help-26

[rugged idol]

hey everyone !

Does someone have some hint or could provide some intution on how to approach this ?
I tried but failed to find any entry point.

[rugged idol]

Only thing that I could think of was building an argument based on how many vertices an edge has to its left and right

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[boreal sand]

Hi guys can you help me with this question

[topaz sinew]

Please don't occupy multiple help channels.

[magic lake]

solve each of the questions

simplify c and d

and then look at the question again

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[winged wraith]

How would you do part b

.open

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[acoustic pecan]

oops

!msgdel

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[winged wraith]

lol

[alpine mist]

part a) doesn't put any restrictions on x or y, so that's just true for any pair of positive numbers.
Split up your fractions in b) and use that result with all the combinations of w,x,y,z until you have at least 12

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[winged wraith]

Okay thank you

[winged wraith]

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@harsh spruce Has your question been resolved?

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[long beacon]

i had this question :
number of non negative integral solutions of x1 + x2 + x3 <_ 20

i was getting 23C3
is that the correct answeR? cause the answer key says otherwise

[long beacon]

i converted the inequality into :
x1 + x2 + x3 + t = 20
and then just (r+n-1)C(r-1)

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[full kiln]

Since arcsin x has to have a restricted domain does that make it not a function

But also we know that sin inverse is conventionally the inverse function for sine so im confused

[normal tapir]

What does it mean precisely for a function to be invertible and have an inverse

[full kiln]

Range and domain switch

Reflected over y=x

[keen venture]

If someone taught you this, unlearn it. sin and arcsin are not proper inverses

[full kiln]

Function passes horizontal line test

[full kiln]

Yeah they're not proper inverses but in this case the domain is restricted to -1,1

[keen venture]

If you take sin, restrict the domain, then take the inverse, you get arcsin

So this "restricted sin" and arcsin are inverses of eachother

But "restricted sin" is not sin

[full kiln]

Ok

So to be an inverse function does it have to be defined for all x

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[unkempt osprey]

Who knows how to do Expand binomial expression and or Expanding further binomial expressions

[topaz sinew]

Please don't occupy multiple help channels.

[normal tapir]

Just ask the question

[eternal cave]

(a^2 - b^2) = (a+b)(a-b)

Use this formula to solve it yourself 👏

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[torpid wagon]

wats us p:2=2:3 and q:r=4:7 find p:q:r

[topaz sinew]

Please don't occupy multiple help channels.

[woeful drift]

!nosols

[topaz sinew]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[woeful drift]

you very much are

[torpid sparrow]

Did you help?

[woeful drift]

I think you need to read the bot message again

[torpid sparrow]

That message is telling you not to give the solution

Yes, giving the answer wont help him

[woeful drift]

Giving the majority of the steps for them isn't great either

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[glass matrix]

So i asked earlier, and i know angle 3 & 4 are congruent, but i still dont understand the n value, i know the rest, add n with the numbers and subtract with 90 to get value of Y, im just stuck

[topaz sinew]

@glass matrix Has your question been resolved?

[karmic panther]

hello

3 and 4 are congruent

[glass matrix]

hi i was scared to ping helpers

[karmic panther]

therefore
4n+8 and 3n+28 are congruent

[glass matrix]

but then how do i solve for n?

[karmic panther]

do you know algebra?

[glass matrix]

i mean just a little bit, i tried using 4n+8+3n+28, combine like terms and subtract, n ended up being 2.8 degrees

which im not sure is correct

so i got the process wrong

[karmic panther]

what is congruent?

whats the meaning of it?

[glass matrix]

equal..?

[karmic panther]

exactly

[karmic panther]

so when i say this i mean?

[glass matrix]

theyre equal?

[karmic panther]

exactly

[glass matrix]

i mean i know if i subtract them with 90 ill get the value of Y

but i just cant get a grasp of like the process of finding n

[karmic panther]

no no stop that

listen to the words we are saying

[glass matrix]

or atleast i just wanna know the formula-

[karmic panther]

4n+8 = 3n+28

[glass matrix]

ok wait can i ask

[karmic panther]

[glass matrix]

4n+8 are 3 different numbers right...

[glass matrix]

or am i getting this wrong

I just dont get it fr

[torpid wagon]

where

[karmic panther]

are you familiar with algebra?

thats my question

[glass matrix]

at this point im not sure

[karmic panther]

fair enough

[glass matrix]

im in year 8 so im just beginning

[karmic panther]

4n+8 = 3n+28

so essentially we do things to both sides

so first we subtract both sides by 3n

so 4n - 3n is 1n or just n

and 3n-3n is 0

understand?

[glass matrix]

yeah so far

[karmic panther]

and now we subtract 8 from both sides

so 8-8 is

well

and 28-8 is 20

[glass matrix]

n = 20?

[karmic panther]

yeah exactly

[glass matrix]

WHY DID IT TAKE ME THAT LONG

im so sorry

[karmic panther]

nah

[glass matrix]

thanks so much 💀

[karmic panther]

aight

[glass matrix]

.close

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[glass matrix]

.reopen

[topaz sinew]

✅

[glass matrix]

i was about to be happy until i realized

once i have n, do i add 4 and n and 8 to find the measure of angle 3?

or multiplication

[karmic panther]

multiply

if you had to add it would be 4 + n + 8

which is just 12 + n

[glass matrix]

and after that i subtract 90 degrees on either angle 3 or 4 to find the value of Y?

[karmic panther]

yes use only 1 angle

[glass matrix]

i see, thank you

.close

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[south pasture]

can someone show me a way on how to learn these things?

anyways i think i found the note for this

.close

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[obsidian pawn]

not really sure how to approach this

[topaz sinew]

@obsidian pawn Has your question been resolved?

[obsidian pawn]

.close

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[kindred arrow]

Where did I go wrong

[topaz sinew]

Please don't occupy multiple help channels.

[quaint mesa]

what are you even trying to do

[kindred arrow]

I’m finding x

But I’m so stuck

[quaint mesa]

how did you reach to 2nd last line

[kindred arrow]

Well it’s wrong im@pretty shre

I font nnow what step I messed up

[quaint mesa]

take your time with grammar and spelling

[kindred arrow]

I don’t have time

It’s really urgent

[quaint mesa]

answer this question

[kindred arrow]

So

K turned 2/cos^2x jnto 2sec^2x

But it’s wrong I think

[quaint mesa]

you just reverted it back

[kindred arrow]

Ok well what do I do

[quaint mesa]

you have 2sec^2 in original question

[kindred arrow]

Oh ok

[quaint mesa]

use tan^2+1=sec^2

[quaint mesa]

I'm not even gonna question the last line

[kindred arrow]

Up to here I get

[quaint mesa]

it will be better to use tan^2x+1=sec^2x

[kindred arrow]

Oh I’m so 2(tan^2 + 1)?

[quaint mesa]

2(tan^2+1)+tan^2-3=0 yes

[kindred arrow]

Ok

[kindred arrow]

This?

[quaint mesa]

yeah go on

[quaint mesa]

dont forget the x

[kindred arrow]

Oh ok

This next?

@quaint mesa

[quaint mesa]

why

[kindred arrow]

Why what

[quaint mesa]

just why

[kindred arrow]

Thsts wrong

Oh

Sorry

Do I factor

[quaint mesa]

how did you forget to collect like terms

[kindred arrow]

OMG IM SO DUMB

I’m so stressed

[quaint mesa]

dont stress

[kindred arrow]

How’s this sir

[quaint mesa]

why use sir lmao

[kindred arrow]

Ok scratch the sir

How’s it now

[quaint mesa]

dont forget negative

[kindred arrow]

What negative

[quaint mesa]

,w tan^2x=1/3

[thorny flame]

Results provided by WolframAlpha

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

Requested by theprophetofthedamned

[kindred arrow]

How

[quaint mesa]

tanx=-1/sqrt(3)

[kindred arrow]

My friend says those answers are good

[quaint mesa]

if x is positive then ig

[kindred arrow]

What do you mean tan could be negative

[topaz sinew]

@kindred arrow Has your question been resolved?

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[smoky sparrow]

What have you tried?

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[trim tinsel]

None of the above

[craggy haven]

okay, elaborate

[smoky sparrow]

It literally tells you what to do for this question

[trim tinsel]

Ye

But like the

The

What the hell is a partial fraction

[cursive patrol]

"partial fraction decomposition" refers to method of rewriting a rational function such as:

[craggy haven]

you almost certainly had some earlier homework exercises involving these... you should go re-do or review those, because this problem is fairly involved

[topaz sinew]

@trim tinsel Has your question been resolved?

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[sour estuary]

i dont really know how to start solving this problem, one of my friends has solved it already, and idk if she did it right or not

[sour estuary]

but id like to know how to like do it myself

this is her work

[dense ridge]

Your friend is right

[sour estuary]

for all of it/

?*

[dense ridge]

Yes

[sour estuary]

okay

can you help me understand like how to go through it though

[dense ridge]

What's your problem 🤔

[sour estuary]

wdym its this .

[dense ridge]

Can your problem be more specific ?

which statement you don't understand

[sour estuary]

uh part 1

part A

where it starts i guess

[dense ridge]

Amplitude is the distance between max height and average height
Or the distance between lowest height and average height (It's symmetric)

From the problem we know the distance between max height and lowest height
So divide it by 2 get the amplitude

[sour estuary]

8 by 4 right

[dense ridge]

？

[sour estuary]

for the amplitude

divide 8 by 4 to get amplitude

[dense ridge]

No

8 is the average height

In the problem 「the distance from the highest and lowest points is 4 feet」

So amplitude=4÷2=2feet

[sour estuary]

ohh okay

[sour estuary]

the period of the function is 24 seconds right

[dense ridge]

Yes

[sour estuary]

ok

[dense ridge]

There are 3 period of wave
The time travels 1 entire wave is period
So the distance marked by dark blue is entire wave
They are all the same
From average to average、from highest to highest、from lowest to lowest

[sour estuary]

okay

would that be it for part B

i mean part A

is this ok

[dense ridge]

This is part A
Then move to the part B

In common way
List the general form of sin wave

As your friend listed
A*sin(ωt+Φ)+b

[sour estuary]

what is this

Φ

is that the angle

sign

[dense ridge]

Φ is the phasor

[sour estuary]

whats a phasor

[dense ridge]

You can think it as some offset of the wave

[sour estuary]

is it like y= asin(bx+c) + d

isnt that the sin function

[sour estuary]

and they used cosine

[dense ridge]

This form also OK

[sour estuary]

ok

[dense ridge]

move entire wave to the left or the right
In this graph the shape of two waves are the same,but their position is not

[sour estuary]

okay, so its the parent function

[dense ridge]

Φ is the number to change the position of the wave

[sour estuary]

okay so the horizontal shift

[dense ridge]

Yes

[sour estuary]

do we use sin or cos

[dense ridge]

The both are OK
Because sinθ=cos(θ-π/2)
Horizontal shift to get another
But Φ in these two form are different

[sour estuary]

ok

what do i do next

[dense ridge]

A is amplitude
ω is angular frequency
ω=2πf
f is the frequency
And we know f=1/T
T is period
b is the average

[sour estuary]

lets just use cos

[dense ridge]

It's the same
A*cos(ωt+Φ)+b

Just the value Φ is different

[sour estuary]

y = acos(bx+c) + d works too right

because thats the formula my teacher told me to use

[dense ridge]

Yes
I just explained the meaning the variable

[sour estuary]

<@&286206848099549185>

so y = 2cos(bx + c) + d

how do we find b

[dense ridge]

This

b is ω

[sour estuary]

so what would i plug in

[dense ridge]

Didn't I type the formula here？👀

[sour estuary]

like what values do i put in

[dense ridge]

b=ω=2πf=2π/T

[sour estuary]

and t i x

is*

[dense ridge]

👀

I think it's clear enough...

[sour estuary]

for part b it says t = 0

[dense ridge]

t and T are not the same thing

[dense ridge]

t is x in your function

[sour estuary]

ok

b = pi/12

[dense ridge]

Yes

[sour estuary]

is this right

[dense ridge]

Yes but actually
There are two possible value of c
We choose one of them because of the limit of problem
Do you know?

[sour estuary]

so it could be positive and negative

[dense ridge]

Yes ±π/2 but +π/2 is not satisfied in this problem

[sour estuary]

okay

[dense ridge]

Do you know why?

[sour estuary]

uhh no

[dense ridge]

In the problem 「moves upwards after」

So when t is little bigger than 0
f(t) is larger than 8

[sour estuary]

ohh okay

so it has to be negative because it cant be above that or

[dense ridge]

When c=+π/2
cos((π/12)t+(π/2)) is negative when t is a little bigger than 0

[sour estuary]

ok

[dense ridge]

So f(t) is less than 8 in this case

[sour estuary]

what about for part c

[dense ridge]

There are two ways to compute it

FIrst one: use the function already listed

The value of cos changes as t changes

When f(t) is the lowest , the value of cos is smallest

So the min of cos is?

[sour estuary]

t?

[dense ridge]

min is minimum

what is the range of cos

[sour estuary]

-1?

[dense ridge]

Yes the minimum of cos is -1

If cosθ=-1 then θ=?

[sour estuary]

1?

[dense ridge]

Are you sure...?

[sour estuary]

uhh

is it just -1

[dense ridge]

What is the value of
cos(π/2) and cos(π)

[sour estuary]

-.5

and -1

[dense ridge]

No cos(π/2)=0

[dense ridge]

So you know the value of θ now?

[sour estuary]

oh it was in radians sorry

[sour estuary]

is it 0?

[dense ridge]

You know
cos(π/2)=0
cos(π)=-1
So θ=?

[sour estuary]

im confused

[dense ridge]

cosθ=-1

So θ=?

[sour estuary]

-1???

oh wait

pi?

[dense ridge]

Yes

Finally...

[sour estuary]

im a bit dumb

[dense ridge]

So in the function
bt+c=π

Then you can solve t

This is the first way to solve

[sour estuary]

okay

[dense ridge]

Second way

Draw the graph

[sour estuary]

pi/12t - pi/2 = pi?

[dense ridge]

Yes

The left green point is the position when t=0

The the nearest lowest point is the right green point

From the graph
What fraction of an entire wave to reach the Lowest point?

[sour estuary]

uhh

idk what you mean

[dense ridge]

The red curve is a wave in one period
along the red curve
The fraction of red curve is the distance to one green point to another?

[sour estuary]

pi/12?

[dense ridge]

Hmm....
How about left green point to the purple point

What fraction

[sour estuary]

pi/2?

[dense ridge]

I try to change my way to ask...
What is θ of the the purple point
If this is the graph of sin wave

[sour estuary]

uh i dont understand

[dense ridge]

Left green point θ=0

sin0=0 right？

[sour estuary]

yes..

is it 1

[dense ridge]

sinθ=0 then θ=0 or ?

I am little dizzy
Jump to the conclusion

The entire wave
θ from 0 to 2π

So the Lowest point
θ=3π/2

[sour estuary]

oh okay

[dense ridge]

Then two green point is 3/4 wave
So the time travels from one to another is 3/4 period
So the answer is (3/4)×24=18(seconds)

[sour estuary]

okay thank you

.close

[topaz sinew]

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[heady goblet]

could someone explain plz how they got P=2

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[small lagoon]

what is the formula for trilateration in 3d, I can find formula online for 2d, but not 3d. I have 3 known points and those points respective distance to a unknown point
Also how do I use the formula, just plug in numbers??

[mental basin]

you cannot trilaterate in 3d space

or rather, you can, but you will get 2 possible points in space

you would need 4 known distances to determine a location in any 3d space

to visualize: just as two circles on a plane can jntersect in 2 points, but 3 circles (of different origin) can only intersect in one, try imagining the same scenario with 3d spheres

[small lagoon]

ahh okay, that explains it

[mental basin]

In application, you usually can use 3 points

if, you trilaterate ie. from sattelites in space, then one of those 2 intersection points will lie off the surface of earth, even further into space than the sattelites, and thus your GPS can assume that you'll be at the other one.

[small lagoon]

but for math, in order to objectivly find 1 point you need 4 points?

[mental basin]

correct.
You can generalize this

for an n-dimensional space, you need n+1 points

on a line (1 dimension) the distance to 2 points is sufficient

[small lagoon]

ohh, ive heard about that with shadows, ex a 4th dimensional object's shadow is 3d

[mental basin]

in 15d space (whatever that means), you'd need 16 points

[mental basin]

this one should be intuitive. Take the number line. If I tell you my number is "a distance of 4 from the point x=5" then that could be 1 or 9

[small lagoon]

oh thats like |x|

[mental basin]

if I also tell you the distance from 10 tho, then you're suddenly certain of which point I'm talking about

[small lagoon]

oki, that makes more sense

just 1 more question, i still would like a formula

is that even a thing for trilateration?

[junior pumice]

you said there is an unknown point you must find. what if you consider this point as the center of the region sharing space with all 3 spheres?

[small lagoon]

then wouldent you have like, multiple points

?

[junior pumice]

do you have a specific problem, or you were just curious about 3d trilateration?

[small lagoon]

I code c++, and am trying to figure out a way to do it

just a passion project tho

[junior pumice]

from wiki

In three-dimensional geometry, when it is known that a point lies on the surfaces of three spheres, then the centers of the three spheres along with their radii also provide sufficient information to narrow the possible locations down to no more than two (unless the centers lie on a straight line).

[mental basin]

you have points A, B, C, D in 3d space

and your distances a, b, c, d from each point

construct a sphere centered on A with radius a

and a sphere centered on B with radius b

these will either not intersect (which means you made a measurement mistake, if quadrilateration is possible they WILL intersect)
or they intersect in the shape of a circle

specifically, a circle on a plane perpendicular to line AB

[small lagoon]

ill try that

[mental basin]

then create a sphere centered on C with radius c

[mental basin]

it will intersect with that circle in 2 points

check which point lies on the sphere around D with radius d

that is your position

[mental basin]

what do your point/distance parameters look like?

a struct of {x,y,z} for the points and a float for distance?

[small lagoon]

std::vector<Point3D> knownPoints = {
{1, 4, 2}, // Coordinates of first known point
{2, 5, 4}, // Coordinates of second known point
{7, 4, 2}, // Coordinates of third known point
{1, 4, 5} // Coordinates of fourth known point
};

std::vector<double> distances = {
    3,            // Distance from first known point to unknown point
    std::sqrt(2), // Distance from second known point to unknown point
    std::sqrt(21),// Distance from third known point to unknown point
    std::sqrt(6)  // Distance from fourth known point to unknown point
};

actually i maybe found why it wont work

if it rounds the sqrt's, its just gonna... break

[junior pumice]

https://github.com/kwikius/Trilateration/tree/master

[mental basin]

so to construct a sphere in {x,y,z} space on point {a,b,c} with radius r

[junior pumice]

both in C++ and openscad

[mental basin]

you would select all points for which (x-a)²+(y-b)²+(z-c)²=r²

[junior pumice]

is Point3D a type you made yourself? if not, whatever library you are using should have some handy functions to help you with 3d calculations

[small lagoon]

point 3D is a struct i made myself

im gonna double check that my points can even quadrilaterate

[mental basin]

the computationally efficient way is probably applying a transform to have A lie on the origin, rotate B onto the x axis then work in transformed space using linear calculation before transforming your result back

a possible example implementation is something like this
https://github.com/kwikius/Trilateration/blob/master/trilateration.cpp

(not my work)

[small lagoon]

yeah, currently trying to figure out that

gonna download a library rq

[junior pumice]

found a stackoverflow answer that explains step by step

https://stackoverflow.com/questions/16176656/trilateration-and-locating-the-point-x-y-z

you're solving a system, so you have a bit of freedom in how you go about it

[mental basin]

if you wish to be efficient about it, you should break it down to a linear system in analytical form in your code and then solve that using an LR (Cholesky?) decomposition at runtime

no sure if Cholesky would work in the general case, if so that's faster, if not, use any LR decomp.

[junior pumice]

yep, linear algebra will be the best way to do this.

[small lagoon]

how does that work?

ideally instead of trying the computer to process a 3d image, it could just plug in numbers

[junior pumice]

taht is what a 3d image is

3d image is a projection and loads of linear computations

[mental basin]

https://en.wikipedia.org/wiki/LU_decomposition
https://en.wikipedia.org/wiki/Cholesky_decomposition

there's a reason people use existing libraries for this btw

[junior pumice]

LAPACK comes to mind

[small lagoon]

i have so many tabs 😭

[junior pumice]

welcome to programming

[small lagoon]

do yall code?

[mental basin]

yes

[junior pumice]

in todays world, programming is pretty embedded in most sciences, and math is the great unifier of all of them.,

if you are going to continue work in 3D, i highly suggest learning the basics of graphics programming and enough linear algebra to solve a 4x4 matrix by hand.

[small lagoon]

slightly off topic question, as you may have guessed im 'fairly' new to coding, and have never used github

if you dont have time its fine, but how would one download a library from github?

[mental basin]

basic numerical analysis as it applies to matrices and systems of linear equations will also come in handy, since with a floating-point number of limited precision, you're working with approximations by default

[junior pumice]

normalization is extremely common in graphics as well

so a lot of [-1, 1] and [0, 1]

[small lagoon]

i may just go down this whole conversation and take like 10 pictures

i cant internalize this much XD

[junior pumice]

well, unfortunately the reality is that 3D computation gets very complex very fast. there's a lot of math involved in matrices and their properties.

[small lagoon]

yeah

[junior pumice]

linear algebra is pretty much required. you need to be familiar with not just number spaces, but function spaces.

[small lagoon]

i tried brute forcing the quadratillation by finding every point on the outer line of each triangle and seeing if there are any that all are the same but jeez

360^4 combinations does not look appealing

[junior pumice]

thats why linear algebra is the key. it vastly simplifies a lot of very difficult problems

https://learnopengl.com/Getting-started/Transformations

[small lagoon]

im first gonna try the github, then ill cry and learn linear algebra

[junior pumice]

you could try and get by through just learning graphics

but you'll realize quickly there's gonna be math no matter what

[small lagoon]

lmao

ill try a few things

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[small lagoon]

o/

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[merry mason]

And I have a question where he solves with the other formula which doesn't match with this one and the answer ends up right but using this derived formula, the answer turns to be wrong

I'm confused over which formula is right coz before this question I used to think derived formula is instead right

.close

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[merry mason]

Yes

I thought I won't get an answer to this so I wanted to skip but if you can help it then I'd be very glad

Lol okay

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[oblique bloom]

Find the eccentricity and the equation of the directrix for the following equation. Identify and sketch the conic section.

r=4/(5 - 4 sin (theta))

I would like to get a second opinion on whether my answer and working is correct

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[distant linden]

Is this the correct way to find the derivative

[worthy storm]

almost

why is it -cos

[distant linden]

I tried to find the derivative of sin2x

so I assumed

[worthy storm]

derivative of sin is +cos, not -cos

aside from that it's correct

[distant linden]

ohhh

ok ty

.close

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[half pike]

can someone help me with the first one

like do i use law to cosine or sine or sin cos tan

and also for the second one, how do i only solve for the cos theta

like how do i type that into my calculator

[acoustic pecan]

you would use soh cah toa for 1, at least thats one way

[half pike]

so like tan to get CD

[acoustic pecan]

the second one look cosine ruley

[half pike]

yeaa

wait so i got 13 when i did tan for CD

then i did tan(x)=13/10

how do i put it into a calculator so that it’ll give me a degree

[acoustic pecan]

tan(41)=y/15 tan(x)=y/10 15tan(41)=10tan(x)

[half pike]

wait does tan(13/10) = x work?

[acoustic pecan]

uh, you mean arctan?

[half pike]

yes

ohhh

[acoustic pecan]

where did 13/10 come from btw

[half pike]

from CD

it’s 13.04

[acoustic pecan]

elaborate

[half pike]

i did tan(41)=y/15

[acoustic pecan]

,calc tan(41pi/180)

[thorny flame]

Result:

0.86928673781623

[half pike]

oh

[acoustic pecan]

,calc tan(41pi/180)*15/10

[thorny flame]

Result:

1.3039301067243

[acoustic pecan]

is tanx

[half pike]

?

[half pike]

it’s ok i figured it out. for the second question, how do i solve for cos theta with my calculator?

do i need to do arccos or smth?

[acoustic pecan]

that would get rid of cos

which it asks you not to do

just set up the cosine rule, make cos the subject

hey presto

[half pike]

sorry

[half pike]

wdym?

[half pike]

oh so how do i get rid of it

do the formula but remove the cos?

im confused

[acoustic pecan]

it never asks you to get rid of it

it literally wants you to find it

[half pike]

oh mb

i mean how do i keep it

[acoustic pecan]

by not getting rid of it

just set up the cosine rule

[half pike]

i did

but how do i keep the cos

[half pike]

is it like 2^2 = 4^2 + 5^2 - 2(4)(5) * theta

[acoustic pecan]

your numbers are in the wrong places, look again

[half pike]

4^2 = 2^2 + 5^2 - 2(2)(5) cos theta?

[acoustic pecan]

good

[half pike]

then what

[acoustic pecan]

do what it asked you to do

[half pike]

but if i solve for it i get theta

not cos theta

[acoustic pecan]

you get three of those

just solve for cos theta

im not sure why you can solve for theta but not cos theta

you have to do one to do the other

[half pike]

bro i srsly dont get it 😭

im so confused

can you show me an example

[acoustic pecan]

so if i said solve 12+5y-2cos(x)=4 for cos(x), you couldnt do that?

[half pike]

yea

idk how to solve for that

[acoustic pecan]

but if i asked you to solve for y youd have no issue?

[half pike]

yea if i knew what x is

[acoustic pecan]

that is odd

12+5y-2cos(x)=4 so 8+5y=2cos(x), cos(x)=4+5y/2, done

you dont need to know what anything is to rearrange an equation

if i had 2a+3b+5c+7d+35543z=34p+9q, i could still solve for d

it just means making it into d=...

[half pike]

so fr the other question, its 4^2 - 2^2 - 5^2 / 2(2)(5) = cos theta?

[acoustic pecan]

brackets!, but yeah, thats all

[half pike]

where should the brackets go?

[acoustic pecan]

actually you have a sign issue too

give it another go, be careful

[half pike]

4^2 - 2^2 - 5^2 / 2 (-2)(-5)?

[acoustic pecan]

still a sign issue

and brackets around the numerator

[half pike]

is it in the numerator?

[acoustic pecan]

well, its in the denominator technically speaking

[half pike]

is it suppose to be like 2/-2/-5

[acoustic pecan]

idk what you mean by that

[half pike]

like the -2(2)(5)

is it that part?

[acoustic pecan]

a^2=b^2+c^2-2bc cos(A)

[acoustic pecan]

yes

cos(A)=[b^2+c^2-a^2]/[2bc]

[half pike]

ohh

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[cunning yacht]

any kind soul wanna help me with

[cunning yacht]

never mind got it

can help this

why this incorredct?

[normal tapir]

you forgot to square y+5

[cursive mango]

And you don’t have an equal sign lol

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@cunning yacht Has your question been resolved?

[cunning yacht]

how was this incorrect?

[normal tapir]

whatever that expression evaluates to is the radius

not the equation of the sphere

[cunning yacht]

how would I get the equation of the sphere from what ive done so far?

[normal tapir]

equate this to the square of the radius

[cunning yacht]

like = (value) ?

[normal tapir]

yes

[cunning yacht]

would the value be r^2?

[normal tapir]

yes

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[fathom sequoia]

can some1 help me with B

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[fathom sequoia]

so look i have a question

i evaluated k'(x) at x= 4

and got a negative answer

so i said because k'(x) is decreasing, it implies that its concave down

am i right?

[remote agate]

increasing and decreasing has no correlation with concavity

for concavity you check the second derivative

[fathom sequoia]

see 4b

i think it does

[remote agate]

from x=4 to x=6, the function is decreasing but concave upwards

[glacial adder]

you have to check the second derivative

[fathom sequoia]

but its concave down tho

[glacial adder]

a function can be decreasing and concave up

or decreasing and concave down

first derivative doesn’t say anything about the concavity

[remote agate]

think of a rice bowl, a rice bowl is concave upwards

a cave is concave downwards

[fathom sequoia]

see

[remote agate]

f’ is decreasing, not f is decreasing

[glacial adder]

f’ is decreasing

not f

f’ is decreasing means f’’ is negative

[remote agate]

what is the marking scheme on about tho

[glacial adder]

but f is decreasing only implies that f’ is negative

not anything about f’’

[remote agate]

it thinks (4,6) is part of the answer?

[glacial adder]

it is

cuz that was the graph of f’

[fathom sequoia]

i dont get it

[remote agate]

I’m sorry I’m braindead

[fathom sequoia]

@remote agate

can you please explain

@glacial adder

[remote agate]

the graph shown is f’

not f

so when f’ decreases, f’’ is negative so f is concave downwards in those intervals

[fathom sequoia]

oh

but to know if "f'" is concave down

i must find f''

but if f' is decreasing then f is concave down?

this is confuring

confusing

[remote agate]

yes

just evaluate k”(4) and if it’s positive then it’s concave up, negative then it’s concave down

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[wraith frigate]

a submarine is under 1mil pascal of pressure underwater
its windows dimensions are 25 * 20 cm , how much energy (newton ) is being put on the window

[wraith frigate]

i just need

the solution

ill do the math

[wheat grove]

energy does not come in newtons

[wraith frigate]

idfk thats what the question is wanting me to answer

[wheat grove]

im sorry, we dont give out solutions

[wraith frigate]

like just hints on how to solve it?!

[wheat grove]

!original

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[wraith frigate]

i mean

ok

ill post the original question ( its not in english )

[wraith frigate]

basicaly this*

[wheat grove]

do you think they mean force?

[wraith frigate]

ill guess we go by force

yea ok

do i just do 1mil/25 * 20 or is there a specifiec solution for it

[wheat grove]

what is the orientation of the window?

[wraith frigate]

so like only 200 pascal of pressure on the window?!!?

doesnt sound that right

[wraith frigate]

?

the dimensions are

25 cm and 20 cm

basically 500 cm^2

is the surface area

[wheat grove]

the pressure is 10^6 Pa, no?

[wraith frigate]

yea 200 wouldnt make that much of a sense

[wheat grove]

keep things in SI

[wraith frigate]

yes

[wheat grove]

you've been given what pressure is in the question

[wheat grove]

so i dont know where you got that from

[wraith frigate]

1 mil divided by 500

its stupid

ik

[wheat grove]

why?

[wraith frigate]

forget it

[wheat grove]

Pressure is force acting per unit area, right?`(when force is constant)

according to basic definition

[wheat grove]

no tell me why you did that, so we know why you made that mistake

[wraith frigate]

i lack the brain

so uhh

[wheat grove]

have you see this formula

P = F/A

[wraith frigate]

what was F again

[wheat grove]

Force

[wraith frigate]

right

force / area

= pressure

[wheat grove]

sorry for capitalistion

[wraith frigate]

np

[wheat grove]

yes yes

you want to find force right

[wraith frigate]

yes

so like

pressure is 1 mil so F / 500 has to be 1 mil

is that right

[wheat grove]

no

[wraith frigate]

oh

[wheat grove]

tiny error there

500 is your area in cm^2

[wraith frigate]

oh right it has to be in m^2

[wheat grove]

if you want to find force in newtons, use SI units

[wheat grove]

yes

you should convert that

[wraith frigate]

so its

0.05 m^2?!

[wheat grove]

yes

[wraith frigate]

and then 1 mil has to be F / 0.05

so force has to be 50k

newtones

[wheat grove]

yes looks like it

[wraith frigate]

right

thx

catagree

[wheat grove]

you are welcome

[wraith frigate]

.close

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[weak fable]

Really simple question but

[weak fable]

What is the difference between

5.8 Sin (Pi/6 (6+1)) + 16

and

5.8 Sin ((Pi/6 )(6+1)) + 16

I get different answers on my calculater

[versed cairn]

first one is $$\frac{\pi}{6(6+1)}$$ second one is $$\frac{\pi}{6} \times (6+1)$$

[thorny flame]

JustToPro

[weak fable]

ohhhhh

That makes sense

Thank you very much :))

[versed cairn]

np

[weak fable]

.close

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[solid marsh]

how can you approach this question without using the sec trigs?? i’ve put the answer below it

[ivory sorrel]

wdym sec trigs, you don't want to use tan(x)=u?

[solid marsh]

idk i tried searching it on an website but it keeps giving me sec x = 1 / cos x. to solve it

and i’ve not learned that

[ivory sorrel]

can you re-write this in terms of sec(x) and tan(x)

[ivory sorrel]

wdym, you haven't learnt that

that sub, or sec(x) in general

[solid marsh]

nope..

it’s not learn in my school

just cos tan sin

[ivory sorrel]

better learn it, it's very useful

you can't solve a lot of trig problems without sec(x)

[versed cairn]

change tan into sin/cos then
sin^3/cos^5
sin^2 = 1-cos^2
1-cos^2/cos^5 * sin

and then u sub

[solid marsh]

okay i’ll try this

[versed cairn]

also its best to learn sec/cot/cosec

[solid marsh]

for some reason we still haven’t learnt it and i’m still like at highschool level

[versed cairn]

dont u learn it with the rest of trignometry?

[ivory sorrel]

this should have been covered before you started integral calculus

[solid marsh]

like it’s never been required for us

[versed cairn]

so what do u do when u are asked to find derivative of tanx?

change into sin/cos and then quotient rule?

[solid marsh]

that’s the long way they give, instead we were given quick answer to that like (1 + tan^2 x) and ( 1/cos^2 x)

[ivory sorrel]

sec(x)=1/cos(x)

that's it

[solid marsh]

that is what pops up for me but we’ve never covered that in class

that nor csc and cot

[solid marsh]

this helped thanks!!!

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[rich wolf]

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[neon iron]

im getting 6.6 x 6.6 x 3.3

but the ans is 6x6x4

[restive inlet]

reading the clarification in ()
no netting is needed for the ground

so you should only have 3xy, not 4xy

[neon iron]

mm

thanks

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[polar drum]

is this matrix regular?

[polar drum]

since

but

[odd pagoda]

well it just didnt simplify it fully for some reason

but thats the identity matrix

[polar drum]

ah nice so its regular then?

[odd pagoda]

well as long as you can divide by a^2+b^2

[polar drum]

hm can i?

they are components of complex number

z=a+bi

yes i have non zero complex number

so i can

[odd pagoda]

can a^2+b^2=0? thats the only problem you could have

[polar drum]

yes

it can not

so thx a lot

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[lilac whale]

I'm doing some abstract algebra HW and I think I proved these two properties as lemmas in a larger proof, but before I continue I want to make sure this is correct. Can anyone verify that these two properties are true?:

1. Quotient rings of Principle Ideal Domains (PIDs) are PIDs
2. The only submodules of a PID (over itself) are its ideals

[lilac whale]

<@&286206848099549185>

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[native moth]

How about sharing your proofs?

It will illuminate better if you solved it right

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[stuck cedar]

semicircle (O; R), diameter AB, Ax is the tangent at A, point M of Ax so that AM > R, MB intersects the semicircle at K, perpendicular line goes through A, perpendicular to MO at I, AI intersects the semicircle at C, perpendicular line CH is perpendicular to AB, CH intersects MB at N

[stuck cedar]

1. prove that a circle that goes through A, I, K, M exists
2. angle IKB = angle ACH, IN // AB

3. a line that goes through H and is parallel to AC, intersects with BI at P
   prove that NP is perpendicular to AC

so far I have only solved 1)

[eternal cave]

Hows M is defined?

H too

Or M is just a random point on that line?

[stuck cedar]

M is just a random point on that line, H is relative to C, which is relative to AI, which is relative to MO which is relative to M

also a random point on that line such that AM is greater than the radius

[eternal cave]

H relatives to C how?

Oh

AI perpendicular to MO

[stuck cedar]

yes

[stuck cedar]

heres the figure for 3)

[eternal cave]

For 1

I will give u the way to solve it

To prove there's a circle goes through A I K M, u just need to prove there's a point, let called it Z, such that ZA = ZI = ZK = ZM

We can clearly see if ZA = ZM this must mean Z is the mid point of AM

Then u just seperate triangle MIA which has angle I = 90deg; which mean ZI = ZA = ZM

Then prove AK is perpendicular to MB

[stuck cedar]

oh I solved 1 already

i was asking for 2

[eternal cave]

Bruh

[stuck cedar]

.

[eternal cave]

For 2

[stuck cedar]

2. angle IKB = angle ACH, IN // AB

[eternal cave]

IN // AB

And

[stuck cedar]

I connected IN

hope that helps

[eternal cave]

Hmm

We need to prove that KI is perpendicular to IN

[stuck cedar]

yea

oh I figured it out!!!

[eternal cave]

HOWW????

[stuck cedar]

here I will draw it out, writing is too hard

[eternal cave]

Im thinking about using the beta angle but its a bit complicated

[stuck cedar]

Ok I had housework to do sorry so

I dont know the 'sd' term in English

but since MAI is an angle formed by the tangent and AC, ABC is an angle formed by 3 points that lie on the circle

you probably know

@eternal cave

[eternal cave]

sđ?

[stuck cedar]

yes

[eternal cave]

whats thats?

[stuck cedar]

circular measure or something, its in my native language

[eternal cave]

Whats ur native language?

[stuck cedar]

Vietnamese.

[eternal cave]

vãi :)))

[stuck cedar]

alright

[eternal cave]

Toán lớp 9?

[stuck cedar]

đúng

số đo cung

[eternal cave]

Lâu rồi ko đụng hình học cái quên ngang

:(((

[stuck cedar]

Ok, thế còn 3) thì sao

[stuck cedar]

.

[stuck cedar]

hình

[eternal cave]

cchứng minh NP vuông với đường H

Ê để chỉ thằng này cái

[stuck cedar]

sao

cchứng minh NP vuông góc AC

tthôi kệ đi, 3) là câu nâng cao, cô giáo không chửi đâu :)

thế thôi nhá

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[true spindle]

would the solution to all of the upper bounds, lower inf, etc be dne because every coord on the unit circle squared is 1?

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[true spindle]

<@&286206848099549185>

[thorny flame]

Pratham_Shetty

[normal tapir]

how is your ordering of R^2 defined

[true spindle]

just the cartesian product of R^2

R x R

i mean

so x,y x in R y in R

[normal tapir]

you need a way to compare elements

[remote agate]

how would you compare something like (1,0) and (0,1)

[normal tapir]

the usual relation is (a,b) < (c,d) if a < c or (a = c and b < d)

[true spindle]

im confused

[normal tapir]

like are you just training an ai model yourself

or do you just copy paste into chat gpt

[normal tapir]

you need a partial order on your set

in order to even be able to talk about bounds

in R, the normal partial order that's used is less than equal to

so it makes sense to say something like 5 <= 10

in R^2