help-0

[alpine sable]

[full wasp]

i would say take logs of both sides but wtf is log10(500000) without a calculator looooool

[alpine sable]

it's easier to divide both sides by 2000 first

[muted raft]

2^(x/30) = 500000/2000 = x/30 * log(2) = log(500/2)

[alpine sable]

won't i still end up with log(5)

log 2 and log 5 are 0.30 and 0.70, they r standard values u can learn

but it doesn't say to use log5 as 0.7

[indigo jetty]

lg 5 = lg(10/2) = lg10 -lg2

u are given lg2 = 0.3

[alpine sable]

oh

[full wasp]

wtf i didnt think of that

me and my electron-sized brain

[worldly oxide]

@wraith locust is correct answer -5??

[civic hearth]

I need help

[worldly oxide]

How can I help??

[civic hearth]

This

B. And C.

[wraith locust]

@worldly oxide yes -5

[dry echo]

Can someone help me visualize this?

Don't solve it for me though, I wanna know what's happening

[worldly oxide]

@wraith locust want soln?

[full wasp]

hold on

[olive fiber]

does anyone know how to do this

[full wasp]

@dry echo does this help lol

[dry echo]

OHHH

man, this is great

thank you so much!

[dry echo]

I think you have to use law of sines or cosines iirc

[full wasp]

this is about the extent of my abilities with blender lmao

[worldly oxide]

@full wasp you know any reagent which can reduce Fe+2??

[full wasp]

idk maybe like Ag(s)

[dry echo]

I'm not 100% sure but I think this is how you do it

true

[worldly oxide]

@full wasp does Li work as it is strongest Reducing agent??

[brave ice]

or cos54 = x/28, X=28*cos54

[dry echo]

those are way simpler yeah lol

[brave ice]

oops

[dry echo]

good enough for me lol

[full wasp]

yeah it would

[brave ice]

https://cdn.discordapp.com/emojis/728609470388633693.gif?v=1&size=64

[tiny cedar]

if i have cos x = 5/6, then cos 2x will be 5/3 ??

or it dosnt works like that

[oak chasm]

@tiny cedar It doesn't work like that.

[tiny cedar]

oh

how can i find it then

[oak chasm]

$$\cos(x) = \frac56$$

[ocean seal]

Chai T. Rex

[oak chasm]

Take arccos of both sides.

$$\arccos(\cos(x)) = \arccos\left(\frac56\right)$$

[ocean seal]

Chai T. Rex

Chai T. Rex

[tiny cedar]

uh fuck

[oak chasm]

If you only want one solution, that should be enough to start you off.

[tiny cedar]

i mean

im supposed to do it w/o calculator

so is there rlly no way i can do this

this is the problem, its in spanish but i think the words dont rlly matter

i found cos x

wich is -5/6

[oak chasm]

Sorry, I have to go.

But here's something useful:

,w simplify cos(2arccos(a))

Oh, wait.

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

Chai T. Rex

[oak chasm]

,calc cos(2acos(5/6))

[ocean seal]

Result:

0.38888888888889

[tiny cedar]

oh

[oak chasm]

,calc 2(5/6)^2 - 1

[ocean seal]

Result:

0.38888888888889

[oak chasm]

But now I have to go 🙂

[worldly oxide]

@languid ore 400??

[languid ore]

@worldly oxide How would you find that answer?

[languid ore]

where does the 45 come from

we dont use cos in my class could you explain how i could solve it without cos @worldly oxide

how?

please

okay

[stuck kestrel]

yes

x = 20

[wraith dew]

help!

[full wasp]

ah this isnt too bad

although is this a test

[wraith dew]

nono its an ungraded content check

[languid ore]

my fault

im not sure how ur getting 20

[alpine sable]

U calc volume for both hemisphere and the cone, and subtract cone from hemisphere

[full wasp]

cone volume is like 1/3 πr²h (h = r tho)

and hemisphere volume is 2/3 πr³

[wraith dew]

ok so i got the hemisphere volume

but im just confused on the cone's volume

[alpine sable]

Cone’s volume is given as 1/3 pi r^2 h

[full wasp]

the height of the cone is equal to the radius of the hemisphere

[wraith dew]

so the height equals the radius?

ohhhh

i got ot

it

tysm!!!

ok i got 28.3 as my final answer

[south stream]

Why is 9-(-13) = +22 shouldn't it be negative because the 13 is greater?

[worldly oxide]

@south stream thats not 13 it is -13

[south stream]

Oh

So 9 became greater

[worldly oxide]

Yeah

And you're giving 13 extra to 9

[alpine sable]

ye a positive number is of course greater than a negative number if u think it like that

[south stream]

But...
(-63) + 49 = -14

[worldly oxide]

Why dont you write it like 49-63

[south stream]

The operation change then the negative sign of the first term

[worldly oxide]

When you subtract a negative term it is basically you're adding both digit

[soft echo]

is this free?

[worldly oxide]

??

[alpine sable]

Yep

[soft echo]

alright

wait

[worldly oxide]

Want area??

[soft echo]

no

what angle is this

[worldly oxide]

Which??

[soft echo]

the one in the ss

[soft echo]

.

[limpid rock]

there are 4 of them

[worldly oxide]

Which angle mention the quadrant

[soft echo]

hw question

i named the angle parallelogram is that correct?

[brave ice]

https://cdn.discordapp.com/emojis/770547436333563905.png?v=1&size=64

[soft echo]

oh

alright thanks

[patent hearth]

I'm struggling with part b can anyone help?

[soft echo]

is this a test?

[soft echo]

hey?

is that a test?

[patent hearth]

No its hw

[soft echo]

oh ok

do you know the answer?

I am not sure

but lets see

[alpine sable]

men and projects are directly proportional, men and hours are directly proportional, hours and projects are inversely proportional

[soft echo]

lol

[alpine sable]

(m*h)/p=constant

[patent hearth]

I dnt get it lol srry

[soft echo]

which grade are you in

[alpine sable]

do you know abt direct/inverse proportionality?

[patent hearth]

Yes

But not this kind

Ik that sound stupid

[alpine sable]

ok, first lets imagine we keep the number of hours constant

so for example lets say we fix the time at one hour

more men = more projects completed

less men = less projects completed

#men and #projects are directly proportional

does that make sense

[patent hearth]

Yes it does

[alpine sable]

now let's imagine we keep the number of men constant

for example we fix it at 2 men

if they have more hours, they can complete more projects

if they have fewer hours, they can complete fewer projects

so #hours and #projects are directly proportional

do you follow

[patent hearth]

Yes

[alpine sable]

ok now imagine keeping the number of projects constant

more men will finish the projects in fewer hours

if we have less men working then they will take more hours to finish th eprojects

so #men and #projects are inversely proportional

[patent hearth]

Yes

[alpine sable]

so now we have mh/p=constant

[patent hearth]

Ohh
I think I got it
Thanks
This should make solving other qs easier

[alpine sable]

np

[soft echo]

can you tell me the answer

I did the maths another way

lets see if it works

[patent hearth]

I haven't solved it yet

[soft echo]

after solving it

[patent hearth]

Sure ill send it

[soft echo]

l

[patent hearth]

I got 32
What bout u?

[soft echo]

k

[soft echo]

oh

Lol I somehow got 135

LMAO

[patent hearth]

K lol

[alpine sable]

32 is correct

[soft echo]

yes ik

[elfin lynx]

Can someone explain b. I having trouble seeing how you get to that number

[alpine sable]

Ok, quick simple question. Is >18 greater than or less than? Debate in another server

[elfin lynx]

greater than

[lone vapor]

none

[alpine sable]

If it is greater than, then is 0>18 true? No...

[muted raft]

that makes no sense at all.

[alpine sable]

Hmmm

Well it is just a symbol referring whether something is greater or less than

In that case, I am wondering why people think it is greater

[muted raft]

Yes which is why >18 does not make sense

there is no quantity on the left

[alpine sable]

Yes

[muted raft]

18 does not make sense but i guess people might assume it as numbers greater than 18?

[covert glade]

Can someone please help me

I came across this question and idk what to do

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 47 feet?

Be sure to realize that the perimeter is just the outside of the window.

please lmn asap

[alpine sable]

looks like an optimization problem

first step draw a diagram if you haven't already

so let's say l is the length of the rectangle and w is the width of the rectangle

find an expression for the perimeter in terms of l and w

then find an expression for the area in terms of l and w

[covert glade]

Okay

what should we do after?

[alpine sable]

so using the perimeter equation, solve for l in terms of w, or w in terms of l, whichever one is neater

then substitute that into the area equation

now that you have the area functon in 1 variable, find the critical points of the area function

[indigo glade]

you still need help?

[gleaming granite]

The way my first grade teacher taught us was to imagine the signs as alligators trying to eat the bigger number, so since the 'alligator' is facing away from the 18, 18 is less then the other number so [x>18] x is greater than 18.

kinda weird lmao

[bold token]

is this available?

i guess it is

what does this mean?

[noble bolt]

y" means double differentiation of y

[alpine sable]

is there a channel on this server to help with a math course ill be taking in a months time , it kicked my ass once before and i know ill need help with it

[bold token]

so at y' do I use dy/dx?

[noble bolt]

That is d^2(y)/(dx)^2

[bold token]

oh wow

[noble bolt]

Yes

[bold token]

then after dy/dx?

the first derive

what do I do next?

derive the next equation and discard the dy/dx at the left?

[noble bolt]

Differentiate dy/dx again

[bold token]

wdym

oh I use dy/dx as the equation I derive?

[bold token]

is the dy/dx on the left be affected?

[noble bolt]

I'll explain from start

First take everything except y to rhs

Find dy/dx

Now replace dy/dx with y'

Now find dy'/dx

@bold token

[bold token]

so it would be 8yy'?

[noble bolt]

No..

Wait I'll solve and send you

[bold token]

oh didnt really need that, but thx

[tranquil matrix]

Can anyone help I’m doing past papers but I don’t know how to do this

[coral pagoda]

Yep. That is correct

At least for the 4y^2 part

[bold token]

hm

[coral pagoda]

What is the derivative of x^2?

[bold token]

2x

[coral pagoda]

And the derivative of 4?

[bold token]

y' would be 2x+8yy'=0?

that's what im thinking

but my teacher didnt explain that further xD

[coral pagoda]

No no, this is not what y' is equal to

However, we can solve for y'

[ 2x+8yy'=0\Rightarrow 8yy'=-2x] Finish the rest

[noble bolt]

We have to find y" so there should be no y term

[ocean seal]

dackid (jump king +)

[coral pagoda]

This is false

[bold token]

um

[noble bolt]

F I was wrong it seems

[bold token]

Im pretty sure some y would be left or smth

[coral pagoda]

We are just doing algebra here by solving for y'

[bold token]

so 2x/8y?

then I get its derivative

[coral pagoda]

You forgot the negative, but yes

[bold token]

so it would be y''?

[grand kelp]

$x^2 + 4y^2 = 4$ is an equation of an ellipse

[ocean seal]

NickPro

[coral pagoda]

No, that is y'. In order to get y'' we need to evaluate again

[bold token]

graphing is not needed atm

[grand kelp]

So the value of y clearly matters

[bold token]

yeah that's why y'=-2x/8y

then I derive -2x/8y to get y''?

[coral pagoda]

So we have $y'=-\frac{x}{4y}$

[ocean seal]

dackid (jump king +)

[bold token]

wait somethinglike that

[coral pagoda]

Now you need to differentiate again

[grand kelp]

Yes, then you differentiate this fraction

[coral pagoda]

As we see, the chain rule will come in to effect again

[bold token]

yeah

so what do I use next now?

dy/dx?

y'?

or y"?

[coral pagoda]

Take the derivative of -x/4y

[noble bolt]

Ans should be in terms of x from what I have learned

[bold token]

yeah whats the derivative of 4y?

[grand kelp]

It's generally not a good idea to change the system of notations in the middle of your solution

[coral pagoda]

Still false

[bold token]

4(dy/dx)?

[grand kelp]

4y'

Yeah

[coral pagoda]

You have a quotient of two functions -x and 4y

[bold token]

yes i know qouteinet rule

[coral pagoda]

So you need the quotient rule here to take the derivative

[bold token]

jsut the 4y im worried

[grand kelp]

It cannot be in terms of x since you can have two different values for y for which the equation works

[smoky barn]

How did you understand the importance of variables for data analysis?

can someone help? im stuck on this question

[coral pagoda]

Well y is a function of x, so you use the chain rule. And you are correct since the derivative of 4y is 4y'

[grand kelp]

So you would have to add plus-minus in the front

[noble bolt]

What's wrong with this?

[bold token]

Im not following

[coral pagoda]

y is not a function

[bold token]

let me clear

[coral pagoda]

Please ignore them Yogurt

[bold token]

with -x/4y,

i do the qoutient rule

[coral pagoda]

Yes

[bold token]

now what would be the derivative of 4y?

[coral pagoda]

You mentioned it earlier

4y'

[bold token]

4dy/dx?

why 4y'?

[coral pagoda]

They are the same thing

[grand kelp]

That's the same thing

[bold token]

oh xD

[grand kelp]

Just in different notation

[bold token]

so now if I get the equation

I get y' in either sides of the equation right?

[coral pagoda]

This will not be an equation this time

[bold token]

so I just disregard y' on the left?

[coral pagoda]

You'll have $y''=\dots$

[ocean seal]

dackid (jump king +)

[coral pagoda]

The derivative of y' is y''

[bold token]

oh so y''=blahblah with y'

[noble bolt]

Why can't we take y as a function here ?

[bold token]

right?

[coral pagoda]

That is the definition of the 2nd derivative

[coral pagoda]

You will get two outputs for y

But if you recall the vertical line test, that means y is not a function

[noble bolt]

Ohh....

[bold token]

is this correct?

[noble bolt]

Ok thanks got it 👍

[coral pagoda]

Its yogurt, take the derivative of -x/4y

[bold token]

aight

[noble bolt]

Didn't think of verifying whether it's a function or not

[coral pagoda]

You are asking questions you'll know the answer to if you just take the derivative

[coral pagoda]

This is why implicit differentiation plays a big role: you can still evaluate derivatives of curves that are not necessarily functions

[noble bolt]

I see

[grand kelp]

They can also still be functions, but with no clear analytic expression

[coral pagoda]

Also true

[bold token]

i feel

[grand kelp]

Like inverse to a degree 5 polynomial

[bold token]

that my ans is wrong

[noble bolt]

So we differentiate y^2=4ax the same way right implicitly?

[bold token]

is (-4y+4xy')/16y^2 wrong?

[coral pagoda]

Okay, recall the quotient rule [ \left(\frac{f}{g}\right)'=\frac{f'g-g'f}{g^2}]

[ocean seal]

dackid (jump king +)

[coral pagoda]

In our case f(x)=-x and g(x)=4y

[bold token]

yeah I got this

[coral pagoda]

Okay, so it looks good

Now the catch: what is y'?

[bold token]

dy/dx?

[grand kelp]

You calculated the derivative of y like 3 minutes ago

[bold token]

y' is

[grand kelp]

Why not just plug that in

[bold token]

-x/wy?

2y?

[coral pagoda]

-x/4y

[bold token]

4y

something

[coral pagoda]

Yes

[bold token]

so I plug that

in the y'' equation

[coral pagoda]

You replace y' with -x/4y

[grand kelp]

Yes

[bold token]

aight on it

[noble bolt]

Ok so you replace y' in the end

[coral pagoda]

Yes

[noble bolt]

Can this be done for functions too?

[grand kelp]

Indeed

[coral pagoda]

Sure, but if we can write y=f(x), then the question becomes pretty straightforward

[noble bolt]

Nice this makes differentiation a bit easier

[coral pagoda]

Nothing special here

[grand kelp]

This can be done for any curve given that it's differentiable

[noble bolt]

Ok

Gotcha

[bold token]

[-4x-4x^2/4y])/16y^2?

[grand kelp]

That's one of the ways we prove that the derivative of ln(x) is 1/x

[coral pagoda]

Simplify, but yes

[bold token]

welp thx everyone

[noble bolt]

I see

[coral pagoda]

You bet

[noble bolt]

Same way we can find derivative of a^x

[coral pagoda]

\begin{align}
y=\ln(x) \Rightarrow x=e^y
\end{align}
\begin{align*}
\dv{x}(e^y)&=\dv{x}(x)\
y'e^y&=1\
y'&=\frac{1}{e^y}\
y'&=\frac{1}{x};; (\text{Recall equation 1})
\end{align*}

There ya go

[ocean seal]

dackid (jump king +)

[coral pagoda]

Nah, that ones a bit different

Also, there is your proof for the derivative of ln(x)

[noble bolt]

But I found it

[coral pagoda]

The derivative of a^x makes use of the chain rule

Note $a^x=e^{x\ln(a)}$

[ocean seal]

dackid (jump king +)

[coral pagoda]

And so by the chain rule: $(a^x)'=\ln(a)a^x$

[ocean seal]

dackid (jump king +)

[noble bolt]

Oh

I did it the long way

I am nub

[coral pagoda]

Nah, it's okay

Try finding the derivative of $\log_x(a)$

[ocean seal]

dackid (jump king +)

[noble bolt]

Give me a min I'll solve it

[coral pagoda]

Alright. This one's a little tricky at first

[noble bolt]

Yes it is indeed

[coral pagoda]

Keep in mind the variable is the base of the logarithm

[noble bolt]

Yes

[tribal geyser]

Hey guys I need help with 12

Like I did the working and I got the answers however the answers only have two of the answers I have

[grand kelp]

Look at the question

They only asked alpha and beta

[tribal geyser]

Yh

So?

I found alpha and beta

and I have plus or minus 1/2 and 2/3 or 3/2

The answer gives me only 1/2,2/3

[noble bolt]

Help me I am stuck

[tribal geyser]

@grand kelp

[coral pagoda]

[ \log_x(a)=\frac{\ln(a)}{\ln(x)}]

[ocean seal]

dackid (jump king +)

[grand kelp]

That's honestly a very strange way to solve a quartic equation

Lemme look at this for a moment

[noble bolt]

I didn't think of that sheesh

[coral pagoda]

It helps quite a bit

,w plot log_x(a)

[grand kelp]

@tribal geyser First, you lost the 18x^2 term in your equation

[ocean seal]

Results provided by WolframAlpha

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

Requested by dackid (jump king +)#4103

[coral pagoda]

Nice job wolfram -_-

[tribal geyser]

@grand kelp it’s using sum and products lol

so if u could explain that’ll be great

@grand kelp I didn’t lose it lol I wrote in at the top

[grand kelp]

You didn't

[coral pagoda]

So I know the product is equal to -6, but what about the sum?

[grand kelp]

The sum is 52 / 24 afair

[coral pagoda]

I don't know what the sum of the roots are for higher polynomials

[tribal geyser]

yh

If u put it on a calculator it also gives u what I got lol

I got plus and minus 1/2 and 2/3 3/2

[grand kelp]

It just works the same, since you have $(x - x_0)(x - x_1)...(x - x_n)$

[ocean seal]

NickPro

[noble bolt]

Is this right?

[tribal geyser]

But the equations gives 4 solutions

[coral pagoda]

Well anyways [ \beta \cdot \frac{1}{\beta}\alpha\cdot -\alpha=-\alpha ^2]

[tribal geyser]

How did u know which one?

[ocean seal]

dackid (jump king +)

[tribal geyser]

Channel taken sorry

@alpine sable

[alpine sable]

no worries

[coral pagoda]

And [ \frac{1}{\beta}+\beta +\alpha-\alpha=\frac{1}{\beta}+\beta]

[ocean seal]

dackid (jump king +)

[tribal geyser]

Yes

I’ve done all of that

[coral pagoda]

Looks good yeah!

So $\alpha=\sqrt{6}, -\alpha=-\sqrt{6}$

[ocean seal]

dackid (jump king +)

[tribal geyser]

Like if u try solve it u will get 4 solutions

[noble bolt]

Dackid give me more of those kinds of questions if possible

[coral pagoda]

Care to move to the #calculus channel?

[tribal geyser]

I’m lost

[noble bolt]

Yes

[tribal geyser]

Can anyone help?

[grand kelp]

@tribal geyser What's your problem once again?

You don't know what solution to choose in a pair?

[tribal geyser]

Yes because I figured out alpha which has two solutions and beta which also has two

So which one am I suppose to use

[grand kelp]

It doesn't matter because if you change the sign of alpha or replace beta with its reciprocal the solutions would stay the same

[tribal geyser]

Are u sure because why would the answer only state 2 then?

[grand kelp]

Well, there isn't a valid reason to say that either of these answers is wrong so I assume the authors just gave one of the options

@coral pagoda It's not sqrt(6) since you have to divide that 6 by 24

[torpid hazel]

sry

[jovial mica]

can someone help with this question?

[coral pagoda]

Ah. My bad

[autumn timber]

idk

[alpine sable]

Less of a problem question but more understanding. When I have a taylor series, am I evaluating f(x)^n by the value of a?

Lets say ln x centered at a = 1. When expanding it, am I evaluating ln(x) and its derivatives at the value of a?

So it would be ln(1), 1/(1), -1/(1^2), 2/(1)^3....

[livid crypt]

can someone help me with this problem?
how do I start it

[jovial mica]

Alright thanks.

[strong furnace]

are there any particular instructions (integration by parts / integration by substitution) to solve this problem?

[alpine sable]

i don't know what techniques you know, but one boring way I see immediately would be to expand the fraction by sqrt(25+x^2) so that you get rid of the root in numerator.

Could you proceed from there? Then you'd have to use an algorithm for such integrals.

[livid crypt]

im pretty sure it can be either way but which ever way is the easiest is preferable

[strong furnace]

adding to that you can also substitute x = 5sin(theta)

[alpine sable]

oh yes that's probably the most elegant solution

[livid crypt]

wait why would you substitute x = 5sin(theta)

[alpine sable]

i suggest you to try it and see for yourself what happens

if you are still confused then ask again

it's something that you have to see once or twice to be able to think of it

[hollow owl]

hi I need help with how to solve this

I dont know how to start solve when there is sin and cos

[strong furnace]

did you use the hint?

[hollow owl]

I put the hint instead cosx and what then? how do I continue

[strong furnace]

have you learned about this limit ? sin(x)/x

[hollow owl]

equal to 1

yes

[alpine sable]

expand by (1+cosx)

[strong furnace]

substitute x/2 = t in the given problem and then relate (sint/t)^2 with that limit

[grand kelp]

This particular integral is actually pretty easy since this is a semi-circle centered at the origin with a radius 5

What you need is the top-right quarter of the circle

[iron swift]

yeah then integrate the area of the top right quarter

[grand kelp]

It would be 25pi/4 I believe

[alpine sable]

how would u determine that 12a starts at 1?

without calculator?\

[lament wyvern]

what is sin(pi/4)

[alpine sable]

nvm i got it

thnaks

anyway

[grand kelp]

$\sin\frac{\pi}{4} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}$

[ocean seal]

NickPro

[hollow owl]

how from this you get to sint/t

I just get to 2sin(t)^2/x^2

[grand kelp]

Notice that $\frac{2\sin^2{\frac{x}{2}}}{x^2} = 2(\frac{\sin{\frac{x}{2}}}{x})^2$

[ocean seal]

NickPro

[grand kelp]

Now you can replace x/2 with t and get $2(\frac{\sin t}{2t})^2$

[ocean seal]

NickPro

[grand kelp]

@hollow owl

[hollow owl]

wow very nice text bot

ok I understand you cuz 2*x/2 = x. thank you

[grand kelp]

no problem

[hardy geyser]

Is there an easier way to do this on the calculator instead of guess checking

[lament wyvern]

xy = 36
find all the factors of 36

1,2,3,4,6, 9, 12, 18

[hardy geyser]

how about on the calculator

[lament wyvern]

not everything needs to be done on a calculator

[hardy geyser]

I’m trying to make the act faster im on time crunch

[grand kelp]

This doesn't have to be done on calculator

[hardy geyser]

but if I did it on the calculator it would be faster?

[lament wyvern]

no

[grand kelp]

1 + 36 = 37
2 + 18 = 20
3 + 12 = 15
4 + 9 = 13
6 + 6 = 12

All the options

@hardy geyser I don't know how you can find the divisors of a number on a calculator

[hardy geyser]

so guess check would be the fastest way

[grand kelp]

I mean, 36 isn't a very large number

You can even check all the possible options, of which there's not too many

[hardy geyser]

what if they give me a larger number

[grand kelp]

There are some techniques that you can use like estimating the numbers you can get, checking the remainders, etc.

Not sure the remainders would work but who knows

For example we have just found that all the options are 12 or larger

[hardy geyser]

nvm I found a YouTube video I got it ty

[grand kelp]

Okay

[leaden hill]

guys

how can I solve this

it want A degree

[grand kelp]

Is that a pyramid?

[leaden hill]

are u kidding?

[woeful pulsar]

so it's flat?

[grand kelp]

I'm not, it maybe a triangle or a pyramid

[leaden hill]

triangle

ABC is a triangle

[grand kelp]

Okay

[carmine lion]

48??

[leaden hill]

how did u guys solve it

[carmine lion]

because the triangles are the same

[grand kelp]

This can't be true

[carmine lion]

the sides are equal

why cant it be true

[grand kelp]

Because you're getting that the sum of angles is 144 degrees, not 180

[leaden hill]

ye

nick is right

what u say for this question @grand kelp

[grand kelp]

I'm thinking

That's a weird question

[woeful pulsar]

yeah you have a triangle and the circumcenter

but it should be determinable

[leaden hill]

I agree its damn weird .d

but I have to solve it

[woeful pulsar]

tho it's definitely solvable

[leaden hill]

@woeful pulsar can u solve and explain if u can

[woeful pulsar]

there are lots of isosceles triangles

try marking down all the equal angles

see what relations you can make too

[grand kelp]

Ah, yeah

If D is the circumcenter, then BAC is half of BDC

So it is 66 degrees

[leaden hill]

u sure?

[grand kelp]

Yes

[leaden hill]

what u mean with circumcenter

[carmine lion]

64?

[grand kelp]

@leaden hill You can draw a circle around the triangle

Have you studied things like that?

[leaden hill]

no kinda

new in thesethings

and what u say about that

ise means if

ABC is a triangle

it want how much is the X

[grand kelp]

Ever heard of Menelaus's theorem?

[leaden hill]

yeah

[grand kelp]

You can apply it for ABE and the line CD

[leaden hill]

I am gonna try

wait

[coral ridge]

thalesle yapıyosun onu

[leaden hill]

yetiyo mu

thales

emin misin

[coral ridge]

yep

2/5=x/(x+9)

bunu yap

[leaden hill]

aga

o oran altta geçerli ama

[coral ridge]

cevap 6 değil mi

[leaden hill]

o oranı

altta şey yapıyor ama

[coral ridge]

ef/fb oranı de/bc oranı demek zaten

de/bc = ae/ac

thales işte

@leaden hill anladın mı

[alpine sable]

How would I approach this problem in a time effective manner?

[woeful pulsar]

what is this question asking for?

is it some sort of taylor series?

[alpine sable]

Whoops, sorry

[woeful pulsar]

firstly you can ignore the x^10 and just differentiate ln(1+8x)

this should give you 8/(1+8x), which you should be able to write the taylor series for easily, which you can integrate

[alpine sable]

I will write down my work and see how it goes

Thank you for the help

[carmine lion]

i don't quite understand how im going wrong for this question

if sin(a)=-4/5 pi<a<3pi/2 and cos(b) =-5/13, pi/2<b<pi, evaluate tan(a+b)

[alpine sable]

This works beautifully

Thank you so much!

[west nimbus]

How would I solve this on a graph?

[autumn timber]

idk sorry

[twin pebble]

how does the determinant of (m-lambda*I) make the eqn 0?

[fading zephyr]

the idea is that v is not zero, and neither is M - lambda*I

the only way you can get zero out of that matrix-vector product is if the columns of M - lambda*I are linearly dependent

[round raven]

if im given f'x and f(1) how would i find fx

[twin pebble]

integrate

[round raven]

thanks

[fading zephyr]

you integrate and find the integration constant using f(1)

[round raven]

so like just substitute c for f(1)

[fading zephyr]

no

you have f'(x), let's call its antiderivative F(x)

this F(x) is equal to f(x) + c

you know f(1)

so F(1) = f(1)

for example, say f'(x) = 1

and f(1) = 10

the integral of f'(x) is x

and 1 is definitely not equal to 10

however, there's also the integration constant in there, so that F(x) = x + c

then we say F(1) = f(1)

so 1 + c = 10

or c = 9

[round raven]

thanks

[rich basin]

I'm going to need some help with this mathematical problem

[woeful pulsar]

you know the product of all 4 roots?

[rich basin]

I managed to get to when i got it to +- 2

what do you mean by products of all 4 roots?

[woeful pulsar]

nice you are ahead of where I'm suggesting

hold on while I think what to say

[rich basin]

you mean a + b +c +d = -b/a

[woeful pulsar]

though you can try factoring it into two quadratics

[rich basin]

So do I make ab = 2 and cd = -2

and then swap around with ab =2 and cd = 2

as well as ab and cd = -2

[woeful pulsar]

actually there are just two cases

[rich basin]

oh yeah, my bad

so why acn't ab and cd be positive 2

and only can be negative 2

[woeful pulsar]

$6x^4-11x^3-26x^2+22x+24=6(x^2+Ax+2)(x^2+Bx+2)$

OR

$6x^4-11x^3-26x^2+22x+24=6(x^2+Ax-2)(x^2+Bx-2)$

[rich basin]

My friend and I were wondering why it can't be negative 2

[ocean seal]

Element118

[woeful pulsar]

just need to find A and B

[rich basin]

can't really see the image

@woeful pulsar I mean why it can't be positive 2

[woeful pulsar]

erm

you have to try both cases

$6x^4-11x^3-26x^2+22x+24=6(x^2+Ax+2)(x^2+Bx+2)$

OR

$6x^4-11x^3-26x^2+22x+24=6(x^2+Ax-2)(x^2+Bx-2)$

[ocean seal]

Element118

[woeful pulsar]

hopefully it renders this time

if you can't see the image, try reading the LaTeX

[rich basin]

I don't think I have LaTeX

[strong furnace]

if you start by evaluating the condition for the sum of 3 roots taken at a time you will get k=-2

[rich basin]

what are the conditions

[strong furnace]

-22/6 = abc+bcd+cda+dab if a,b,c,d are roots

[rich basin]

yeah

[strong furnace]

assume ab = cd = k

[rich basin]

I mean is it possible if you can prove it with when you sub ab in into abcd

where ab becoem +- 2

but +2 for some reasons was rejected

[strong furnace]

we cannot make a conclusion from just abcd

[woeful pulsar]

yeah

so you need to use the rest of the polynomial to figure out

[alpine sable]

Hey I'm really confused with this question could someone help?

This is part of my working out l and it shows where I got stuck

I'm pretty sure this question makes a 4x3 by 4x1 order

Which is not defined

Ahh I'm so confused

[lament wyvern]

a looks about right

but for AX=B, X is your variables

i.e. x y z

@alpine sable

A should be n x m where n = number of equations and m = number of variables, X is then m x 1, forcing B to be n x 1

[alpine sable]

Whaat

Wait so how should I put it?

@lament wyvern

[lament wyvern]

so AX = B

if X = the column vector (x, y, z)

[alpine sable]

Hmmm?

Ahh yes

[lament wyvern]

first row of A times X gives you

$\Sigma A_{1j} x_j$

[ocean seal]

PrettyPrincessKitty FS

[lament wyvern]

which is ax + by + cz

[alpine sable]

Ahh alright

[lament wyvern]

if you write out A to be [a b c // d e f // g h i] and X to be [x // y // z] and multiply it out

you'll see it

[alpine sable]

So is question c just asking inverse of a

[lament wyvern]

C wants you to find x, y, z

[alpine sable]

Hmm

Its still not working though

It says dimension error...

[fading fern]

math is tough

[alpine sable]

@lament wyvern

[lament wyvern]

why is A a 3x4

[alpine sable]

Oh wait is that wrong

So it was right the way I had it before...

[lament wyvern]

each row corresponds to 1 equation

[alpine sable]

Yes

And x

[lament wyvern]

you have 3 rows, yet 4 equations

[alpine sable]

Is corresponding to x passengers

See on the question it has three rows

[lament wyvern]

I count 4 rows

[alpine sable]

Opos I mean four

Yep

[lament wyvern]

so your matrix should have 4 rows

[alpine sable]

And I don't see how column can rep the corresponding equations

Ok so I was right like this:

[lament wyvern]

yes

[alpine sable]

Then why isn't it working

[lament wyvern]

because it's AX=B

not XA=B

[alpine sable]

On my CAS inputs

Wait..

So my a is my x and my x is my a?

[lament wyvern]

A is a 4x3

X is a 3x1

[alpine sable]

Ues

Hmm

Could you please show me visually

[lament wyvern]

if you write out A to be [a b c // d e f // g h i] and X to be [x // y // z] and multiply it out
you'll see it

[alpine sable]

Like as in draw it Because I can't understand it sorry

I'm sorry, I just can't visualise that.

[lament wyvern]

AX=B
you have your A
you have your X
idk how else to explain it

[alpine sable]

Draw?

Pls.

[alpine sable]

Yes but I can't just do xyz

What do I put in there?

[lament wyvern]

you can, though

[alpine sable]

Woohoo.

Wait

So then

Where does the 20240

[lament wyvern]

so I've drawn it
if you do the multiplication, you'll get ax + by + cz

[alpine sable]

So where does the total taking ls go?

[lament wyvern]

where can it go?

[alpine sable]

So like this

?

@lament wyvern

Wow I'm so confused

@lament wyvern

[lament wyvern]

why are you inverting it

[alpine sable]

Because it wants a^-1

[lament wyvern]

I mean you don't need to throw it in a calculator

[alpine sable]

I'm though because it goes against what I have been learning, usually the x,y,z is just for reference and then you times the other two and invert the equation matrix

Here I'll show you

[lament wyvern]

yeah I mean maybe you've been taught different

but usually you put it in an augmented form, row reduce the matrix, read off the solution

[alpine sable]

Ignore everything above the r ed line

[lament wyvern]

ah okay, so what you're doing there is you have AX = B
A^-1AX = A^-1B
IX = A^-1B
X = A^-1B

[alpine sable]

And there's the question

Yes but I'm pretty sure that's what it's asking

Not only thAt but it's a 3x3

[lament wyvern]

yeah, how you get from AX=B to X=[thing] is c)

are we on c) now?

[alpine sable]

So idk

Yes this c

[lament wyvern]

then you know what A is

oh my bad didn't see the thing asks for a calculator

[alpine sable]

Np

[lament wyvern]

yeah you know what A is

[alpine sable]

Yes

[lament wyvern]

idk how to use a CAS to find the inverse

[alpine sable]

I do

Its just the matrix

Then

^-1

[lament wyvern]

okay, so you should be able to put that A matrix in

[alpine sable]

Matrix a ^-1

Yes

[lament wyvern]

just the A matrix, nothing else

[alpine sable]

Wait and is that it??

BRUHHH

[lament wyvern]

[alpine sable]

I asked thAt

BRUHHHHhhhHhh

[lament wyvern]

sorry, I got confused by what you were asking

[alpine sable]

Ok

Brb

Ummm

Its still NOT WORKING

@lament wyvern

[lament wyvern]

yeah sadly I have no idea how to solve that, it seems like a calculator problem

[alpine sable]

I think

Its because it's not a square matrix

[lament wyvern]

nonsquare matrices can have inverses

[alpine sable]

Therefore Its undefined

I don't think so

Because all the calculators online are asking for perfect square matrices

And wont let me modify it to 4x3

Oh well

[lament wyvern]

or rather, it has 2 inverses (if it's not singular)

[alpine sable]

Thank you anyway for your help

Oh yes true

[lament wyvern]

oh wait, no

[alpine sable]

Much appreciated

Oh wait

[lament wyvern]

yeah because the commuting makes no sense

[alpine sable]

What

[lament wyvern]

A-1A = I = AA-1
doesn't make sense for nonsquare

so then you have (A-1L)A = I = A(A-1R)

for the left and right inverses

[alpine sable]

So i was right

?

[lament wyvern]

I've gotta be honest, the question is confusing me

because A cannot be square

and yet it wants an inverse

[alpine sable]

Yes

Thats what I was getting at

Maybe it has something to do with the question

Or maybe ijt doesnt

Maybe it's an absolute giga brain equation

Anyway thanks again @lament wyvern

[lament wyvern]

np, sorry Icouldn't help more

[alpine sable]

Your time and all the other helpers is much appreciated

Np

[whole palm]

3 plus 1?

[lament wyvern]

I mean yeah you could just ignore one equation

then A is a 3x3

[oblique plinth]

btw was wondering if anyone could help me with this. unsure what where this 3/5 come from

[lament wyvern]

uh, looks like they've multiplied the entire thing in the step before by 3/3

so you get $\frac{3sin(3x)}{3.5x.cos(3x)}$

[ocean seal]

PrettyPrincessKitty FS

[lament wyvern]

then you can pull out the sin(x)/x => 1 bit

[alpine sable]

\cdot ,\sin and \cos

[lament wyvern]

ty

[pine lake]

Can someone help me with this question?

[lament wyvern]

you get 2 simultaneous equations

[pine lake]

Oh

[nocturne summit]

write the first equation in terms of powers of 3 and compare powers

[pine lake]

First equation i got x=y

Correct?

[nocturne summit]

2x+1=3y i think

[pine lake]

Uh

How

[nocturne summit]

3x3^2x=3^2x+1

[pine lake]

What

How

[low terrace]

Umm... I'm new to this server, saw this question and I hope this helps you... (Pardon the handwriting plz)

[nocturne summit]

laws of exponents
its 3x3^2x so powers will be added

[pine lake]

Thanks!

But i found the ans

Appreciate ur help

[naive plaza]

Can chi-squared test use the value 0 (zero) as the frequency?

[glass lichen]

is it an ideal gas?

If the gas is assumed ideal then the calculation is simple, if it's not assumed ideal you need the van der waals

Ok so you can assume it's ideal?

$PV=nRT\implies V=\frac{P}{nRT}$

[ocean seal]

moshill1

[glass lichen]

Yeah that's the ideal gas equation

ok so .09atm is 9.11925kPa

so then plug in all the numbers

$V=\left(\frac{9.11925}{(7.7)(8.314)(56)}\right)^{-1}$ cba to tex in the units

[ocean seal]

moshill1

[glass lichen]

realized I messed up the re-arranging

Im getting ~393L

[harsh zodiac]

How many meters are in 279 inches?

My bad

[glass lichen]

,w calculate (7.78.31456)/(9.11925)

[ocean seal]

Results provided by WolframAlpha

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

Requested by moshill1#9771

[glass lichen]

Yeah but you got on the order of 2000L, when it should be around 1/5 of that

Im saying im shit at sig figs LOL

try scientific notation?

$390=3.9\times 10^2$

[ocean seal]

moshill1

[glass lichen]

Yeah well math says the answer is 390 so I'd talk to your teacher / prof about it

[strong furnace]

significant figures play a role in approximation i don't know how exactly but you can read about it

[glass lichen]

try 400

cause i cant recall if .09 is 1 or 2

Ok so it was to 1 sig

Yeah you had 2, 1 and 2, so division takes the fewest

Yeah sig figs are just a thing you do

[strong furnace]

they help in error propagation; I think

[glass lichen]

I mean I'd want the most accuracy in error prop not a sig fig value

then round off the average and deviation

[strong furnace]

the intention is to give the most accurate approximation keeping the error propagation in mind

iirc

[glass lichen]

My 2 cents is just round appropriately / that's what I plan on teaching

yes

keep to 4 sig figs

That's my guess, yes

Well yeah, the answer is ~.301 so the answer bank is probably wrong

[brave fossil]

how do i approach the first one?

do i try get it into reduced row e form with the variables

[tough hatch]

existence of free variables means the solution isn't unique

yeah it helps to get M_2 into RREF

so you can see what the leading 1s and therefore what the leading variables are

[brave fossil]

right i'll try do that

[high gate]

Help pls

[winter bay]

That number is 0.4 and the 4 is in the tenths place

Which means whatever number is in the tenths place is divided by 10

[brave fossil]

you still there?

[tough hatch]

any progress?

[brave fossil]

i have been trying to rref it but i feel im doing smthing

wrong

is the first step to do r3/ 9-k?

[tough hatch]

did u do gauss-jordan elimination?

[brave fossil]

nope

[tough hatch]

do u know gauss-jordan elimination?

[brave fossil]

i dont know what is exactly

i might but i dont know the name

[tough hatch]

it's a method of reducing a matrix to its RREF

[brave fossil]

oh yea ik that

i just looked it up

[tough hatch]

can you show what you did

[brave fossil]

so basically first i divide R3 by 9-k to get a one in the bottom left

and i work my way to get to the rref and have values with k and h in the augmented part

umm

if i try get the ref for m1

[tough hatch]

nvm

[brave fossil]

that just gives me m2

any other ideas?

[tough hatch]

yeah

well

[ocean seal]

!superficialsicko

[tough hatch]

because otherwise there is no solution

[brave fossil]

i think i can give the solutions in terms of k and l

yeaa

[tough hatch]

assume that condition

then find the rref

so u can divide R3 by itself

[brave fossil]

by itself u mean 9-k right?

[tough hatch]

yeah

and divide 10-h by 9-k as well

[brave fossil]

and then i get z=10-h/9-k where k isnt 9

right i see

[fossil meteor]

take lcm from the lower most term

[tough hatch]

so you should get

what @brave fossil

[fossil meteor]

come in Q3 or some other which is vacant

[brave fossil]

sorry?

[tough hatch]

what's the rref

[brave fossil]

im still doing it

[tough hatch]

ayt

tell me when u're done

[brave fossil]

just to make sure im on the right track, i should get x y and z in terms of h and k right @tough hatch

after rref

[tough hatch]

x y and z are the variables you are going to classify as either leading or free

then if one of them is free

no unique solution

[brave fossil]

right gotcha

i'll try finish it hold up

[tough hatch]

?