help-27

[winter patrol]

all

easily searchable

there's also a nice summary pinned in #geometry-and-trigonometry

[devout snow]

@hasty wing Has your question been resolved?

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[fluid pagoda]

hi

[fluid pagoda]

is 0*inf an undefined form?

if i get it during the calculation of my limit

[low vault]

yes

[fluid pagoda]

ok thank you

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[ornate jolt]

Bit stuck

[devout snow]

@ornate jolt Has your question been resolved?

[ornate jolt]

<@&286206848099549185>

<@&286206848099549185>

[ornate jolt]

I’m aware on how to solve these I’m just confused why it’s asking me to “show it”

[grim jungle]

Show it means solve

In general, you should be including the work you’ve done and what you’re confused about in your original question. Asking in #discussion isn’t really the place to go either

[ornate jolt]

When I said confused I meant idk how to do it

[grim jungle]

You said you know how here. Showing is the same as finding the angle

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[paper zealot]

how do I go from this

[paper zealot]

to this

I'm mostly confused by that 1

[lusty sapphire]

[2(2+B)]? That doesn't feel right

[paper zealot]

That's an alpha haha

[lusty sapphire]

ohhh

[paper zealot]

[2(a+B)]

[lusty sapphire]

That makes way more sense

Looks like an honest-to-goodness 2

[paper zealot]

Not my handwriting :P

Do you know where that 1 came from?

[lusty sapphire]

If I had to guess, it might be some sin²+cos² shenanigans

I see additions and squares, so my guess is to play with the trig sum and double angle identities.

See if you can work your way to an answer

[paper zealot]

I'm just confused, cause I get where the 2s came from, cause (2(a+b)) / 2 is just (a+b) but where did that one come from

[lusty sapphire]

It's not 2(a+b)/2

It's cos[2(a+b)]

All that divided by 2

division does not distribute from outside to inside of cosine (or any other trig functions)

That is to say, $cos(x/2)!=cos(x)/2$

Argh how do I do LateX on this group

[wooden veldt]

Bot is dead

[paper zealot]

ohw

well then I'm just confused how we got to that then

lmao

[lusty sapphire]

Seems you might need some trig review. You feel comfortable at all with the basics?

Like, what do cos and sin represent? The addition or double angle rules?

Any of that ring any bells?

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[fluid flax]

The difference between the area of ​​a rectangle and the area of ​​a square is 72
cm2. If we know that the length of the rectangle is twice the side of the
square, and the width exceeds it by 3 cm, what are the dimensions of the
two parallelograms?

[devout snow]

Please don't occupy multiple help channels.

[fluid flax]

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[cursive totem]

when solving a system of ode's with complex eigenvalues you can use the solutions corresponding to one of the eigenvalues to get a full solution, why are you allowed to just ignore the other eigenvalue

[cursive totem]

https://tutorial.math.lamar.edu/classes/de/ComplexEigenvalues.aspx

example one here says that we can ignore the solution of the second eigenvalue, but never really explains it

[stone stump]

you could try including it and see that you get nothing new

[cursive totem]

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[humble meteor]

Quick question please

[humble meteor]

i found it 1287

is my answer correct ?

oh nvm, yes it is

.close

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[lusty seal]

I am unsure how to solve the system of equations

I have all the partial derivatives and have 2 points but don't know how to make sure I have all of them

[devout snow]

@lusty seal Has your question been resolved?

[lusty seal]

<@&286206848099549185>

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@lusty seal Has your question been resolved?

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[bitter patrol]

Hey

[bitter patrol]

Is my proof correct

Trying to prove if A is on the perpendicular bisector of BC

Plz ping me when someone helps 😊

[hidden lichen]

Thats correct

[bitter patrol]

really?

@hidden lichen

you sure?

this is an important grade

just wana make sure

[hidden lichen]

wait would x be the perpendicular bisector because a is an angle not an bisector

[bitter patrol]

No A is on the perpendicular bisector

thats what were trying to prove

[hidden lichen]

AX is the perpendicular bisector

[bitter patrol]

yea

[hidden lichen]

yea

[bitter patrol]

so is it correct

[hidden lichen]

yea

[bitter patrol]

you 100% sure?

[hidden lichen]

yes i am

[bitter patrol]

alr thx

apprecite it

[hidden lichen]

np

[bitter patrol]

wait

what grade u in

@hidden lichen

[hidden lichen]

11th

[bitter patrol]

oh

alr

thx

.close

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[rose flower]

hello

[rose flower]

i keep getting letter e wrong

everything else is right

.close

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[cedar schooner]

Hello I have the inequality of picture and I got integer solution for them

[cedar schooner]

what does integer solution mean?

[topaz axle]

both x and y are integer

[cedar schooner]

I expected that answer though these are also the complex roots of said function

but there are other x and y listed as real roots above who are also integers

do these solution have an additional property?

[devout snow]

@cedar schooner Has your question been resolved?

[cedar schooner]

<@&286206848099549185>

[glacial briar]

I’m not sure what he question is anymore. Integer solutions are as frowny said above.

[topaz axle]

yeah, it's not like real solutions have some property besides being real

you're like ok sure we want to know what solutions are real, but who cares about integers

like you don't even need to name this property of real solutions because everyone knows what it is

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[restive river]

https://media.discordapp.net/attachments/1049505747098140754/1049507044455092254/image.png

[restive river]

can someone please explain how -208 goes to -i sqrt 16*13 to 4i sqrt 13

imaginary numbers are killing me

[long kettle]

√(-x) = i√(x) for positive x

So √(-208) = i √208

[restive river]

what about the 4i sqrt 13

[cedar ginkgo]

dio could you help me out in #help-10 after this like 6 people posted in help the second i posted mine

[long kettle]

I don't do requests

And don't advertise your channel in others'

[long kettle]

Notice that 208 = 16 * 13

[restive river]

yes i see trhat

[long kettle]

So √208 = √(16 * 13)

[restive river]

makes sense so far

[long kettle]

= √(16) * √(13)

[restive river]

yes

[restive river]

all you did was separate them right here right?

[long kettle]

Yes

[restive river]

ok yes i got that so far

[long kettle]

Should be straightforward from there

[restive river]

where did they get hte 4 from?

thats the part that is confusing me the most

[long kettle]

√16

[restive river]

whats the reason for doing this tho?

like cant you just leave it to be like

i√208

[long kettle]

No, cuz it'd be i √(208)/4

Which is not simplified

[restive river]

oh your doing that to simplify it?

[long kettle]

Yes

[restive river]

omg tysm

one more thing @long kettle

https://media.discordapp.net/attachments/1030229532671737907/1049510560821166180/C984B387-4F3C-4220-A9B3-67F3DC26E6CD.png?width=961&height=672

where would I go from here?

[long kettle]

What have you tried

[restive river]

tried doing i sqrt 4

but thats not the right answer

i understand the step before this but i dont get the last step

[long kettle]

You can simplify i √(4)

[restive river]

how?

4/1 is 4

[long kettle]

What's √4

[restive river]

2

[long kettle]

So it's (4 ± 2i)/2

Now divide by 2

[restive river]

2 + i

[long kettle]

Tada

[restive river]

ohh I think I get it now

[restive river]

when you simplify 4 tho shouldnt it turn into 2 tho?

since √4 = 2

[long kettle]

Yes

That's why it's 2i

[restive river]

oh and youre adding 4 because of the term on the left

ohh thsi makes sm more sense now

tysm

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[devout snow]

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[astral portal]

what is the formula of cot (a + b)

[hybrid snow]

cot(a+b) = 1/tan(a+b)

[astral portal]

thank you

btw

is this also correct?

cot (a+b) = cos(a+b)/sin(a+b)

nvm i think it is

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[vernal anvil]

stuck on this one

[vernal anvil]

did some long division but not sure where to go after the remainder

[narrow zodiac]

you can start by integrating (x-4)

[vernal anvil]

but that is just the denominator

[narrow zodiac]

https://www.integral-calculator.com/

best site

ever

for integrals

[pliant oracle]

Oh this is that fraction decomposition stuff

[vernal anvil]

right but

the steps they used confuse me

[narrow zodiac]

yeah, they're using a different method in this one. this one is really hard wtf

hmmmm

sry, man I cant help you with this one unfortunately, you can tag helpers ig

[pliant oracle]

I mean just look at this

Really isnt too hard

[vernal anvil]

right

the coefficient collection isnt the problem

its what i do afterwards that i am lost on

[pliant oracle]

Oh so you solve for A and B then you solve the individual integrals

A/(x+3) + B/(x+1) in your case

[vernal anvil]

yup

got that part

give me one second

[pliant oracle]

Individual integrals will be easy

[vernal anvil]

so i got

a=9

b=4?

[pliant oracle]

Oh i see where youre getting hung up on now

Gimme a sec

[vernal anvil]

how does this look

[pliant oracle]

Yeah its 9 and 4

Dont forget + C

[vernal anvil]

right

.close

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[meager skiff]

why did my teacher use instantaneous rate of change formula for this question

[meager skiff]

<@&286206848099549185>

[devout snow]

@meager skiff Has your question been resolved?

[inland kiln]

what do the other 4 questions before say

pts A-D

[inland kiln]

i see

so the question is asking whether the speed at which he hits the water is greater or less than 58 m/s, so in order to answer it, you must find the velocity when he hits the water. You know he hits the water at 3 seconds, and you know his velocity is the rate of change of his height, so you must find the instantaneous rate of change of his height at 3 seconds.

[meager skiff]

wait how do we know the velocity is the rate of change of his height lol

[inland kiln]

rate of change is the same as slope. A height graph will have a Y value of his height (in meters) and an X value of time (in seconds). So the slope/rate of change is meters per second or in other words, his velocity

[meager skiff]

oh right

got it

thx

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[cedar ginkgo]

can someone tell me if my array is correct (this is to show the probability of two dice being rolled simulatenously)

[inland kiln]

It is

[cedar ginkgo]

cool thanks

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[neon patio]

Is this not correct

[devout snow]

Please don't occupy multiple help channels.

[neon patio]

I plugged in every and rounded and it still said I was wrong

[pale hearth]

#❓how-to-get-help

[neon patio]

Done

.close

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[smoky gyro]

why does the graph of y=cosx + 1 begin at point 2

and not 1

[lone ravine]

Normal cos x is already 1 for x = 0

[smoky gyro]

ah i see

alright thanks

that was a super fast reply btw haha

and also

im not sure what this one quite does, i mean i can see the obvious change of the sine graph but

y = sin(x + pi/2)

what actually happened

why did it turn into a cos graph

[lone ravine]

The +π/2 moves the sin function π/2 units to the left making it cos x

[smoky gyro]

Ohhhhhhhh

yeah that makes sense

[lone ravine]

There are more rigorous ways of explaining that, but that's the easiest one

[devout snow]

@smoky gyro Has your question been resolved?

[devout snow]

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[scenic flax]

hi guys, i would like to get some help with this exercise

[twilit blade]

sanest notation\
so your task is?\
find $i_h$?

[woven radish]

Zabbx

[scarlet sequoia]

I guess finding i1 and v7

[scenic flax]

oh sorry yeah

i have to find i1 and v7

i already tried doing the Requivalent but i dont know how to go on

[twilit blade]

note all parallels

I don't know how you exercised it, but its generally best to rewrite the graph to show all parallelisms better

[scenic flax]

and i did it

and it turns like 29/23 ohm in parallel 1V in parallel 1ohm

are you graphing it in your mind?

and then what? how could i find the i1 and v7 now?

<@&286206848099549185>

[devout snow]

@scenic flax Has your question been resolved?

[devout snow]

@scenic flax Has your question been resolved?

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[mortal rivet]

I need something that gets smaller based on how big it is but not proportionally. Like I have 16 and I want it getting smaller every time by a half. So 16, 8, 4, 2, 1... But this is too much for Me I want, for example if it is 16, then get smaller by 1,5, if it is 2, I want is smaller by 2,5, but the amount gets reduced is still bigger as the base number is.

[mortal rivet]

I am doing this in programming. Currently it is: number=number/2.

I need help.

[devout snow]

@mortal rivet Has your question been resolved?

[mortal rivet]

How is this possible?

Shuldn't it get smaller!?

[restive river]

It is??

You're not very clear

[mortal rivet]

?

My message dissappeared, good.

It is not 6.

It should be far smaller that this.

It gets bigger.

It is not possible.

[restive river]

Dude

You took 6.8*10^(-4) and divided it by something >1

You get 6.79*10^(-4)

6.79 * 10^(-4) < 6.8 * 10^(-4)

It's smaller

[mortal rivet]

What even is that?

Look the number it shows Me, it is not correct.

[restive river]

Ho you cannot read the calculator maybe?

[mortal rivet]

I don't know, ignore the calculator, it is not what I need.

Yeah man, that seems good!

[restive river]

Yeah what's your problem exactly

[mortal rivet]

Well, I can not calculate it by head but definitely a bit smaller that 0,00068, what is exactly what I would expect.
I do not know how to better explain what I want, just to have number getting smaller in a speciffic way.

I can not send you My thoughts, try understanding what I have wroten, try asking Me which part you do not understand.

[restive river]

Well i don't think i can help

[mortal rivet]

It is okay.

[mortal rivet]

How nobody knows this? This seems very simple.

[devout snow]

@mortal rivet Has your question been resolved?

[mortal rivet]

No man, I can not do this alone, I am good waiting.

[mortal rivet]

I am not out of ideas yet.

I found something. It is not great but.

.close

[devout snow]

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[restive river]

How do I understand $\sum$ symbol?

[woven radish]

yuul

[sharp axle]

This symbol is pretty simple

It has 3 parts, the bottom, the top, and the parts in front of it

The bottom tells you where to start summing

The top tells you where to end summing

And the front tells you what sequence you're summing

[restive river]

I don't get it

Then what does

[long kettle]

#❓how-to-get-help

[restive river]

What does this mean $$\sum_{j=0}^{n-1} x^j = \frac{x^n-1}{x-1}$$

[woven radish]

yuul

[sharp axle]

This means "the sum of the sequence x^j from j = 0 till j = n-1 has the same value as xⁿ..." You get the rest

[restive river]

So we're saying left side = right side

[sharp axle]

Yeah

[restive river]

$$\sum_{i=0}^{n} i = 0 + 1 + \cdots + n$$ Does this make sense then?

[sharp axle]

No

Because you're saying to start at i=0

There's no i in (n)

[woven radish]

yuul

[restive river]

So like this?

[sharp axle]

Yes

This does make sense

[restive river]

not to me

it does not make sense

[sharp axle]

I think the weird part might be the fact that i has multiple values in the expansion

i = 0, i = 1, i = 2, ... i = n

And you're adding all those values

[restive river]

I see it as an interval [i, n]

But the boundary is not the issue, it's the i next to the sigma and the right hand side representation that confuses me

How about like

$\sum_{i=0}^{n} \frac{\phi^i + 1}{n + \sqrt{2}}$

[woven radish]

yuul

[restive river]

what is this saying like, I should choose an "n"?

So for n = 2, I hvae like

$\sum_{i=0}^{n} \frac{\phi^i + 1}{n + \sqrt{2}} = \frac{\phi^0 + 1}{2 + \sqrt{2}} + \frac{\phi^1 + 1}{2 + \sqrt{2}} + \frac{\phi^2 + 1}{2 + \sqrt{2}}$ for $n = 2$ ?

[woven radish]

yuul

[sharp axle]

Yeah you do choose an n (an arbitrary limit on where to stop summing)

And yes that expansion is correct

[restive river]

This is just too confusing, I will just skip this chapter I'll go back to trig

[sharp axle]

You seem to know how to expand things that are already there

Do you also know how to construct some sums on your own?

Like if I told you "write the sum of the 1st 5 odd numbers starting from 1"

Can you write the correct sigma representation?

[restive river]

Probably, but the notation is just too stupid for me to understand more complex summations

like when we see stuff like n(n +1)/2

[sharp axle]

$n=4, \sum_{i=0}^{n} 2i+1$

[restive river]

I get that it's basically just a for-loop but the mathematical notation is just so confusing it looks alien

yeah what is this saying?

[woven radish]

jafar/جعفر

[sharp axle]

If I write it in pseudo code or c++ code would it be more understandable?

[restive river]

No, I would understand the code but not the mathematical notation

It doesn't translate two ways

for me

You can write a complex for-loop for me I would get it easily, but when you write it with sigma I'm lost

[sharp axle]

Well why not? Why is the notation not understandable?

[restive river]

I don't know

Can't connect the dots

[sharp axle]

for (i=0; i≤4; i++)
{
sum += 2i+1;
}

This is the equivalent for loop

See where the 4 lies?

[restive river]

Is there an artist in this server than can draw sum vs for loop

[sharp axle]

See where the front lies?

I think you should probably go in #discussion, maybe

[restive river]

yeah sorry

.close

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[devout snow]

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[blazing edge]

Hello, i could really use some help understanding this proof, especially how you get the second b,

[blazing edge]

i have used laplace expansion

[devout snow]

@blazing edge Has your question been resolved?

[blazing edge]

.helpers

<@&286206848099549185>

[devout snow]

@blazing edge Has your question been resolved?

[blazing edge]

.helpers

<@&286206848099549185>

<@&286206848099549185>

.close

[devout snow]

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[blazing edge]

Hello i would like understanding this proof

and how i ge thte second b

.close

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[fossil moth]

can someone help explain to me how to get the algebraic and geometric multiplicity?

[fossil moth]

lets say for this example

[pliant oracle]

Algebraic multiplicity is how many times a root of characteristic poly is repeated

Geometric is dimension of eigenspace

[fossil moth]

so with that question, we get lambda values of 3 and 4 but the alg multiplicity is 1

[pliant oracle]

Yes

[fossil moth]

what does it mean that it is repeated

like it has two eigen values but they are repeated(???) which gives alg multi of 1

im stuck on that part

[pliant oracle]

Yeah so if i were to get lambda1= 1 lambda2= 1 then the eigenvalue 1 has an algebraic mult of 2

Its like having a double root

[fossil moth]

so if each lambda value is different then you get 1? if you have 2 lambda values that are the same then you get 2?

[pliant oracle]

Yes

[fossil moth]

like (lamda - 2)^2 would give alg multi of 2?

[pliant oracle]

Yes

Obviously it has to equal something

It has to be with respect to the lambda value

[fossil moth]

yea

alright that makes much more sense

[pliant oracle]

Lmk if you get stuck on geometric mult

You just have to plug eigenvalues into the diagonal of original matrix and solve for coefficients

[fossil moth]

alright, thank you for the help

[fossil moth]

.close

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[pliant oracle]

Like the bottom part here

Depends on how you did characteristic poly

.close

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[restive river]

A woman stands on the scale, while pulling herself up slightly on the rope so that not all of her weight is on the scale. If the scale reads 451 N,what is the tension in the rope?

[restive river]

Draw a freebody diagram @restive river

[zenith jacinth]

#❓how-to-get-help

[restive river]

.close

[devout snow]

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[restive river]

You already sent that question in another channel that wasn't yours and pinged someone unnecessarily. Read up on the rules

[ocean palm]

Hello

I have a question

What is the equation of line D?

[restive river]

make ur own channel

[ocean palm]

I can do that?

[restive river]

#❓how-to-get-help

[devout snow]

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[restive river]

What have you tried

[twin gorge]

i am little confuse for trying it with sin

like x = sinx

[restive river]

What. Why are we talking about sin

[twin gorge]

I thought i can convert it into cosx^3

[restive river]

cant u use ftc and find the derivative of the integral

set that = 0 to find critical points

[twin gorge]

what is ftc

[restive river]

Yes. That's my thinking too I believe

this stuff

[restive river]

Fundamental theorem of calculus

[restive river]

You don't have to integrate

[twin gorge]

like this

i just need to add values

and then i get f'(x) and putting as zero i can find critical points?

is ittrue

[restive river]

Oh wow, you managed to make your life considerably harder on yourself for doing all of that

I suppose it's good practice..

But yeah it's right

[twin gorge]

ok thanks

[slender mirage]

it's right? which part is?... their derivative expression is: 3/2 [1 - s²]^{1/2}

[restive river]

Their evaluation of the critical points. Their steps for the integration seem to be confusing

[slender mirage]

it'll be tough to decide on the convexity/min-max with that (incorrect) expression

[restive river]

Yeah sorry, I didn't really double check their method. My bad

[slender mirage]

oh don't be! mistakes happen :D

[restive river]

Although seemingly their answer for the critical points still match when it is wrong. Finding the concavity and other stuff sure will be interesting tho, with that method

[devout snow]

@twin gorge Has your question been resolved?

[devout snow]

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[fallow wren]

Hey

[fallow wren]

Need help with this integration question

I can integrate it twice to get the y equation which will be y= x^3 -2x^2 +c

But idk where to go from there

<@&286206848099549185>

[upper schooner]

I think you need two constants if you’ve integrated twice?

[upper schooner]

Can you show the steps you did please?

[fallow wren]

Aight one sec

I crossed it out lemme do it again

[upper schooner]

No worries, just reply to one of my messages/@ me once you’ve sent it 😇

[fallow wren]

@upper schooner

[upper schooner]

Ah, note that c integrates to cx, and for the integration of dy/dx, it’s a good idea to make the constant you get there a different letter, say d

[fallow wren]

Oooo ur right

[upper schooner]

Nice nice! Now when you do that, let’s see what you have

[fallow wren]

• x^3 -2x^2 +CX +d

How would I find both c and d

[upper schooner]

Yep, that’s y= that

[fallow wren]

Yea

[upper schooner]

My lazy crystal ball 🔮 says to keep dy/dx in terms of c somewhere visible, as we worked that out earlier

Now, saying you have a minimum at (-2,-6) is really telling you two things at once, yea?

[fallow wren]

So i would sub in x into the dy/dx eqn. And equate to 0 since gradient is 0?

[upper schooner]

Yep, substitute the x value they give you and that’s zero, which should find you one of the constants

[fallow wren]

Yess

@upper schooner hey i got the right answer now tysm for the help but could you also help me out with another similar question?

[upper schooner]

Sure send it up!

[fallow wren]

2nd qn.

[upper schooner]

Ah cool cool, what have you tried so far with it?

[fallow wren]

Finding gradient using y2-y1/x2-x1 then subbing that into dy/dx to find k

Then integrating and subbing into the y eqn. one of the two coordinates they gave to find c

[upper schooner]

😱 that’s very naughty to do

Don’t do that 😂

[fallow wren]

Ayo??

Why not 💀

[upper schooner]

Let me draw something out, give me a sec

[fallow wren]

Alrr

[upper schooner]

Pictures are worth a thousand words

Let this be some graph which I’m too lazy to give an equation for

[fallow wren]

Uh huh

[upper schooner]

The gradient between the two points isn’t really useful in telling you the gradient at either point

[fallow wren]

Ah

That's what Y2-Y1 does?

Finds the gradient between?

[upper schooner]

If you did equate the gradient to dy/dx you’d get an equation in terms of k

Mind you, there’s someone who can explain that better than me, but for now, just take my word for it

[upper schooner]

Gives you the gradient between the first point and the second

[fallow wren]

Ah

[upper schooner]

But anyways, you have dy/dx=…something

[fallow wren]

Yea

[upper schooner]

You can integrate that to find an equation for y in terms of that k and an integration constant, say c

[fallow wren]

Yep

[upper schooner]

You have two points on the graph, which should give you simultaneous equations to find them

[fallow wren]

Oh god

[upper schooner]

Easy peesy lemon squeezy 🍋

[fallow wren]

Forgot how to do simultaneous 💀

[upper schooner]

Ah, if you want, you can form those simultaneous equations and we can do them together?

[fallow wren]

Sure

So first i just make 2 eqns by subbing in both coordinates on both rhs and LHS?

[upper schooner]

Yep yep!

[fallow wren]

Alright done

Oops I misplaced y

[upper schooner]

Yep yep, now e.g. we can simplify the LHS a bit more?

[fallow wren]

I made it -1/6k +c and 1/3k+c idk if it's right

[upper schooner]

That’s a bit easier to work with, or at least visualise what to do imo

Of course don’t forget what they’re equal to!

[fallow wren]

Yup yup

Do i subtract the bottom and top so it becomes -3/6 =1.5

-2k =1.5

[upper schooner]

Hmm, shouldn’t that give you something slightly different

[fallow wren]

-1/6 - 1/3, no?

[upper schooner]

Assuming you're doing $\left(-\frac{1}{6}k + c = 2.5\right)$ - $\left(-\frac{1}{3}k + c = 1\right)$

[fallow wren]

Yea

[woven radish]

chartbit

[upper schooner]

Oh no ignore me!

[fallow wren]

Oh

[upper schooner]

I'm being slow

Give me a second

[fallow wren]

Lmao we all have our days

Aight

[upper schooner]

This should be $\left(-\frac{1}{6}k + c = 2.5\right)$ - $\left(\frac{1}{3}k + c = 1\right)$

[woven radish]

chartbit

[upper schooner]

My bad, sorry!

[upper schooner]

Amen to that, didn't read the points properly on my side!

[fallow wren]

It's alright

[fallow wren]

Yea

[upper schooner]

In any case, you can find k like that 😂

Then from there find c

[fallow wren]

So -2/3k = 1.5 right 😭

Could you do a massive favour by writing down the steps of the simentanous eqn and sending a picture pls 🙏

[upper schooner]

Hmm I get $-\frac{1}{2}k = 1.5$

[woven radish]

chartbit

[upper schooner]

From $-\frac{1}{6}k - \frac{1}{3}k$

[woven radish]

chartbit

[fallow wren]

Oh god I'm stupid asf

Right my bad

Idk how tf i got -2/3

Ty man i got it now

[upper schooner]

Mind you, I always make the same mistakes even up to this point 😂

I'm not much better on that front

[upper schooner]

No worries!

[fallow wren]

Lmaoo

[fallow wren]

🙏

.close

[upper schooner]

Assuming you don't need these any more? Generally my working out is messy and I tend to verbalise what I'm doing usually

[devout snow]

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[devout snow]

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[tame dagger]

I need help with simplifying complex rational expressions. I get the process but I keep getting mixed up with negative and positive signs so I just need walked through a question

[tame dagger]

This is an example of one of my questions

[honest aurora]

$\frac{-\frac{3}{y}-\frac{6}{x}}{2x}=-\frac{\frac{3}{y}}{2x}-\frac{\frac{6}{x}}{2x}=-\frac{3}{2xy}-\frac{6}{2x^2}$

actually let me add a middle step there

[woven radish]

Duh Hello

[honest aurora]

notice that the denominators of the expressions in the numerator essentially just jump down to the denominator

[tame dagger]

Ok let me try that by myself real quick so see if I actually get it

[honest aurora]

for a simpler example. lets say we divide 1.5 by 2, we then have $$\frac{1.5}{2}=\frac{\frac{3}{2}}{2}=\frac{3}{2\cdot 2}=0.75$$

[woven radish]

Duh Hello

[tame dagger]

This is the explanation I was given but it doesn't make any sense

[honest aurora]

that is just 1 more step after what i gave, but an alternate way of doing it. since you didnt post exactly what the question is i couldnt really tell what the question was asking. it seems they want it as one fraction with no fractions in the numerator

what they did was multiply the top and bottom by the least common multiple of the denominators

what i did was split them into two fractions and then find the least common multiple of those two denominators (which would have been the next step)

$\frac{-\frac{3}{y}-\frac{6}{x}}{2x}=-\frac{\frac{3}{y}}{2x}-\frac{\frac{6}{x}}{2x}=-\frac{3}{2xy}-\frac{6}{2x^2}=-\frac{3x}{2x^2y}-\frac{6y}{2x^2y}=-\frac{3x+6y}{2x^2y}$

[woven radish]

Duh Hello

[tame dagger]

Ok that makes sense let me try it one more time

I think I got it ☺️

.close

[devout snow]

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[tame dagger]

Thank you!!

[devout snow]

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[clear bronze]

can someone explain to me what this M=business is

[pastel pasture]

You have been given an expression M

In terms of two variables

And you need to find values for those variables such that the conditions are satisfied

[devout snow]

@clear bronze Has your question been resolved?

[devout snow]

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[restive river]

And how can u represent an equati

[devout snow]

Please don't occupy multiple help channels.

[restive river]

Nobodys helping me aint my fault

[pliant oracle]

your question doesnt really make sense

like 5000-400=460??

is probably why nobody is helping

and we dont understand how ownership works without definition

but if youre asking for what percentage of the company they have shares in, it seems like you have it figured out

you just forgot to multiply the decimal by 100

[restive river]

No

[restive river]

Tats all I needed to no, tn

Thx

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[iron pier]

im looking for help on how to understand this and do it please there are also formulas at the very end please help if you can <@&286206848099549185>

[oblique birch]

Hi @iron pier

I'll do my best to help!

[iron pier]

Hello thank you so much

[oblique birch]

No problem, but I do apologize in advance for late replies.

Which question did you need help on?

[midnight dirge]

a pdf :0

[iron pier]

practically all but number 1 is more important

[oblique birch]

Ok.

Let me get my textbook real quick.

[iron pier]

alright

[oblique birch]

Sorry, I'm new to learning about gradient functions, so this may be a bit difficult to explain.

[iron pier]

I'm also new to so its okay

[oblique birch]

Hmm...you have a lot of formulas at the bottom, I'm just trying to figure out which one I'm supposed to use...I honestly kind of suck at this..

[iron pier]

okay so for number 1 i thinks its the first formula at the top so like f(x) = f'(x)

[oblique birch]

I would ask another helper about this, I'm undergraduate..

[iron pier]

okay thanks!

[devout snow]

@iron pier Has your question been resolved?

[midnight dirge]

lol

mayb post an image

idw to dl a pdf

[iron pier]

oh ok

[restive river]

isnt the gradient of a one variable function just a regular derivative?

[dire quartz]

yes yes it is

[restive river]

ah

[dire quartz]

the first one is 12e^3x-7/2x^2 -5

im not sure about the second one.

[restive river]

okay since those are one variable functions, taking the gradient function of them is just taking a regular derivative

do u know how to differentiate @iron pier?

[iron pier]

tbh no

kinda

so like B) should be some like pie cos piex

how would i go about this

[devout snow]

@iron pier Has your question been resolved?

[lilac portal]

Should you derive this first?

and then substitute it with pi

using the chain rule, cos(3x)
cos(u) = -sin(u)

[devout snow]

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[scenic surge]

Suppose a migrating bird flies at a constant altitude of 5 km, with a velocity of 42 km/h. At time t= 0
the bird passes directly above a radar station, where tis measured in hours.

How fast is the distance between the bird and the radar station changing after 10 minutes? Round your
final answer to 2 decimal places and provide units.

[scenic surge]

Im so confusedddd

How do I even find the equation

for this equationn

[devout snow]

@scenic surge Has your question been resolved?

[torn crane]

I'd love to help but that question seems to have some problem with grammar/words and feels imprecise

[scenic surge]

U think so?

Ive been stuck on it

[torn crane]

can you fix "where tis measured in hours"

what is measured

[scenic surge]

where t is measured in hours

shit

[vital patrol]

its just a case of related rates no?

altitude = 5km, distance travelled = x. distance between bird and radar = sqrt(25+x^2). derivative of the distance(bird-radar) = 2xdx/2sqrt(25+x^2)

$L=\sqrt(25+x^2)$

[woven radish]

metalbubble

[scenic surge]

oh wait

Oh shit

nvm

[vital patrol]

$dL=\frac{xdx}{\sqrt{25+x^2}}$

[scenic surge]

ty

[woven radish]

metalbubble

[vital patrol]

yw

[scenic surge]

I remember now

I got it

.close

[devout snow]

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[devout snow]

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[surreal dirge]

Hi!

[devout snow]

Please don't occupy multiple help channels.

[surreal dirge]

can anyone help me on comparing fractions?

[uncut crow]

someone probably can, just post the question 🙂

[surreal dirge]

This is the question!

anyone?

[merry flicker]

yellow region looks half of the circle

and the orange region looks half of the other circle as well

so maybe "="

[restive river]

Yea its jsut half a circle but ones split into two other split into three both still equal a half

[surreal dirge]

so is it equal?

[restive river]

yes both are a 1/2

do you know how to simplify

2/4 is the one on the left 3/6 is the one on the right both simplify into 1/2

making them =

[surreal dirge]

what grade r u in?

[restive river]

first year of college

[surreal dirge]

freshman college?

[restive river]

ye

[surreal dirge]

ohh

[restive river]

Try the next one on your own

[surreal dirge]

k

[restive river]

and reply the answer you think it is

[surreal dirge]

k

[restive river]

did you get an answer
?

[surreal dirge]

yea

this is what I got.

[vital patrol]

noo so close

[surreal dirge]

ohhh

I can explain whyyy

[restive river]

The pictures a bit weird but it depends on how you explain it

so whats your explanation to your answer ?

[surreal dirge]

Look at those lines

[restive river]

thats the right answer but why, do you know ?

[surreal dirge]

wdym why do I know?

[restive river]

Let me rephrase it do you know why thats the right answer ?

[surreal dirge]

which one?

[restive river]

this one

[surreal dirge]

This?

[restive river]

yes

[surreal dirge]

oh yeah

so basically I multiplied it depending on what fraction it is depending on what number it is I was multiplying it to see if it was equal but it was not and so when I multiplied it with the numbers that it makes I got this fraction.

does that make sense?

that’s what my teacher told me to do when comparing numbers.

[restive river]

You can also tell from looking at the picture do you see how the blue one takes up more of the circle vs the green one?

[surreal dirge]

yeppp

[restive river]

good job im going to finish up my homework now but if you have more questions im sure someone else will be able to help you have a good one.

[surreal dirge]

tyyy

I figured it out.

[devout snow]

@surreal dirge Has your question been resolved?

[devout snow]

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[short bone]

Ain't sure if it belongs here, but is there a way i can calculate 16^(2/5) without calci

[pliant oracle]

yes

but its ugly

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[tribal lava]

how to solve this?

[carmine aspen]

substitute x with 180

or post the full question

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[gentle lotus]

i understand how to get the answer

but if it's a frictionless table then what is causing it to not speed up indefinitely

[restive river]

the spring causes the acceleration

and once it leaves the spring, theres no more acceleration

[gentle lotus]

oh im brain damaged i understand now

thx

.close

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[pulsar ermine]

I’m struggling to understand the difference between probability mass function and probability measure

[pulsar ermine]

Is the probability mass function more general as it applies to random variables aswell

[polar bolt]

What?

Probability measure is way more general

[pulsar ermine]

Do you mind elaborating a bit?

[polar bolt]

If $X$ is a set and $\Sigma$ is a $\sigma$-algebra over $X$ then a set function $\mu$ from $\Sigma$ to the extended reals is called a measure if it satisfies that its non-negative, measure of empty set is 0 and countable additivity is a measure. A probability measure is just a measure where $\mu(X)=1$.

This is much more general than PMF/PDF

[woven radish]

ScapeProf

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[rapid ridge]

hi

[sweet zinc]

did you draw the fun function y=x^3

[rapid ridge]

yes

[sweet zinc]

about the x-axis

now

[rapid ridge]

so its 3 to 0

[sweet zinc]

what is method of cylinder

[rapid ridge]

is this it

and the answer is also that pi

ok the answer 891/4 pi is wrong

i used that to set it up in my calc ^^

so how do

like wherd i go wrong

[devout snow]

@rapid ridge Has your question been resolved?

[rapid ridge]

<@&286206848099549185>

[rapid ridge]

.close

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[verbal crane]

To disprove that the Union of two sub spaces is not a subspace

[verbal crane]

Can I just say that if you add one element from U and one from V (the two sub spaces) there is nothing that guarantees the addition to being apart of the Union

As the subspace closure of addition only applies to the same subspace

[restive river]

yes, and you should find an explicit counter example

[verbal crane]

But if I dont

That’s not proof enough

Right

[restive river]

yeah, because the union of the zero subspace with a subspace is still a subspace

so its sometimes true

[verbal crane]

Also the question states that “prove (what I said above) is not nessecarily true”

So technically I proved THIS statement

[restive river]

saying "nothing guarantees" is not a proof

[verbal crane]

Okay I see thanks for the help

.close

[devout snow]

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[stone stump]

.reopen

[devout snow]

✅

[stone stump]

you can try proving that UuW is a subspace iff U subset W or W subset U

@verbal crane

.close

[devout snow]

Channel closed

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[restive river]

Interesting. When you reopen it it is under their name still

Noted

[stone stump]

why should it be under another name

it hadn't even fully closed yet

it's still their channel

[restive river]

.hmmm so if you keep reopening some else's thread, you can stop them from opening new threads

[restive river]

Because you are the one reopening it, not them technically

[restive river]

Oh yeah that's a good idea

Instead of people like closing and opening

Reopen the same channel

But idk if that flies well with the mods of the server

.reopen

[devout snow]

✅

[restive river]

Okay this was just a test

.close

[devout snow]

Channel closed

Closed by @reef sable

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[verbal crane]

Thanks for the help, just saw it now

.close

[devout snow]

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[buoyant escarp]

How to solve 8?

[buoyant escarp]

27^2x =9^9
Original problem ^

I just need an example

[jaunty stream]

im on it

@buoyant escarp

[buoyant escarp]

Oh ok! Thanks!! :D

So basically x is just simplify it to -

[jaunty stream]

yep. find the value of the variable

[buoyant escarp]

Many thanks!

.close

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[covert knot]

how do i solve this question

[devout snow]

@covert knot Has your question been resolved?

[restive river]

How many numbers from 1 to 40 are multiples of 4 or 5

[devout snow]

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[buoyant ibex]

hello i have this 2 functions 1 is f'(x) and 2 is the f(x) and its defined in 4>=x>= -1

[buoyant ibex]

and g(x) = ln(f(x))

i have to find asymptotes for g(X)

and i need help with that im not sure how to done it

[devout snow]

@buoyant ibex Has your question been resolved?

[devout snow]

@buoyant ibex Has your question been resolved?

[buoyant ibex]

help xd ?

!close

.close

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[hybrid snow]

!15m

[devout snow]

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

[hybrid snow]

The graph gives you those calues

Know the significance of m and c

[devout snow]

Channel closed

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[restive river]

.close

.solved

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[pure socket]

How could I solve the following equation: 4096= 1/16 * 2^(n-1) specifically how do I deal with the 1/16

[torn crane]

1/16 = 2^(-4)

@pure socket

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[sage kernel]

Did i find p correctly?

[sage kernel]

This is the problem

[devout snow]

@sage kernel Has your question been resolved?