal]

Try to subtract the second and the first

[alpine sable]

I actually did that

[true crystal]

then for x = 2 you get something

[alpine sable]

Ohhh

Got it

ThNks

I didn't know what can be done with the x

[oak chasm]

Did you expand the two?

[alpine sable]

No substracted both the things

I get 2

And that is correct

Today I learnt so much about polynomials

It's confusing how did I do that

[oak chasm]

That's not always correct.

[alpine sable]

I know I can expand stuff

[oak chasm]

For example, a = c and b = d is possible, which gives you 0/0.

[alpine sable]

[shadow furnace]

We are probably assuming they are different.

[oak chasm]

You shouldn't.

[alpine sable]

No

Uhm

But the key says 2 only

[oak chasm]

Well, as demonstrated, the key is wrong.

[alpine sable]

x-2 is a common factor

[oak chasm]

x - 2 is also a common factor when the polynomials are identical.

[shadow furnace]

Well, it might not be the only common factor.

[alpine sable]

It is possible that c=d

But it's also possible that c != d

[oak chasm]

Right, so there are multiple answers.

[alpine sable]

As demonstrated you are wrong

[oak chasm]

OK, well good luck.

"The answer key says you're wrong" is a very good bit of reasoning.

Answer keys are always right.

[alpine sable]

You said answer key was wrong because c = d was possible

But it also might be that c != d

That basically means multiple answers (0 and 2)

And that was just me meming

Sory

[sage vale]

hi, I need help- figured out dzya and dxda, but unsure about dyda. based on the graph, 1) there's no cross section on the xz plane I can use to find xz bounds and 2) there aren't 2 y surfaces for the y bounds. one of them is literally a line??

[fossil tree]

how do i determine if vectors are coplanar, also what does coplanar mean

[glass lichen]

coplanar mean they share a plane

so any set of 2 R3 vectors will be coplanar since you need 2 vectors to span to get a plane

[grand shell]

$X^2 - Y^2 = 4P$ where $X,Y,P \in \mathbb{Z}$ has a solution $X = P-1$ and $Y = P+1$. Is there a way to find the smallest solution X,Y?

[ocean seal]

Rahakasvi

[mortal void]

is this channel free now?

i have a small doubt bout a thing its pretty basic

11/4hrs is the value of time give to me on a question what its real value i should be putting

cause its value coming is 2.75hrs

so does that mean its value should be 2hrs 45minutes?

[remote heron]

yea

does it make sense?

[mortal void]

thankyou

[remote heron]

np

[mortal void]

not really

[remote heron]

which part?

[mortal void]

i just thought that 75 is 75% of the 3rd hour

[remote heron]

it is 😄

its just confused because of the fact that a whole hour is 60 minutes

not 100 like youd intuitively expect it to be probably, with percent

its maybe easier to see like

75% = 3/4 = (1+1+1)/4

so three quarters of an hour, a quarter of an hour is 15 minutes

hope some of that makes sense 🤔

[mortal void]

yeah

[remote heron]

this is probably a good time to go back to thinking of it as pies/pizza or whatever is helpful with percentages since a clock is divided in the same way

[mortal void]

yeah thankyou its clear now

[glossy forge]

Idk what’s the error

[remote heron]

is it really just that 5 becoming a three

that seems so dumb

[mortal void]

hhaha

[remote heron]

,w 26=3(x+1)^2-1

[ocean seal]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[glossy forge]

Is it???

[remote heron]

theres a sign error too

[mortal void]

lol i didnt saw the question and i was like his maths was perfect there

[remote heron]

,w 26 = 5(x+1)^2-1

[ocean seal]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[remote heron]

the sign error is somewhere other than the 5

probably just a typo

[mortal void]

can you tell me where are you doing it?

[glossy forge]

I didn’t think it was the 5

[mortal void]

is it some kinda app where we will solve and it will tell us our result

[remote heron]

theres some weirdness in this step

i thought you might be able to "eat" it with the plus or minus

but now im not sure

[glass lichen]

$x=-1\pm 3$

[remote heron]

ye

[glossy forge]

There is no 5 though

[remote heron]

there is a 5 in the prompt but i think its just a typo

[ocean seal]

Mosh

[glossy forge]

I think it’s the error

[fluid crown]

does anyone know how this can transform into an equation

[glossy forge]

Is this a correct way of doing it to

[remote heron]

i dont think theres a correct way

unless your class is using something specific

the answer is correct

[remote heron]

what even is this

like you want to write the repeating decimal?

[topaz scaffold]

You can change it into a fraction if it's a repeating decimal

But not an equation

[wooden crag]

could have skipped a few steps by using quadratic formula

if it's been taught to you

[glossy forge]

Can you explain why it’s suppose to be -1

[vapid ermine]

@glossy forge its true but useless one

[remote heron]

try out the algebra

they maybe skipped some steps they shouldnt have

[loud turtle]

I have a quick question for anyone whos got time

[remote heron]

specifically they sort of switched the sides which you can do but its a little confusing

but just do like

[vapid ermine]

move the -1 to the opposite side and divide by 3 @glossy forge it will be easy

[loud turtle]

I have the value of ph but I dont know how to isolate the OH since this is my first time using log

[ocean seal]

jan Niku

[vapid ermine]

then it will be so
(x+1)²=9
x+1= 3 x+1=-3
x=2 x=-4

[true crystal]

You're formula is clearly wrong

[glass lichen]

isolate for log(H) then use definition of log

[glossy forge]

ok thanks

[loud turtle]

it is? the teacher gave me this

[wooden crag]

is OH a single variable or O * H

[loud turtle]

its a chem formula

[glass lichen]

yeah, pH is measure of hydrogen, not hydroxide

[true crystal]

pH is with H3O+

[glass lichen]

anyway, the math is the same regardless

[loud turtle]

but it tells me that its also with OH

[true crystal]

no

[loud turtle]

you arent wrong I also have your version of the formula

oh well that doesnt matter the math is what matters here

[glass lichen]

King is just pointing out an error in the question, however the math to isolate for whatever's in the log is the same

yes

[true crystal]

yes

[loud turtle]

I dont know what definition of log is this is my first time

[glass lichen]

$a^b=c\iff \log_a(c)=b$

[ocean seal]

Mosh

[glass lichen]

definition of log is how logs are defined...

[loud turtle]

my bad I learn in french

but I understand that thank you

[true crystal]

In this case log is in base 10

I agree there might be some ambiguity

[fluid crown]

apparantly its some kind of equation which is derived after using godels numbering

[hardy vault]

can someone help

[naive field]

the rules are : in case of basic medium ph=14+log oh , in case of acidic medium ph=-log h30

in basic, the concentration of ho is 10 exponent 14+ph , in acidic the concentration oh h30 is 10 exponent -ph

[jagged rapids]

Won't that be $\binom{9}{5}$

[ocean seal]

killBird

[hardy vault]

oh bruh lol

[jagged rapids]

As we choose any 5 numbers and then order them in only the increasing way

[wicked plover]

Hello could someone walk me through this question?

[glass lichen]

have you drawn it?

[wicked plover]

i have to draw it?

[glass lichen]

well I'd hope you'd make a diagram if it isnt provided...

since it's clearly geometry

[wicked plover]

how do i know where to mark B, A, T

in the triangle

[oak chasm]

It's arbitrary. You can write B, A, and T on any three different vertexes.

[wicked plover]

Oh

thank you so much

[oak chasm]

@hallow flax No, a is the opposite side of A.

[hallow flax]

Ok, then my apologies, different from what we learn here in europe.

[oak chasm]

t is the opposite of T. b is the opposite of B.

[wicked plover]

could you draw it out for me? if possible

[hallow flax]

https://i.imgur.com/hbA3qeP.png

[hallow flax]

Makes sense, thanks!

[wicked plover]

Okok

after i draw it out what is the next step

[hallow flax]

Do you have any idea?

[oak chasm]

Fill in the values you know.

[wicked plover]

Oh yea

ok let me write this down for future purposes

im not the best with trig

[celest anvil]

need help with a and b

[oak chasm]

@celest anvil Sorry, channel is busy.

[wicked plover]

yeah

i filled in the variables

[hallow flax]

Ok, do you have an idea?

How to continue?

[wicked plover]

but i dont know what is A

<A

i know what a B and T are

[hallow flax]

You have two angles of a triangle, so you can find out the third one.

Do you know how?

[wicked plover]

i add them together?

[hallow flax]

You can the sum of angles in a triangle is 180°

[wicked plover]

and then try to get them to addu p to 180

so its 62?

[hallow flax]

Yes.

Any idea going forward?

[wicked plover]

i have to find b and t

i have no idea

[hallow flax]

Correct.

It isn't a rectangle triangle, so you have two laws, you can use. Do you know which ones?

[wicked plover]

Sine Law and Cosine Law

[hallow flax]

Exactly! To find out sides, I suggest the law of sines. So you can just figure the remaining sides out, using the law of sines.

Do you know what the law of sines says?

[wicked plover]

my issue is

last year

i slept through the trig online class

so i actually have no idea or any background information about cosine law and sine law

[hallow flax]

the law of sines says: $\frac{sin(\alpha)}{a}=\frac{sin(\beta)}{b}=\frac{sin(\gamma)}{c}$

[ocean seal]

Sparender

[hallow flax]

or, the inverse:

$\frac{a}{sin(\alpha)}=\frac{b}{sin(\beta)}=\frac{c}{sin(\gamma)}$

[ocean seal]

Sparender

[hallow flax]

https://cdn.discordapp.com/attachments/269573202018041856/868214658983682108/1200px-Triangle_-_angles_vertices_sides.svg.png

In a triangle, with the angles and sides arranged as in this sketch.

[wicked plover]

oh okook

[hallow flax]

Basically, what it says, is the sin of the angle opposite to a certain side / this certain side, equals the sin of an angle opposite to another certain side / that other certain side.

You get it?

[wicked plover]

Yeah

so their all equal to eachother

[hallow flax]

What exactly do you mean, by "their all equal to eachother"?

[wicked plover]

I mean like

i have no idea

[hallow flax]

Check the formulas the "TeXit" Bot sent, and check them with the sketch a sent.

Perhaps it makes sense then 🙂

[wicked plover]

Oh ok ok i get it

i know that a = 35.2m

[hallow flax]

Yes.

So, with the law of sines, how could you proceed?

[wicked plover]

sin(35.2)

?

[hallow flax]

you have your sketch infront of you, right?

[wicked plover]

yea

[hallow flax]

ok, you wanna get side t

you know, a = 35.2m

[wicked plover]

yeah

[hallow flax]

and A = 62°

[wicked plover]

yep

[hallow flax]

Now you have one part of the law of sines:

send that again.

I did not get to see it.

[wicked plover]

would it be

a
__
sin(a)

[hallow flax]

$\frac{35,2}{sin(62°)}=\frac{t}{sin(T)}$

[ocean seal]

Sparender

[wicked plover]

yeah

[hallow flax]

Does that make sense?

[wicked plover]

thats what i meant

yeah

[hallow flax]

$\frac{35,2}{sin(62°)}=\frac{t}{sin(83)}$

[ocean seal]

Sparender

[hallow flax]

Ok, you have that. Do you know, how to proceed?

[wicked plover]

howw did u get 83

[hallow flax]

It says in the problem you sent.

angleT = 83°

[wicked plover]

oh yes

= 83

sorry

[hallow flax]

$\frac{35,2}{sin(62°)}=\frac{t}{sin(83°)}$

[ocean seal]

Sparender

[hallow flax]

Perfect, so, do you know, how to move on?

[wicked plover]

Uhh

nope

sorry

[hallow flax]

you just have to rearange that, to have t on one side, and then plug it into your calc, and then you got it

[wicked plover]

how?

would i reaarange it

[hallow flax]

Look at this again: $\frac{35,2}{sin(62°)}=\frac{t}{sin(83°)}$

[ocean seal]

Sparender

[hallow flax]

how could you get rid of the sin(83) to have t on the right side, isolated?

[wicked plover]

Ummm

no idea

divide it?

[hallow flax]

you can just multiply by sin(83)

then you get: $\frac{35,2}{sin(62°)}*{sin(83°)}={t}$

[ocean seal]

Sparender

[wicked plover]

Ohhhhhhhhhhhhhh

Shit

39.5?

[hallow flax]

Wait, I have to plug that into my calc, one sec.

Almost, check your rounding again.

40, yes, or 39,6, or 39,57

[wicked plover]

40

[hallow flax]

depending on how precise of a result you need, that should be stated by your teacher.

[wicked plover]

🙂

yeah she didnt say anythin

[hallow flax]

Perfect, hope that solves your question 🙂

[wicked plover]

oh my goodness

u a goat

thanks bro i understand now

[hallow flax]

Perfect, pleased to hear!

[wicked plover]

Hey but i have a question

[hallow flax]

Yes 🙂

[wicked plover]

i have another question and its reversed

[hallow flax]

Send it.

[wicked plover]

it says

FIND B

and gives me a b and c

[hallow flax]

Draw a little sketch

[wicked plover]

Ok

[hallow flax]

Then we can go through it together.

[wicked plover]

by the way you are an amazing tutor

[hallow flax]

Thanks, happy to hear that! 🙂

Do you have a sketch?

[wicked plover]

yeah

i plugged in the variables

[hallow flax]

Good, so, we now have a problem.

The law of sines, gives us two possible solutions for angles in triangles.

Do you know about the unit circle?

[wicked plover]

no i sadly dont

[hallow flax]

Ok, the problem is, for a set sin, cos value, there [in most cases!] are two possible solutions between 0 and 360°.

For the these solutions [considering our problem] will be between 0° and 180°, so in theory, both angles could be possible for a triangle.

So, we have to use the law of cosines, as this law will give us only one possible solution for triangles [sum of all angles 180°, thats why].

You get that?

[wicked plover]

Yeah

I ge tit

what would be the first thing we do?

[hallow flax]

Do you know anything about the law of cosines?

$a^2 = b^2 + c^2 - 2bc\cos(\alpha)$ and $b^2 = a^2 + c^2 - 2ac\cos(\beta)$ and $c^2 = b^2 + a^2 - 2ba\cos(\gamma)$

[ocean seal]

Sparender

[hallow flax]

these are the three which you should know, imo.

again, considering this triangle: https://cdn.discordapp.com/attachments/269573202018041856/868214658983682108/1200px-Triangle_-_angles_vertices_sides.svg.png

[wicked plover]

Oh

no i didnt know anything about the law of cosines

but

I see

i have no idea

a = b + c

[hallow flax]

You want Angle B, so, the pertinent one for you, would be the one starting with $b^2$

[ocean seal]

Sparender

[hallow flax]

As the two other ones, wouldn't give you angle B.

Do you understand that?

[wicked plover]

Umm yea

[hallow flax]

Good, so we will use the following formula:

[wicked plover]

c = b + a

?

[hallow flax]

$b^2 = a^2 + c^2 - 2ac\cos(\beta)$

[ocean seal]

Sparender

[wicked plover]

oh

[hallow flax]

you now have your different values, given in the task. You can just plug them into this formula, and solve it.

Do you know how?

or better, what I mean

[wicked plover]

Yeah

ok ok

[hallow flax]

Try it out, and see if it works 🙂

[wicked plover]

yeah

how do i plug in

b squared = a squared

?

[hallow flax]

b = 6, a = 5, c = 7

[wicked plover]

yeah

but

[hallow flax]

$b^2 = 36$

[ocean seal]

Sparender

[hallow flax]

$a^2 = 25$

[ocean seal]

Sparender

[hallow flax]

$c^2=49$

[ocean seal]

Sparender

[hallow flax]

Yes

[wicked plover]

like this?

[hallow flax]

I think you mean 36 instaed of 35 🙂

but, yes, and now the rest 🙂

[wicked plover]

idk

how to plug it in

could you plug it in and show me how u did it

[hallow flax]

yes:

$36=25+49-257*cos(B)$

[ocean seal]

Sparender

[wicked plover]

Oh d

Okok

wait

we dont have B though

[hallow flax]

Yes, thats what we want to find out.

[wicked plover]

my calculator doesnt give me a answer

[hallow flax]

now you have to rearrange this equation again, so that "cos(B)" is isolated on one side, I would suggest.

[hallow flax]

What kind of a calculator do you have?

Does it have CAS?

[wicked plover]

im using

https://www.desmos.com/scientific

[hallow flax]

try this: https://www.geogebra.org/calculator

However, I suggest you use a physical calculator, you also get to use it during examinations, etc.. to get a bit of extra practice in rearranging equations, etc. [if it isn't a CAS calculator] it won't harm for sure.

[wicked plover]

Oh

but to get it isolated

we need to use multiplication

[hallow flax]

I would start off with the easy stuff.

25 +49, you can get to the right side, just by - 25 and - 49

then you have the following: $-38=-70*cos(B)$

[ocean seal]

Sparender

[hallow flax]

You get that?

What I did, is just basically I moved the 25 and 49 to the left, by simply subtracting, so [-25] and [-49], that gets rid of them on the right, and on the left it makes 36-25-49, and that equals to -38.

.

Then I simplyfied $-257$

[ocean seal]

Sparender

[wicked plover]

Ohhhhhhhhhhhh

now what?

[hallow flax]

now you have that:

$-38=-70*cos(B)$

[ocean seal]

Sparender

[hallow flax]

With that, you are almost there!

How can you get cos(B) to be the only thing on the right?

[wicked plover]

38 x 70

?

[hallow flax]

you divide it by -70

then, you get:

$\frac{-38}{-70} = cos(B)$

[ocean seal]

Sparender

[hallow flax]

the - gets cancelled out, so you are left with:

[wicked plover]

Ohh

[hallow flax]

$\frac{38}{70} = cos(B)$

$\frac{38}{70} = cos(B)$

[ocean seal]

Sparender

[wicked plover]

Omg

i get it

[hallow flax]

and now, to get B, you take it arcus cos.

Perfect!

I hope, I could help 🙂 If you have more questions, just send them, I am happy to help 🙂

[wicked plover]

Thank you so much

[hallow flax]

You are welcome!

[glossy forge]

Did I plug this in right, or does only the first x needs to be substituted

[hallow flax]

What is the task?

[wicked plover]

0.5?

[hallow flax]

well, yes, 0,542, and what do you get for the angle then?

[wicked plover]

wht angle?

[hallow flax]

for B

[wicked plover]

0.5

degreez

[hallow flax]

So here, for a, you then have $y=3^2-3*3+2$

[ocean seal]

Sparender

[hallow flax]

You still have to apply arcus cosin

[wicked plover]

whattttttt

[hallow flax]

to get the cos/sin value for a angle you just use the stuff you are used to, probably.

[wicked plover]

0.9?

or 60

[hallow flax]

Yes, sounds pretty much right, it should be 57,121°.

I suggest you not to round intermediate results, to get a precise result at the end.

[hallow flax]

you get that @glossy forge ?

[wicked plover]

ohh

[hallow flax]

What you do for this problem, is you insert 3 for every x in the equation of this quadratic function, then you simplify.

[hallow flax]

🙂

[wicked plover]

i have another question but im just gonna go eat

when are ur availiable times ?

[hallow flax]

Ok, no problem. I should be around for at least another hour or so 🙂

[wicked plover]

Ok great

[glossy forge]

You didn’t answer my question

[glossy forge]

.

[hallow flax]

you have plug the x in for every x in the equation of this function.

You only did that, for the first one.

and on the left side of the equation, you don't have any x, so I suggest to leave something like f(3) or y there.

[glossy forge]

ok thank you

[timber sage]

Can someone help walk through a problem with me?

im really confused on it.

[ionic jewel]

[meager lily]

is this server dead

[glass lichen]

clearly not.. but this is a help channel

[meager lily]

just wondering

where does the 2 come from in the last step

[full cypress]

how are bases with different exponents like terms?

[glossy forge]

Can someone tell me if I plugged these in right or not

[alpine sable]

wdym? pretty sure they are not, which is the reason you cannot add or subtract them when simplifying

[hallow flax]

As far as I can see, I think the channel is in use, however, you should keep something like f(3)= on the left side.

[glossy forge]

Is the =(3) part of the equation or should I leave it out

[hallow flax]

Lets move to channel 3.

[full cypress]

@alpine sable

[glossy forge]

It’s a yes or no question

[full cypress]

in this expression somehow they do

[alpine sable]

here there is no adding or subtracting, so you'd have to use the exponent rule

[full cypress]

so it doesnt matter if they have the same exponent in this case?

[alpine sable]

nope in most cases it only matters when adding and subtracting

here you can use the power of a fraction rule to make it look better

like this

[clever locust]

Not sure if anyone has answered somewhere else, but differentiating sqrt(x) is the same as differentiating x^(1/2), and as you should see then a factor of 1/2 should pop out, which is where the 2 comes from

[alpine sable]

$\frac{(xy^2)^-2)}{(x^2y)^-2}

[full cypress]

"nope" as in they dont matter right?

[alpine sable]

$\frac{(xy^2)^{-2}} {(x^2y)^{-2} }$

[alpine sable]

yes

[full cypress]

ok thanks

thank you for taking time out your day an helping me out with that

[ocean seal]

Venti

[alpine sable]

it's my pleasure

if you need any more help then fire away

[alpine sable]

hmm could you show the full picture, I'm trying to figure it out but I'm as stuck as you at this point lol

[full cypress]

im good now but ill hit up if need help with sum else tho

[alpine sable]

hopefully I'll be awake by then but there other wonderful helpers who are happy to help (I hope) if not

[alpine sable]

I having a feeling it's cuz x cannot = 0

no it doesn't

@meager lily it's because the derivative of u given by du/dx is 1/2*sqrt(x)

completely forgot how derivatives work for a minute there lol

[alpine sable]

Hey, I was wondering why (a^-12) / (b^8) was simplified to 1 / (a^12 * b^8)

[keen socket]

U can write rewrite the fraction as a^-12÷b^8

Then that becomes 1/a^12÷b^8

[alpine sable]

yeah and then how does 1/a^12÷b^8 become 1 ÷ a^12 * b^8?

[keen socket]

Dividing by fliping the b^8

So it becomes 1/a^12 × 1/b^8

Which is 1/a^12 b^8

U could also see the fraction as a^-12×(1/b^8)

Which would then be (1/a^12)×(1/b^8)

Which gives the same result

[keen socket]

Division and multiplication are inverses of each other

[alpine sable]

yeah

[keen socket]

So when u divide by b^8 thats the same as saying the reciprocal of b^8

Which is 1/b^8

[alpine sable]

Okay, I get it now. Thanks for the explanation 👍

[keen socket]

Np

[alpine sable]

It's 1 am for me, so I might just be tired lol. Goodnight anyways

[keen socket]

Goodnight

[alpine sable]

What im confused

not sure if im starting this off right..

i write it down as

$32=27e^{k(12)}$

oops

[ocean seal]

Reverie

[alpine sable]

and i get

$12 ln(\frac{32}{27})$

[ocean seal]

Reverie

[alpine sable]

not sure what im doing wrong

[keen socket]

Its 5 not 32

Its the increase in population

From 1982 to 1994

[alpine sable]

i see

so i write it as

$5=27e^{k(12)}$

[ocean seal]

Reverie

[keen socket]

Yh

[alpine sable]

im still not getting any of the answers

hmm

[keen socket]

Well i got c

When i did it

[alpine sable]

so when putting it in log form

it is

$12 ln(5/27)

[keen socket]

No

[alpine sable]

oh

😒

[keen socket]

Its ln(5/7)/12

[alpine sable]

oh actually would it not be

[keen socket]

Becuz when u natural log e^k(12)

[alpine sable]

1/12 ln(5/27)

[keen socket]

U get 12k

Yes

[alpine sable]

ahhh got it

thank you

huh weird

my calc said its -.14

[keen socket]

My bad ln(32/27)/12

0.014

[wicked plover]

its 0.014

[alpine sable]

oh so it's 32 not 5

[keen socket]

Yes

[alpine sable]

ah got it

[keen socket]

32/27

[alpine sable]

so 1/12ln(32/27)

got me

.014

thank you guy

!

[lethal token]

Please help

[upper pebble]

so (18, 12) would be the vertex

i'm just not sure how to determine a

[topaz scaffold]

Vertex form would be $y = a(x-18)^2+12$

[ocean seal]

RipeOrange

[topaz scaffold]

We know at x = 0, y = 0

So plugging that in you get $0 = a(0-18)^2+12\implies a = \frac{-12}{18^2}$

[ocean seal]

RipeOrange

[upper pebble]

i see

[lethal token]

Thank you

[sour grail]

5=log(50 000P) i need to isolate P and i forget how to do

[topaz scaffold]

Just send in one channel...

[glossy forge]

Did I plug this in correctly

[ionic jewel]

no

its asking for f(x) = 3, not f(3)

[wicked plover]

i neeed helppppppppp >_<

[topaz scaffold]

Law of cosines

[wary stream]

Law of cosines

[topaz scaffold]

Ha I was first

Jkjk

[ionic jewel]

law of cosines

[wicked plover]

oh

how would i use it here

?

[glass lichen]

just plug and chug

[topaz scaffold]

Yep

[wicked plover]

ahh i see

[topaz scaffold]

Plug into the equation

[sleek elbow]

I just learned about law of cosines and its so useful O_O

[topaz scaffold]

Now derive it

[wicked plover]

maybe if i learned 😭

[topaz scaffold]

[sleek elbow]

whats derive? english is not my native language

[topaz scaffold]

Derive just means to get the equation

Discovering it kinda

[sleek elbow]

Oh dw I did :))

[topaz scaffold]

Building it

Idk

[topaz scaffold]

Niceee

[sleek elbow]

Deriving stuff is a lot of fun to me lol

[wicked plover]

wait

[wicked plover]

is the answer 18.71?

[glossy forge]

Is this right?

[ionic jewel]

not in the slightest

theres nothing right about that

[topaz scaffold]

[wicked plover]

hey.. could someone tell me if im right

[ionic jewel]

f(x) = 5x^2+3, they tell you that the output is 3

that means when you plug in the input, you get out 3

so 3 = 5x^2+3

and you solve for x

[topaz scaffold]

,w √(10^2 + 20^2 + 21020*cos(68))

[ocean seal]

Results provided by WolframAlpha

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

Requested by RipeOrange#4907

[wicked plover]

damn it

[topaz scaffold]

Oh wait

[wicked plover]

is that the answer?

[topaz scaffold]

,w √(10^2 + 20^2 - 21020*cos(68))

[ocean seal]

Results provided by WolframAlpha

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

Requested by RipeOrange#4907

[topaz scaffold]

Yea you're right

[wicked plover]

Ayee lesgo

[topaz scaffold]

Apparently I forgot the right formula oof

[wicked plover]

OOF

_<

[silk coral]

Hey kind of confused on what this is asking

[velvet condor]

..............................

[ionic jewel]

the direction of v

[silk coral]

Well I’m not sure how to find it

[ionic jewel]

angle from the positive x axis

[silk coral]

Is it just slope

[ionic jewel]

try drawing a triangle, with the positive x axis and the vector

then using trig to find the angle between them

[silk coral]

So is it A?

[ionic jewel]

yea

[silk coral]

Ok cool

That makes sense

[wicked plover]

is the length 10

[glass lichen]

how'd you get 10.7?

[wicked plover]

sine law

[silk coral]

10 sin 64 is 8.988

[glass lichen]

$\frac{\sin(64)}{\overline{BC}}=\frac{\sin(42)}{10}$

[ocean seal]

Mosh

[wicked plover]

?

so am i right

[silk coral]

I don’t think so

[glass lichen]

no

[shadow furnace]

Well, what are we trying to find in the question?

[glossy forge]

ok thank you

[wicked plover]

length of the side BC

[shadow furnace]

So from this equation can you solve for BC?

[wicked plover]

i have no idea

can i?

[silk coral]

Is this d btw?

Since it’s isosceles

[warm wren]

Isosceles doesn't mean that it's not obtuse or acute. It can be both. However I'm pretty sure that's not an isosceles triangle you got there anyway. @silk coral

It can be obtuse, or right, or acute, and also be isosceles, here's an example:

[small chasm]

how do i do this question?

i need to do it by 12

and im so lost

[shadow furnace]

Which of those questions?

[small chasm]

top

one

[shadow furnace]

Do you remember the formula for the volume of a pyramid?

[small chasm]

yea

look

i need the area base tho and i don’t know how to get it

[shadow furnace]

Hmm, read the question carefully

[small chasm]

i don’t get it tho

like i have to find both then add them

but i cant

[shadow furnace]

What does 'area base' mean? $A_{base}?$

[ocean seal]

ShurjoA

[small chasm]

yes

i think so

[shadow furnace]

Is that the same as the house's base?

[small chasm]

yes

so i do 8x8

for the base?

[shadow furnace]

Yes

[small chasm]

ok

thanks

[shadow furnace]

No problem!

[alpine sable]

yo i just finished calc ii but i left with some existential questions

what does it mean to calculate the cosine of pi/2 radians

or idk the cosine of 3pi/4

[small chasm]

thanks

i got it right

ok how do u calculate the height when they give you the slant height and the radius

like what’s the formula

[woeful pulsar]

cosine is a function, that takes angle to number

if you draw the unit circle and place your angle counterclockwise from the x-axis, then the cosine is just the x-coordinate of the point found.

[small chasm]

^

[woeful pulsar]

what radius?

[alpine sable]

can u use another channel

[woeful pulsar]

you mean cone?

[alpine sable]

uh nvm actually just go on

[woeful pulsar]

yeah notice the right angle triangle

[small chasm]

yes

[alpine sable]

thanks

im remembering now

[woeful pulsar]

use that right angle triangle to calculate the height?

[small chasm]

whats the formula?

i forgot it

[woeful pulsar]

pythagorean

[small chasm]

ok

[alpine sable]

i like your pfp man

i mess with rock lee heavy

[small chasm]

thanks

i keep getting the wrong answer

for my question

idk why

never mind

the height is

12cm

[alpine sable]

someone halp

pls

Are u familiar with zeroes of a polynomial?

@alpine sable

wait sorry

this is 1

right

because -6 and -3

Ye

but idk how u solve for a polynomial function

also I need help with dis

https://cdn.discordapp.com/attachments/845446653578444800/868325499192094740/unknown.png

Well u gotta look for the points in which y=0

So you can analyse the function

why y=0?

owo

so like both x values hav eto equal 0?

Oh no i mean

Give me a second

oo oki

Bru discord is taking ages to open in my PC

[woeful pulsar]

yeah alternatively you can sketch f(x) for various k

[alpine sable]

Anyways

Yea u can plug different x and see what graph has those points

But

oh and btw im speaking of the 1st question about graphs

ohhh

yeah I got 1 because I did -6 and -3

idk why they work tho lmao

[alpine sable]

That would take too long

I really ned to finish alg 1 by the end of the month

or else I wont be able to transfe rto a new hs

if the product of a polynomial is 0, one of the factors has to be 0, right?

you got this!

are all products of polynomials 0

ok so, analyzing the zeroes of the graph of a function can be useful since we know that if y=0 it means that one of the factors is 0

so you gotta find what x's makes the function have a 0

in this case

x + 6 = 0

ye so -6

and -3

but idk why it works TBH

alr if we have a polynomial that equals 0

wait