help-23

[rapid raptor]

im sry

I suck at word problems like these

[halcyon carbon]

Their ages in terms of x

After 22 years

It was x+6 and y+6 after 6 years

[rapid raptor]

x + 22 = y - 3/5

eh

no

[halcyon carbon]

Forget about the 3/5 for now

[rapid raptor]

mk

[halcyon carbon]

so their ages are x+22 and y+22

Agreed?

[rapid raptor]

agreed

[halcyon carbon]

Then the question says

Lincoln age (y+22) is 3/5 of Anna age (x+22) after 22 years

[rapid raptor]

rq question

is it possible

for the equation to have subtraction or no

[halcyon carbon]

It is possible in general but not in this equation

[rapid raptor]

y + 22 = 3/5 + x(22)

[halcyon carbon]

As a general tip is translates to = and of translates to multiply

[rapid raptor]

mhm

[halcyon carbon]

Almost

[rapid raptor]

god christ have mercy

[halcyon carbon]

Why 22x ?

[rapid raptor]

I have no idea

I put it in

as because the 3/6 might change it

some how

because

when it comes down to solving it

wouldnt you need too have one variable and be able to isolate it or sumthing like dat

idek

[halcyon carbon]

I mean you’re almost there

The equation would be

$y+22 = \frac{3}{5} \times (x+22)$

[flat frigate]

Pure

[rapid raptor]

god

thank you

for helping

I believe I can solve it now

[halcyon carbon]

Np

Good good

Well you have a good day

[rapid raptor]

u too

.close

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[lean cipher]

I can’t find a solution for this

[rapid raptor]

wouldnt you need to find the common denominator of both to solve?

than distribute them on top?

Im not sure though im not a tutor

[lean cipher]

In photo math is write me

But in a book

[rapid raptor]

wth

ye I dont understand that problem

<@&286206848099549185>

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[halcyon carbon]

Trying to find I is this the right way to approach this?

[halcyon carbon]

Not sure what to do from here

Could use power series

Got this

Again stuck

[safe radish]

@halcyon carbon Has your question been resolved?

[arctic locust]

Put it between -pi/2 and pi/2

You'll get an odd function in theory

If not let me look at it

[halcyon carbon]

What do you mean put between that

Like change the bounds?

[arctic locust]

Yup

[halcyon carbon]

Why can I just change it?

[arctic locust]

Oh I misread

[safe radish]

@halcyon carbon Has your question been resolved?

[safe radish]

@halcyon carbon Has your question been resolved?

[safe radish]

@halcyon carbon Has your question been resolved?

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[obsidian oxide]

i've done a) but i don't understand b

[quasi bison]

part a gives you recipe for finding a vector orthogonal to a given vector

apply it in part b

[obsidian oxide]

i have to do a dot product?

[quasi bison]

you have to not overthink this

in part a you proved this:
given a vector (a,b), the vector (-b,a) is orthogonal to it.

so now replace a and b with values that give you what you want in part (b)

[obsidian oxide]

so basically v=(2,-3) & w=(3,2)

?

[golden crow]

Looks good to me

[obsidian oxide]

cant you just do v=(2,-3) & w=(0,0)?

[golden crow]

uhh I don't think so

don't quote me on that

[obsidian oxide]

its all good

i found it

[golden crow]

I think zero vectors are special iirc

[obsidian oxide]

v=(2,-3) & w=(6,4)?

[golden crow]

yes

[obsidian oxide]

thank you

[obsidian oxide]

how do i find the unit vectors for c

[golden crow]

use the formula to find unit vectors: u = V/ | |V| |

ok well that didn't work

[obsidian oxide]

oh ok but i know what you meant

[golden crow]

there we go

[obsidian oxide]

so i would just plug v=(2,-3) in there

[golden crow]

yes

u = <2,-3>/| | <2,3> | |

[obsidian oxide]

but this doesn't give me something orthogonal to the vector given

do i just come up with numbers

[golden crow]

uh

try taking the unit vectors of the orthogonal vectors of v

idk though

[obsidian oxide]

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[simple rose]

question: At what point(s) on 4x^2+3y^2 = 10 does the tangent line have a slope of 1?
i implicitly differentiated the equation and found that dy/dx is -3y/4x, but idk how to find the points on the original curve with that

[sudden forum]

right, so

I just helped someone with a similar question

so, since slope of that curve is -3y/4x

we equate it with 1, since thats what the question asks

then we get 1=-3y/4x

from here we can get value of x, and substitute it in the equation of curve

thereby getting some values of x, and corresponding values of y

done

[simple rose]

OHH

thx so much

[sudden forum]

or you can go for hit and trial on 1=-3x/4y, but it'll be ugly

[sudden forum]

np!

[simple rose]

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[full wind]

A+B = 3
A - C = 1
B + C = 2

NEED VALUES OF A B C

[sonic spruce]

have you tried anything so far?

[safe radish]

@full wind Has your question been resolved?

[full wind]

I did but didn't came up with anything

[lean otter]

Okay so basically

A + B = 3

Make A be the only term on the left side

[full wind]

Okay

[lean otter]

How would you do that?

[full wind]

A = 3 - B

Heyo

[lean otter]

Right

So substitute the A in the second equation

What do you have now

[full wind]

(3-B)-C = 1

[lean otter]

Amazing now

Add this new equation you got with the third equation

[full wind]

Alr

(3-B)-C = 1
(0+B)+C = 2

Maybe

[lean otter]

Ah nah, the variable would just cancel, I mistook it in my mind

That's fine though

[full wind]

Mhm

Next

..

@lean otter

[lean otter]

Yeah give me a second to get on my pc

[full wind]

K

[lean otter]

I figured the answer would be A = 3 B = 0 C = 2 intuitively

Just have to write out the process better

[full wind]

Yes

I would be better to see through

If u could provide the process

Did u figured out that

[lean otter]

just got on

[full wind]

Awesome

[lean otter]

Oh okay i see

i don't think you can get a singular solution

i think this has infinite amounts of solutions

[full wind]

Well my friend already answered it

[lean otter]

it just has to satisfies the equations A = C + 1, B = -C +1

[full wind]

A+B = 3
A - C = 1
B + C = 2

Solve 2nd and 3rd equations for A and B

A+B = 3
A = 1 + C
B = 2 - C

Substitute them into the first equation

(1 + C) + (2 - C) = 3

Solve for C
C = 0
Then just sub that into the rest

[lean otter]

can't be infinitely many solutions i suppose

[lean otter]

you would still be getting 3 = 3

[full wind]

Okay

Yes

3 = 3 will be 0 and c - c will be canceled out so there is no logic and no C

Right

[stray bluff]

there is not one set of solutions

[lean otter]

Again, that doesn't change anything, this systems of equations can be satisfied with A = C+1, B = -C+A

[stray bluff]

is the question asking for a set of solutions ?

or all sets ?

[full wind]

It's a question from partial fractions

[stray bluff]

can u show the question ?

[full wind]

Sure

[lean otter]

yeah that would be better

[stray bluff]

partial fraction decomposition ?

[full wind]

Yes

[stray bluff]

kk

is the issue ur denominator is like (x+1)^2?

or something to that effect

[full wind]

2x + 1/(x - 1)(x² + 1)

[lean otter]

wouldn't that be A/(x-1) + Bx+C/x^2+1?

if you are decompsing it

[full wind]

Yeah

Could be

[lean otter]

this means you have 2x+1 = A(x^2+1) + Bx+C(x-1) to deal with here

[stray bluff]

^^^

[full wind]

Absolutely

[lean otter]

try setting x as numbers that would make one side 0

for example, x = 1 would eradicate the right linear term

you would have 3 = 2(A)

i think that should tell you what A is, right?

[full wind]

And x = -1/2

[stray bluff]

you just setup your fractions wrong and got infinite solutions

[full wind]

Yeah maybe try this way

[lean otter]

ah wait you would still have the Bx

let see

[full wind]

Lol I just took x common and did it that way

[stray bluff]

huh

[lean otter]

oh okay so I see where you got your equations from

[stray bluff]

how ?

[lean otter]

haha nvm, forgot the brackets

[full wind]

Like x²(A + B) + x(B - C)

[full wind]

Yeah

[stray bluff]

2x+1 = A(x^2+1) + (Bx+C)(x-1)

[lean otter]

should be (Bx+C)*(x-1) which still would be 0

yeah

exactly

[stray bluff]

just solve like any other pfd

[full wind]

I see

[lean otter]

yeah i kinda did the same mistake as you actually and assumed it would be A +B = 3 at the end

but nah, what i wrote at the beginning seems correct

[full wind]

So taking our x common can take us sometimes to these errors

[stray bluff]

when would u ever factor out the x ?

[lean otter]

anyways, you already got A =3/2

B and C should be easily seen from there

[full wind]

Yup

Alr

Awesome

[lean otter]

do you need help with finding B and C?

[full wind]

No thanks I'll do my self

Thanks a lot

❤️

[lean otter]

alright that's great, just a small hint if you get stuck: ||Substitute the value of A we got earlier and distribute it, then factorise out the x^2. Then expand the two brackets of (Bx+C)(x-1) and factorise x out of that as well and group up the two remaining coefficient terms. You should be able to get a quadratic equation where you could equate the coefficients to the coefficient of 2x+1 on the left side. that should give you a system of linear equations again which you can solve (this time haha) ||

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[safe radish]

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[barren berry]

.close

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[lean otter]

How do i solve this

[quasi bison]

@lean otter open a new channel. this one will close on you shortly.

[lean otter]

.close

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[unreal kindle]

hello, can someone tell me whats the limit

[unreal kindle]

$\lim\limits_{x \to +\infty} a^x$ when $a \le 1 $

[flat frigate]

lilisworld

[unreal kindle]

??

[lean otter]

well lets take a=0.8 for example

,calc 0.8^10

[flat frigate]

Result:

0.1073741824

[lean otter]

,calc 0.8^100

[flat frigate]

Result:

2.0370359763345e-10

[lean otter]

,calc 0.8^1000

[flat frigate]

Result:

1.2302319221612e-97

[unreal kindle]

so it's 0

[lean otter]

yes, for -1<a<1

and whats it for a=1?

[unreal kindle]

1

and x<=-1 it's -oo?

[lean otter]

when x goes to -inf?

[unreal kindle]

no +oo

[lean otter]

oh you mean a<=-1?

[unreal kindle]

yes srry

[lean otter]

thats divergent, cant really tell, its some spiraling complex number whose absolute value goes to infinity

[unreal kindle]

hum? so it's what?

[lean otter]

i think negative a doesnt really make sense anyway

limit does not exist for a≤-1, and for -1<a<0 its only 0 if you allow complex numbers

[barren berry]

H¨¨

[unreal kindle]

ohhh okk

so no limit

thankss

.close

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[chilly thunder]

Hello, can someone explain how do I do this ?

[chilly thunder]

I'm in the topic : Seqeunces and Summation

[raw pivot]

do you know what ∑ is

[chilly thunder]

Sum of ?

[raw pivot]

ye

[chilly thunder]

Ohhh ! Does that means

[raw pivot]

yeah

[chilly thunder]

Since first term , i = 0,

So 2*(3^0) = 2

I see ! Okay thank you so much !!

.close

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[earnest wagon]

F(x)=Sin(alpha), 0<alpha<pi/2, what does this mean?

[earnest wagon]

Is the function a straight line graph or sin x curve from 0 to 1

[thin bridge]

its a sine function with a domain restriction

[earnest wagon]

And it's graph, a portion of sine function?

[thin bridge]

yes

[earnest wagon]

Ok

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[solid crescent]

how do i find the area and perimeter of the top part of this shape?

[neat kiln]

,rccw

[sharp crane]

can you find the radius of this semicircle?

then just use your basic circle formulas

[solid crescent]

i don’t know those 😭

[sharp crane]

Perimeter $= 2 \pi r$
Area $= \pi r^2$

(For a full circle)

[flat frigate]

nvx

[solid crescent]

tysm

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[calm lagoon]

How do I get started with this DE

[dense coral]

First divide by dx

[calm lagoon]

I cannot use separable variables here btw

[stray socket]

Wdym separate variables

You can just divide both sides by dx

[dense coral]

yes

[stray socket]

It works out very nicely

This is a generous question ngl

[calm lagoon]

This expression

This is my very first week learning differential equations

[stray socket]

Your objective is to make it a "dy/dx = " statement right?

So start with dividing both sides by dx

Or you can move the dx terms to one side, factor dx out, and then isolate dy/dx throuh some algebra

[calm lagoon]

Like so?

[sharp crane]

yes

its separable if you introduce a small substitution

[calm lagoon]

The thing is that I cannot use the separable method again

My professor only allows us to use 1 method for each exercise LOL

I solved the first one by using the separable method. But idk what to use on the second one

[sharp crane]

what methods have you learned

[calm lagoon]

Only the separable one

[sharp crane]

then how would you use another method lol

[calm lagoon]

Like, I'm learning the exact method thing

[sharp crane]

its not exact

[calm lagoon]

There's another one called homogeneous

[sharp crane]

for linear DEs?

[calm lagoon]

Or something alike

[sharp crane]

this one isnt linear either

:(

separable & exact is the only easy way to solve a couple of non-linear DEs

[calm lagoon]

What are the hard ones then

[calm lagoon]

Or should I make the first exercise with another method to use separable on the second one?

Our professor kinda want us to guess what to use instead of solve it at once

[calm lagoon]

So, can I use exact on the first DE to use separable on the second one?

[sharp crane]

did you check if the first one is exact?

[calm lagoon]

Nah

It's separable lmao

[calm lagoon]

Thanks for this tho. I'll keep trying it with the separable method

[safe radish]

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[unique valley]

I’ve proven the first question

But how do I go about the second one?

I presume I use the same approach using the axiom on induction like I did with the first question

[foggy salmon]

whats v

[unique valley]

Successor function

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@unique valley Has your question been resolved?

[calm lagoon]

Yes

[safe radish]

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[hidden tide]

.close

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[runic rampart]

is (a) bounded, not monotonic and not convergent?

[split ether]

Yes

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[valid salmon]

help with a please

[nova creek]

What have you tried

[valid salmon]

well first i tried to do x(x+5) and x being the variable but it didnt work out

so im just at a roadblock

[nova creek]

We know (x + 5)f(x) = x² + 8x + 15

So what's f(x)

[valid salmon]

i dont know 😭 i dont recall learning f(x) and this is review from prior yr

[nova creek]

If I knew 5 times some number gives 15, what was that number?

[valid salmon]

3

[nova creek]

How did you find that?

[valid salmon]

5x = 15, then both terms over 5

[nova creek]

So you divided 15 by 5?

[valid salmon]

yes

[nova creek]

So if we know some function times x + 5 gives x² + 8x + 15, how can we find that function?

[valid salmon]

i tried to divide x(x+5) since it is a multiplication problem and i need to inverse it, but im not sure if thats right

[nova creek]

Why are you dividing by x(x + 5) instead of just x + 5

[nova creek]

You didn't divide by 5x on this problem

[valid salmon]

i would put x(x+5) over x+5?

like this?

[nova creek]

It's not x(x + 5)

It's f(x) (x + 5)

You're solving for a function

[valid salmon]

oh i see

from here where do i go

[nova creek]

Solve for f(x) by dividing x + 5

[valid salmon]

do i divide x^2 + 8x + 15 by x+5 too?

[nova creek]

You can't just divide one side

You need to do the same thing to both sides

[valid salmon]

ok i see

now that i eliminated x+5 on the left how do i divide x^2 + 8x + 15 by x+5?

[nova creek]

Long division or synthetic division

Factoring maybe

[valid salmon]

brb i go read my notes on synthetic division and come back bc its been a while

[safe radish]

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[safe radish]

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[loud leaf]

How does one read the set? Does it mean "For all points (x,y) in the function f(x,y) that are equal to c"?

[loud leaf]

Ie that it studies all points with the same z coordinate?

[compact ferry]

yes

say you have a plane of the form

z = c

then that plane intersects with f(x, y) on those (x, y)

[loud leaf]

Yes

ahh

so it's like a 2d slice of the function at c

[compact ferry]

yeah pretty much

i highly recommend math3d.org for multivariable calculus visualisations

[loud leaf]

math3d?

I'll check it out!

Thank you again, my dearest heavy, Gijs!

[loud leaf]

that's pretty damn cool

[compact ferry]

np

it sure is

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[lean otter]

help ping me if you reply

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

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@lean otter Has your question been resolved?

[lean otter]

bro <@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185> ?????

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@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185> hi?

.close

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[dreamy finch]

so i have a question and i have the answer to the question

[dreamy finch]

i just dont understand the solution

here's the question:

and here's the solution:

the only thing i dont get is the 1-9/19 * 8/18 part

please @ me if anyone knows

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[gilded pond]

i know how to solve for x on the triangle diagram but idk how to solve for y

[solemn vault]

So you have two isosceles triangle right??

[gilded pond]

yup

[solemn vault]

Can you give the triangle names so it can easier to point out??

Look the smaller isosceles triangle

[gilded pond]

this is the original img i just copied that to my notes

[solemn vault]

Ok so can you give them a name

Cuz that way it would be easier to point out the angles

[gilded pond]

sure gimme a sec

[solemn vault]

K

[gilded pond]

something like this?

[solemn vault]

Ok

You see angle DBC RIGHT ??

[gilded pond]

yup

[solemn vault]

it's 100°

So angle ABD would be??

[gilded pond]

oh itd equal 80? bc line ac is a straight line and straight lines equal 180

[solemn vault]

Yes

It 80°

Since triangle ABD is a isosceles triangle the base angle are equal

[gilded pond]

lmao that completely slipped my mind.. also, does it matter the order when you are naming triangles?

like would triangle ABC be the same as BAC?

[fossil shuttle]

Yes

[gilded pond]

ty

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[woven cloak]

once i get to the last part

[woven cloak]

what happens after?

does this look right to you?

just following here another example

idk how they got 5

[solemn vault]

So

Once you add -4 on both side

You'll get

2/5y=2

[woven cloak]

wait

yes ok i get that

then what

[solemn vault]

Multiply both side by 5

2y=10

Divide both side by 2

Y=5

Got it??

[woven cloak]

no i give up discord cant help me because

i need visual white board

i cant read what ur saying and put it into my head visually

[solemn vault]

Ok

[woven cloak]

i opened up two tickets but ima just go in

[solemn vault]

Let me write it down

[woven cloak]

tutor face to ace

.close

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[solemn vault]

Ok I could have helped

[woven cloak]

i dont wanna waste time

take care

[solemn vault]

As your wish

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[strong burrow]

In △TRI, if ∠T=(a+10)° and ∠I=(a+20)°, what is the measure of ∠R?

[strong burrow]

is it just (a+10)+(a+20)+x=180?

[thin bridge]

and then solve for x

[strong burrow]

wait a min

(150-2a)°?

[zinc sorrel]

Ya

You can only express it in terms of a

[strong burrow]

ohh I get it, no numeraical value?

Thanks so much!! ❤️

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[wary wave]

could someonbe explain this for me?

[safe radish]

@wary wave Has your question been resolved?

[lean otter]

<@&286206848099549185>

Can someone explain how to do A

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[thin tinsel]

(a) confuses me

because I believe the answer is 2 because even though its a sharp point, both one sided limits meet each other

but my answer key says the limit does not exist

I think my answer key might be wrong, but maybe I'm wrong completely

help?

[merry swift]

both one sided limits meet each other
The one sided limits are not equal

the limit from the RHS is 2, while the limit from the LHS is -2

[thin tinsel]

OHHHHH SHIT

I WAS LOOKING AT x=0

BRUHHHHH

[merry swift]

pogchamp

[thin tinsel]

nvm thanks

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[sterile mortar]

How are x_2 and x_5 the free variables?

[trim swan]

Columns 2 and 5 don't have a pivot

[sterile mortar]

first nonzero entry is called a pivot right?

but they all have a pivot

and there aren't 5 columns right?

im confused 😭

[worthy hemlock]

It's the pivot in that row, based on RREF

[sterile mortar]

ah wait hold on

[trim swan]

The first non-zero entry in a row is called a pivot

[sterile mortar]

so even though there are technically 3 rows, there are an "invisible" like 2 other rows i thinkr ight?

and in this case x_2 and x_5

[trim swan]

I'm talking about the columns, not the rows

[sterile mortar]

does it matter which one i set to s and which one to t?

ohh i see now

[trim swan]

See how you have a pivot in the first, third and fourth column?

And not the second or fifth

[sterile mortar]

yeah

i see it now

makes much more sense

[trim swan]

Cool

[sterile mortar]

thank you so much!

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[trim swan]

No, this doesn't matter

btw

[olive fossil]

Go different channel

@lean otter #❓how-to-get-help

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[marble stratus]

Hello! I've gotten to this step but I'm not sure where to go from here

[marble stratus]

Nvm figured it out

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[foggy salmon]

er

*2

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[naive sinew]

I have spent way too much time on this problem 😅 Can someone please help me?

I thought I was doing the work right but when I try to graph a tangent line it's way off

First I rewrite it like this

[foggy salmon]

er

graph it?

[naive sinew]

Are you asking me to clarify or is that a suggestion?

Then I use chain rule like so:

[fossil shuttle]

Uhh, you do chain rule outside in

So you do $f(x)=x+(x+x^\frac{1}{2})^\frac{1}{2}, g(x)=x^\frac{1}{2}$

[flat frigate]

Estebson

[fossil shuttle]

Then for the derivative of $x+(x+x^\frac{1}{2})^\frac{1}{2}$, you do derivative of x, which is 1, and then what you did

[flat frigate]

Estebson

[fossil shuttle]

So that's gonna be $\frac{[x+(x+x^\frac{1}{2})^\frac{1}{2}]'}{2\sqrt{x+\sqrt{x+\sqrt{x}}}}$

[flat frigate]

Estebson

[fossil shuttle]

$[x+(x+x^\frac{1}{2})^\frac{1}{2}]'$ is gonna be $1+[(x+x^\frac{1}{2})^\frac{1}{2}]'$

[flat frigate]

Estebson

[naive sinew]

So I end up with this..

[fossil shuttle]

It'd be useful to put parenthesis around the sums, but yes.

[naive sinew]

Hmm

I guess it's my simplification, because I've got that answer before, but in the process of trying to find a tangent line it goes awry

I'm gonna try again but just use a calculator and change as little as possible

[fossil shuttle]

Just remember to put () around the part after the multiplication dot

[naive sinew]

yessir 🫡

[fossil shuttle]

Otherwise you're gonna end up with a different thing

Because PEMDAS

[naive sinew]

Awesome thanks for making sure I'm not crazy @fossil shuttle

[fossil shuttle]

lol

It's important to keep the order right

[naive sinew]

I was trying to foil the fraction into the parenthesis earlier.. It's late 😭

[fossil shuttle]

And np!

[naive sinew]

.close

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[safe radish]

@solid crescent Has your question been resolved?

[solid crescent]

help?

<@&286206848099549185>

[fossil shuttle]

Ok, so for each square, you are being given an already complete file

For the first one, -1, -3, and -5

Adding those up gives us -9

Therefore, all our sums must equal -9

Let's start with the row with -1 and 6

That makes 5

So we need to find a number such that when adding 5 to it, we get -9

And we find this by subtracting 5 on both sides

So that gives us -14

For the other diagonal, we have 6 and -3

Adding those up gives us 3

Same technique, we get -12

Then we also have 6 and -5

Added up gives us 1

Doing the thing again gives us -10

So we have:
[ -1 ][ ][-12]
[-14][-6 ][ ]
[ 6 ][-10][ -5 ]

And we can use the same technique to find the missing numbers, 7 and 8

Giving us the square:
[ -1 ][ 7 ][-12]=-9
[-14][-6 ][ 8 ]=-9
[ 6 ][-10][ -5 ]=-9
= = = = =
-9 -9 -9 -9 -9

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@solid crescent Has your question been resolved?

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[lean otter]

how to do this?

I have to find equation for f(x)

Then put that after 1/3?

Then graph?

How do I know what the equation for f(x) is

It’s not symmetrical

nvm

is it the same graph

[woven swan]

i think u just have to drag the red points to a 1/3 of the y where the blue points land

[lean otter]

i cant move the origin one

[woven swan]

the last red point

[lean otter]

but i moved the two other points 1/3

[woven swan]

the points must have the same x coord

as the blue points

it’s just the y that gets scaled by 1/3

[lean otter]

so this is it

[woven swan]

what’s 6 *1/3

[lean otter]

2

[woven swan]

ye

[lean otter]

so this one

[woven swan]

yes that’s good

[lean otter]

ok ty

[woven swan]

np

[lean otter]

it worked

thank u smarty party larty tarty pants

[woven swan]

np :3

[lean otter]

.close

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[lean otter]

how do i do this

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[safe radish]

@lean otter Has your question been resolved?

[solid crescent]

how did u get -6 in the middle

it's -3 ?

[safe radish]

@lean otter Has your question been resolved?

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[polar knot]

(8-b-c)^2 + b^2 + c^2 = 36

(8-b-c)bc = -16

thats all i got

pls ping

[glass carbon]

you know there are no real solutions to this

[compact ferry]

There aren't?

[halcyon carbon]

Yeah only complex

[compact ferry]

Yup

[safe radish]

@polar knot Has your question been resolved?

[polar knot]

oh seriously

[compact ferry]

i plotted it out of curiousity

[polar knot]

thats why i been failing to solve this shit for like 2 hrs

ACCORDING TO MY FRIEND, that was a “moderately easy” question..

[compact ferry]

lmao

time to solve it then

and pretend it was easy

[polar knot]

im a freshman…

well im up to the challenge but idfk how to do it

[compact ferry]

more algebra probably right

[polar knot]

so i got these 2 eqaruons

now what?

[compact ferry]

oh lord

[polar knot]

when does the imaginary part come in

is this even solvable????

[compact ferry]

definitely solvable

[polar knot]

HOW. TO. DO. IT.

[compact ferry]

i reckon the imaginary part comes when we find a quadratic equation in terms of 1 variable

[compact ferry]

just dont give up i guess

[polar knot]

oh i got that part

[compact ferry]

more algebra

more substitutions

[polar knot]

igot the 1 term

i did it i thought it was wrong so i didnt send it

here it is

2b^2 + 2b(-b^2/4 +2b+4) + 2(-b^2/4+2b+4)^2-16b-16(-b^2/4+2b+4)=-28

only 1 variable

[compact ferry]

what the hell

[polar knot]

is it wrong?

[compact ferry]

its just huge

thats all

[polar knot]

😭

[compact ferry]

im sorry im too old for this

i cant do cubics anymore

[polar knot]

c=-b^2/4+2b+4

heres whag i got dor c

[polar knot]

huh

so we cant solve it?

[compact ferry]

of course we can

[polar knot]

does it tell us the solution

[compact ferry]

oh hell no it just tells us theres no real solutions

[polar knot]

the solution is gonna@be loke

x= i-1

or something right

[compact ferry]

yeah very well could be

[worthy hemlock]

It's not

[polar knot]

then what is it

[worthy hemlock]

Complex solutions

[polar knot]

isnt that somehting with i in it

[worthy hemlock]

Yes

[polar knot]

i just meant like the solution will look like x = i + 1 or soemthing like that

so how do i solve that

[polar knot]

i have rhese 2 forunlas rn

[polar knot]

heres rhe one with inly 1 bariable not sure if its coreect tho

now what

[worthy hemlock]

Yes but not that simple of an answer

[polar knot]

yeah

so how do i get something like that

[worthy hemlock]

Using math

It's not going to be easy

[polar knot]

whats step 1

[polar knot]

this?

[worthy hemlock]

Substitution/elimination

[polar knot]

yeah i got it down to 1 variable rn

pretty sure that equatioj is correct

we can redo it if u like

(8-b-c)^2 + b^2 + c^2 = 36

(8-b-c)bc = -16

heres the two “staring” forumale

[worthy hemlock]

Sounds like a tough question, you should just use an online calculator to solve it

[polar knot]

i ttied and it crashed my calculator

also im on phone rn

[polar knot]

can calculatoes solve complex numbers?

[worthy hemlock]

Online calculators should

[polar knot]

can u plug it in for me cuz im on hpnr rn? thx

[worthy hemlock]

Nope

Good luck

Not gonna do your work for you

[polar knot]

aaaaaa i need to wait to tmr tben

[polar knot]

i got the eqution just have to put knto calculator right

uhhhh i dont think this is right

what the helll

im fonna try tmr

.clos

.closs

.close

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[scarlet perch]

how would i go about prooving this statement using De moivre's therom

[compact ferry]

De moivre?

[scarlet perch]

yeah

[plucky elk]

did you do the first part?

[compact ferry]

Write into complex form first I would imagine

[scarlet perch]

thats the part i m stuck on

[lean otter]

sinx cosx = 1/2 sin(2x)

[scarlet perch]

this is the answer but im still so confused

[lean otter]

and sin^2(x) = 1/2(1-cos(2x))

[plucky elk]

which line exactly

there's like 15 steps there

[lean otter]

wow the identities i much easier

[compact ferry]

De moivre will be easier if you practice it more

[scarlet perch]

when they have z^6 +z^-6 how to they turn it into 2cos....... its line 2

[plucky elk]

this?

[scarlet perch]

yeah that

specificly how they go from previous line to that

[plucky elk]

raise both sides to the 6th power

(a+ib)^6 = a^6 + ...

[scarlet perch]

and then equate real parts

?

[plucky elk]

and (a-ib)^6 = a^6 + ....

yes

[scarlet perch]

ok so its just a really long question then

[plucky elk]

it does look that way from the solution

[scarlet perch]

ok thanks then

.close

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[safe radish]

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[untold nacelle]

i need help with this question

and this one

[safe radish]

@untold nacelle Has your question been resolved?

[safe radish]

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[neon knoll]

This is the question and it asks to factor completely

[neon knoll]

This is the answer I got just need to verify if it’s correct or not

[thorny lion]

If you remember the difference of squares formula, (x - a)(x + a) = (x^2 - a^2)

[solemn vault]

,w factor x⁴-3x³-7x²+9x+12

[flat frigate]

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[solemn vault]

Well

[neon knoll]

I did that and it told me it was wrong

[solemn vault]

Yes

[neon knoll]

With the (x^2 - 3)

[thorny lion]

Yeah try with the squareroots

[neon knoll]

So would it be (x - 9)(x + 9)?

[thorny lion]

Does that work?

[neon knoll]

I have one last attempt so that’s why I was trying to verify if that was correct or not

So if all parties agree it’s right I’m putting all my chips on black lol

[thorny lion]

Nah it would be (x - sqrt(3))(x + sqrt(3)) = x^2sqrt(3) - x^2sqrt(3) + x^2 - sqrt(3)^2 = x^3 - 3

[thorny lion]

This would be correct

[neon knoll]

Ok so what I have typed should be correct?

[thorny lion]

fingers crossed lol

[neon knoll]

Your the goat

It was right

Thank you so much

[thorny lion]

np

[neon knoll]

.close

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[thorny lion]

u were the one that solved it lol

[neon knoll]

I know but still second guessing myself lol

.close

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[lean otter]

hello i have a question ummm what is (8x5) + (8x2)

[nova creek]

Use a calculator

Or a pencil

[lean otter]

no

too much work sir

[stray bluff]

https://letmegooglethat.com/?q=(8x5)+%2B+(8x2)

[potent atlas]

56

[nova creek]

Too much work to put the question in the calc?

But not too much work to put the question in a help channel?

[lean otter]

nao

no

actually nevermind

.close

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[vast plover]

Hello
I finished a math test and I want to verify an answer.

The area of a rectangle is equal to x^2+6x-7

A. Find the two sides of the rectangle
B. What values cannot be x

[vast plover]

So for a i found
(x-7) and (x+1)

As sides

And for B i was wondering if i should solve for (x-7)(x+1)=0

Or (x-7)(x+1)>0

[foggy salmon]

(x-7)(x+1)<0

[vast plover]

Yes

[foggy salmon]

area cant b neg

so that

[vast plover]

But why that

Oh

If one side =0 then it cant be a rectangle

[foggy salmon]

well

if 1 side neg u kinda check that separately i think

but idt thrs a case where they both r neg

so it shld b well represented by that

[foggy salmon]

eh idk mayb 0 area rect counts

[vast plover]

Oh cool

Thats what i puy

Put

Bcz if the area is 0

Its not a rectangle

Anyways thx

[foggy salmon]

i feel it cld b either

np

[vast plover]

.close

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[slow fern]

The shape of the D is a circle with center (2,2) and radius 1 unit. So the area is pi square units.

$P(X \geq Y) = P(Y \leq X) = \int_{1}^{3} \int_{1}^{x} \frac{1}{\pi} \dd{y} \dd{x}$

[flat frigate]

QuantumBee

[slow fern]

This is what I did, I got 2/pi as the answer, but it's wrong

Help me

[merry sleet]

,w plot (x-2)^2 +(y-2)^2=1 and x=y

[flat frigate]

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[merry sleet]

actually

,w plot (x-2)^2 +(y-2)^2<=1 and x>=y

[flat frigate]

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[slow fern]

We are to find the proportion of area below the line and divide it with the total area.

[merry sleet]

yeah right

[slow fern]

Where am I going wrong?

[merry sleet]

whats the integral of the whole circle first?

disk*

like how would you calculate its area?

to be fair given how the problem is stated i would just use geometric agruments

and not actually calculate any integral

but we can do it this way if you think that's what is expected

[slow fern]

I wanna learn it both the ways

[merry sleet]

ok so first the easy way

D is a disk

the line x=y passes through the center of D

because the center is (2,2)

so it cuts the disk in half

[slow fern]

Alright got it

[merry sleet]

so D∩{(x,y) x>=y} area

is half of the disk

[slow fern]

What is the next way?

[merry sleet]

so P(X>=Y)=1/2

right

[slow fern]

Yes

[merry sleet]

the next way is computing the area using integrals

which can be useful when its not as simple geometrically

[slow fern]

Can you find what's the mistake in my integral?

[merry sleet]

its definitely weird

[safe radish]

@slow fern Has your question been resolved?

[slow fern]

<@&286206848099549185>

@quasi bison

[quasi bison]

nyeh?

[slow fern]

Umm

[quasi bison]

this integrates over a triangular region at best

1 ≤ y ≤ x ≤ 3

nowhere near the semicircle you want

[slow fern]

So, what will the integral be?

[quasi bison]

eughhhh

you want to set this up as an actual double integral?

because it will be nasty as all hell

[slow fern]

I want know

The geometric way is too easy

I'm curious for the integral, it can help me in some ways

[quasi bison]

not in this problem it won't

i promise

it's very unenlightening

[slow fern]

Is it too big?

[quasi bison]

it's ugly.