#geometry-and-trigonometry | Mathematics | Page 376

trim gust Mar 3, 2022, 2:30 AM

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and I dont know how to find the radius

wintry tundra Mar 3, 2022, 2:30 AM

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give me a moment

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i think i understand now

trim gust Mar 3, 2022, 2:30 AM

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the width I just sent u would reduce to 4inches

wintry tundra Mar 3, 2022, 2:30 AM

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the width wouldnt reduce

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or would it

trim gust Mar 3, 2022, 2:30 AM

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like the length mb

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the length would reduce

wintry tundra Mar 3, 2022, 2:31 AM

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so ur making a parallelogram now

trim gust Mar 3, 2022, 2:31 AM

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no

wintry tundra Mar 3, 2022, 2:31 AM

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with major distance of 4.5 and minor distance of 4

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i mean the circle would eventually have to converge with the square

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and continue straight

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oh shit you might need a diffeq for this

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wack

trim gust Mar 3, 2022, 2:34 AM

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wintry tundra Mar 3, 2022, 2:34 AM

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trim gust

why cant you just trial and error this?

trim gust Mar 3, 2022, 2:34 AM

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cause it has to be precise

soft marten Mar 3, 2022, 2:34 AM

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help

wintry tundra Mar 3, 2022, 2:34 AM

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exact?

trim gust Mar 3, 2022, 2:34 AM

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yes exact

wintry tundra Mar 3, 2022, 2:34 AM

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huh

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as someone who does mech eng i doubt that but eh

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ill go with it

trim gust Mar 3, 2022, 2:35 AM

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my teacher takes off marks if its not at the right measurement

wintry tundra Mar 3, 2022, 2:35 AM

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ohhh

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this is school

trim gust Mar 3, 2022, 2:35 AM

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ill try to help skibidy

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yes

wintry tundra Mar 3, 2022, 2:35 AM

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yeah u help skibidy

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@trim gust i found it

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do u want me to explain the process or just give the exact number

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@trim gust u still there?

trim gust Mar 3, 2022, 2:47 AM

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yes I am sorry just finished skibidys thing

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yes Im curious about the process

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also @soft marten

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lmk if u need any explanation of the proof

wintry tundra Mar 3, 2022, 2:48 AM

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alright i can vc now so hop in math vc

trim gust Mar 3, 2022, 2:48 AM

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kk coming

soft marten Mar 3, 2022, 3:59 AM

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@trim gust howd u get c for 3x

warped ginkgo Mar 3, 2022, 4:10 AM

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If you want answet in cos and sin ,then change sec cosec in 1/cos , 1/sin then do calculation you will get your answer

fallen sleet Mar 3, 2022, 9:19 AM

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proof of corresponding angles theorem anyone pls

fiery jolt Mar 3, 2022, 12:14 PM

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Absolutely no idea

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Anyone can help?

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For 30 and 31

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This is only level 3 but i already cant do it

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There is like 5 levels

upper karma Mar 3, 2022, 1:14 PM

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.

hoary karma Mar 3, 2022, 5:42 PM

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help you need to find x

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o wait

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there

grave pond Mar 3, 2022, 6:02 PM

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The two angles being pointed to is the two acute angles in an right triangle. Hopefully you know what their sum ought to be ...

hoary karma Mar 3, 2022, 6:04 PM

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1

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🙂

hoary karma Mar 3, 2022, 6:20 PM

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i just need someone to solve so i can add this to notes

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hoary karma Mar 3, 2022, 7:17 PM

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actually

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i want someone to help with these

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find the variables

storm portal Mar 3, 2022, 7:30 PM

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hoary karma

What have you tried? And don't ask in multiple channels

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We don't just solve stuff for you.

jovial shale Mar 3, 2022, 8:08 PM

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^

sand zodiac Mar 3, 2022, 9:35 PM

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hoary karma

I can help you but Im not going to solve this for you and simply give you the answer.

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Knowing that the top and bottom lines are parallel

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What angle theorem can help you corrolate the angle 3x and angle x+2 ?

wintry tundra Mar 4, 2022, 12:52 AM

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Does it have direction?

upper karma Mar 4, 2022, 12:52 AM

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wintry tundra Does it have direction?

Outwards id imagine

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If you’re scaling something either you’re expanding or compressing it

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Depending on the scale factor itself

wintry tundra Mar 4, 2022, 1:33 AM

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hoary karma 1

Uh

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90

wintry tundra Mar 4, 2022, 1:33 AM

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upper karma Outwards id imagine

I mean not really

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Outwards isn't a direction if outwards is different directions for multiple different sides

vagrant ore Mar 4, 2022, 2:12 AM

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I'm stuck on this

upper karma Mar 4, 2022, 2:12 AM

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wintry tundra Outwards isn't a direction if outwards is different directions for multiple diff...

"If you’re scaling something either you’re expanding or compressing it"

wintry tundra Mar 4, 2022, 2:13 AM

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Yes but

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A vector has a specific magnitude and a specific direction

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A scalar just has a magnitude I think

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Because think about it

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If I am scaling a square by 2

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The left side is going to the left more

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And the right side is going to the right more

strange reef Mar 4, 2022, 2:55 AM

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Why is this a valid explanation for the second part of this question?

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The only way I could figure this out was by solving for the time it would take the boat and sub to reach the point where their paths crossed

jovial pendant Mar 4, 2022, 4:22 AM

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vagrant ore I'm stuck on this

similar sides are given so you can do either side1/side2 = area1/area2 or you can do side1/area1 = side2/area2

vagrant ore Mar 4, 2022, 4:25 AM

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I got it thanks :)

safe mantle Mar 4, 2022, 7:35 AM

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please how do i do this

nocturne remnant Mar 4, 2022, 9:16 AM

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Actually drawing out the triangle would help considerably

dry wren Mar 4, 2022, 2:12 PM

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draw the triangle and then apply the def of tangent

woeful needle Mar 4, 2022, 2:33 PM

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upper merlin Mar 4, 2022, 6:30 PM

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I feel like there's something silly I'm missing in here

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there's probably some bash with trig and stewart's

dark sparrow Mar 4, 2022, 6:44 PM

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are you sure you can't do it with some vector shit

sullen forum Mar 4, 2022, 8:16 PM

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fossil nebula Mar 4, 2022, 8:55 PM

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pls dm if u can help

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im so dumb

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bruh

spare delta Mar 4, 2022, 9:00 PM

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upper merlin I feel like there's something silly I'm missing in here

yeah i reckon vectors is the best approach here

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broadly what you want to do is
let AC = c; AB = b
express AE and AF in terms of b and c
then try to find how far G is along FE

jovial pendant Mar 4, 2022, 9:49 PM

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fossil nebula

Just use tangent

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Tan(θ)=O/A

near sand Mar 4, 2022, 10:13 PM

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Does anyone know what this is asking me to do?

grave pond Mar 4, 2022, 10:17 PM

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Generally, be clever and find an argument tailored to each shape.

near sand Mar 4, 2022, 10:17 PM

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Do I show that there are n-gons in each shape?

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Like separate them?

grave pond Mar 4, 2022, 10:18 PM

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What I'm saying is I don't think there's a meaningfully common approach between the three parts.

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(Other than perhaps draw the tilings, though that won't feel like much of a proof.

soft marten Mar 4, 2022, 10:19 PM

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what is the altitude

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i dont understand

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I get the hypotenuse part but not the alittude

near sand Mar 4, 2022, 10:20 PM

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grave pond (Other than perhaps draw the tilings, though that won't feel like much of a _pro...

Does it have to be a proof?

grave pond Mar 4, 2022, 10:21 PM

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Hmm, I suppose "show" does sound like a diagram of the tiling would suffice :-)

near sand Mar 4, 2022, 10:21 PM

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I believe a fundamental region is all the tiles in a plane tiling congruent to that single region

grave pond Mar 4, 2022, 10:22 PM

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Yes.

soft marten Mar 4, 2022, 10:23 PM

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what is altitude in geometric mean

grave pond Mar 4, 2022, 10:24 PM

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soft marten what is altitude in geometric mean

An "altitude" in a triangle is a line through one of the corners that is perpendicular to the opposite side.

soft marten Mar 4, 2022, 10:24 PM

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im stuck with this

near sand Mar 4, 2022, 10:24 PM

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So like, I'm still not sure what to do with the problems. I'm thinking of showing multiple n-gons in each shape, but do you think that would suffice?

soft marten Mar 4, 2022, 10:25 PM

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so the altitude would be red line

grave pond Mar 4, 2022, 10:25 PM

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soft marten so the altitude would be red line

Yes, and this divides the large triangle into two similar triangles.

soft marten Mar 4, 2022, 10:25 PM

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oh ok ty

grave pond Mar 4, 2022, 10:26 PM

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near sand So like, I'm still not sure what to do with the problems. I'm thinking of showin...

No, you shouldn't attempt to subdivide the given shape. You should show that multiple copies of them can be combined such that they tile the plane.

near sand Mar 4, 2022, 10:26 PM

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So turn this shape into a tile of multiple shapes

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Like they did here?

grave pond Mar 4, 2022, 10:28 PM

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Hmm, I don't see the connection

near sand Mar 4, 2022, 10:29 PM

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Well I meant the whole tiling thing

grave pond Mar 4, 2022, 10:30 PM

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The shapes you see in the problem are the tiles.

near sand Mar 4, 2022, 10:30 PM

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Oh okay

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I'm not sure still of what I'm supposed to do

near sand Mar 4, 2022, 10:31 PM

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grave pond No, you shouldn't attempt to _subdivide_ the given shape. You should show that _...

I'm tiling the fundamental region in a plane of them? Not tiling but combining multiple of them?

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Like this?

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Ngl drawing that was kinda satisfying

grave pond Mar 4, 2022, 10:34 PM

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Yes!

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And those hexagons can then be repeated to tile the entire plane.

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So you're tiling the plane.

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Not tiling the given shapes.

near sand Mar 4, 2022, 10:34 PM

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Ohh okay, I would wanna continue drawing em but that's a lot of work. Do you think explaining this whole idea would work?

grave pond Mar 4, 2022, 10:36 PM

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Yeah. You can't avoid being a bit hand-wavy anyway because the figure in the problem doesn't rigorously state that the notches have the same shape and size anyway. :-)

near sand Mar 4, 2022, 10:36 PM

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Ah okay

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@grave pond hi sorry about the ping but quick question about this shape. Am I combining them in the right way? I keep trying many combos but am not getting something that looks right

grave pond Mar 4, 2022, 10:45 PM

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Yeah, pretty sure that is the intention.

near sand Mar 4, 2022, 10:45 PM

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Oh okay

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Thank you

grave pond Mar 4, 2022, 10:46 PM

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For the third one you'll probably want graph paper :-)

near sand Mar 4, 2022, 10:51 PM

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My professor didn't want us to do the third thankfully

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ChillBar_pray

near sand Mar 4, 2022, 11:10 PM

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What does it mean for a semi regular tiling has order 1 or order 2? Apparently in my textbook, these Kepler tilings are of order 1.

upper merlin Mar 5, 2022, 3:59 AM

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dark sparrow are you sure you can't do it with some vector shit

idk about vectors 😦

upper karma Mar 5, 2022, 9:07 AM

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woeful needle

alpha and beta are the roots of asinx+bcosx. you have to sub in both of those values and subtract the two equations to get a(cos(alpha)-cos(beta)) +b( sin(alpha)-sin(beta)) = 0

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we then use the sin(a)-sin(b) and cos(a)-cos(b) formulas

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we then get tan (alpha+beta/2)

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then use the equations relating sin2x and cos2x to tanx

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which... if u dont know... can be derived easily by dividing the standard formulas of sin2x and cos2x by cos^2x +sin^2x

woeful needle Mar 6, 2022, 9:00 AM

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tender moss Mar 6, 2022, 9:02 AM

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does bisector line starts from one of vertex of polygon that splits it into equal area always passes through the centroid?

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im getting both yes and no by googling

woeful needle Mar 6, 2022, 9:04 AM

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It will form a parabola right

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Something like this we need to find y

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But unable to

muted sparrow Mar 6, 2022, 10:00 AM

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If I have a convex polygon, does a line starting at one of the vertices $v_i$ and passing through $\frac{1}{N}\sum_{k=1}^Nv_k$ halve the polygon's area?

somber coyoteBOT Mar 6, 2022, 10:00 AM

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criver

muted sparrow Mar 6, 2022, 10:01 AM

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I am aware this is not the case if the line doesn't start from a vertex

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on the other hand this seems to be true for triangles at least

nocturne remnant Mar 6, 2022, 10:17 AM

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muted sparrow If I have a convex polygon, does a line starting at one of the vertices $v_i$ an...

Most definitely not for quadrilaterals in general

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Imagine picking a point on a side of a triangle to be the 4th point

nocturne remnant Mar 6, 2022, 10:35 AM

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And move it slightly just so the new quadrilateral is convex

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But since the “centre” has shifted towards the new point obviously the area condition will not hold anymore

muted sparrow Mar 6, 2022, 10:37 AM

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nocturne remnant But since the “centre” has shifted towards the new point obviously the area cond...

That's not obvious to me

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To be sure, the part about the center shifting is obvious, the part about the area condition being violated is not

nocturne remnant Mar 6, 2022, 11:10 AM

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Like um

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Imagine the new vertex being moved by 0.01mm while the triangle was kilometres wide

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Certainly that wouldn’t compensate enough for the centre being shifted

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(But this is by no means a proof)

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So if a point D some distance below BC was constructed to form a new polygon ABCD with new centre O’, the condition would imply that area of BCD = twice the area of BTT’
Which is not true, not just visually but also because as area of BCD approaches 0, area of BTT’ does not

muted sparrow Mar 6, 2022, 11:46 AM

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Thank you for the sketch. I think I understood the argument. What is bothering me is whether O and O' really do not lie in the same line if D is chosen on the edge BC, or in your image whether BTT' really doesn't go to 0 as D approaches BC.

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I should be able to construct a counterexample though

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B =(-1, -1), C =(1,-1), A = (0, 2) -> c = (0,0), let D= (0,-1), the c_D = (0,-1/4)

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Ok, that does it, this area really doesn't go to zero. Thank you.

grave pond Mar 6, 2022, 2:07 PM

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tender moss does bisector line starts from one of vertex of polygon that splits it into equa...

It is true that the line through a vertex that divides the triangle into parts with equal areas always passes trough the centroid and vice versa. This line is the median
I don't think you will generally be understood if you call the line a "bisector". I initially understood that as "angle bisector", which is definitely not the same line as the median in general.

tender moss Mar 6, 2022, 8:56 PM

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grave pond It is true that the line through a vertex that divides the triangle into parts w...

gotcha

dry python Mar 6, 2022, 11:16 PM

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i need help

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i forgot how to find the area of a pareleagram

chilly marlin Mar 6, 2022, 11:33 PM

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i genuinely just dont understand how to do this

grave pond Mar 6, 2022, 11:45 PM

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Hint: The values of AE and BC are not necessary to answer the question.

clever fable Mar 7, 2022, 3:00 AM

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Hi, I was just wondering if it is possible to solve ${\tan x} = 2 - \surd{3}$ by hand?

somber coyoteBOT Mar 7, 2022, 3:00 AM

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LordEmrys

humble pulsar Mar 7, 2022, 3:06 AM

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yeah, you just wont be able to get an approximate x value by hand

silent plank Mar 7, 2022, 7:24 AM

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since arctan (2-sqrt(3)) is pi/12

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you can do some stuff with compound angle identities

light axle Mar 7, 2022, 7:41 AM

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can someone help me with this

spare delta Mar 7, 2022, 7:45 AM

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-3+5 = 2

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2/18 = 1/9

spare delta Mar 7, 2022, 7:46 AM

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spare delta -3+5 = 2

7+11 =18

crude saffron Mar 7, 2022, 7:47 AM

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spare delta 7+11 =18

oh right im stupid

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osrry its 1/9 lmao

crude saffron Mar 7, 2022, 7:47 AM

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light axle can someone help me with this

its 1/9

spare delta Mar 7, 2022, 7:50 AM

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generally you want to see how much the x value has changed from A to B (-18)
then how much the y value has changed (-2)
and slope = change in y ÷ change in x

upper merlin Mar 7, 2022, 8:39 AM

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Prove that the length of median AM in triangle ABC is greater than (AB+AC-BC)/2

jovial pendant Mar 8, 2022, 2:14 AM

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light axle can someone help me with this

Rise over run. -3–>-5/7–>-11

strange reef Mar 8, 2022, 2:24 AM

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Question: To show that three points A, B, C in R^2 are collinear, we find the vectors AB and AC and see if they are scalar multiples (since vectors are collinear if they are scalar multiples). But aren't A, B, and C ordered pairs, which are vectors? Is one of these statements wrong, or is there something I'm missing?

humble pulsar Mar 8, 2022, 2:27 AM

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strange reef Question: To show that three points A, B, C in R^2 are collinear, we find the ve...

you find the vector b/w A and B

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and the vector b/w A and C

strange reef Mar 8, 2022, 2:28 AM

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(Sorry, what does b/w mean?)

humble pulsar Mar 8, 2022, 2:28 AM

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between

strange reef Mar 8, 2022, 2:28 AM

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Oh right thx

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Yes, and I see why, but I don't have a good explanation for why we can't just check A=kB=k'C that doesn't rely on saying "Well, A, B, C are points, not vectors"

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Is the best we can do to say that "Any vectors A, B, C are collinear if AB is a multiple of AC"?

humble pulsar Mar 8, 2022, 2:40 AM

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cause points and vectors are synonymous pretty much in R^n spaces

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if you know the vector equation of a line, then you're just finding the value of the parameter that reaches B and C on the line

strange reef Mar 8, 2022, 2:43 AM

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So, writing $l=A+t \overrightarrow{d}$, you mean solving for $t$ s.th $l=B$ and $C$?

somber coyoteBOT Mar 8, 2022, 2:43 AM

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person2709505

strange reef Mar 8, 2022, 2:44 AM

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As opposed to the equation Ax+By+C=0

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Actually, I think I get it- the first method is like translating A to the origin and seeing if (0,0), B, C are collinear. The second method makes the translation more explicit with the A term of the equation

near sand Mar 9, 2022, 1:16 AM

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I started off by constructing X on KV so that OX is perpendicular to KV and a Y on QR so that OY is perpendicular to QR. My professor then wants me to prove that it's a rectangle. Can someone help?

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,rotate

somber coyoteBOT Mar 9, 2022, 1:16 AM

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vagrant ore Mar 9, 2022, 7:03 AM

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I need help with this

dark sparrow Mar 9, 2022, 7:32 AM

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@vagrant ore do you still need help with that?

vagrant ore Mar 9, 2022, 7:46 AM

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@dark sparrow ya

dark sparrow Mar 9, 2022, 7:46 AM

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have you found areas of circular segments before?

vagrant ore Mar 9, 2022, 7:48 AM

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Nope

dark sparrow Mar 9, 2022, 7:49 AM

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...what about circular sectors?

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and triangles?

vagrant ore Mar 9, 2022, 7:49 AM

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Yes I've done that

dark sparrow Mar 9, 2022, 7:50 AM

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okay

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are you able to find the area of this circular sector?

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(all i want is a yes or a no, i don't want the value)

vagrant ore Mar 9, 2022, 7:54 AM

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Yes

dark sparrow Mar 9, 2022, 7:54 AM

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and are you able to find the area of this triangle?

vagrant ore Mar 9, 2022, 7:55 AM

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No

dark sparrow Mar 9, 2022, 7:55 AM

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why not?

vagrant ore Mar 9, 2022, 7:56 AM

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I'm not sure what the height is

dark sparrow Mar 9, 2022, 7:56 AM

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there is a formula for the area of a triangle which involves two sides and an angle between them

vagrant ore Mar 9, 2022, 7:59 AM

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So would I cut the triangle in half?

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Because I know the formula for finding the area of a triangle but I don't know the height or how to find it

dark sparrow Mar 9, 2022, 8:01 AM

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there is not one formula for finding the area of a triangle.

dark sparrow Mar 9, 2022, 8:01 AM

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dark sparrow there is a formula for the area of a triangle which involves two sides and an an...

the formula i was talking about here is $A = \frac{1}{2} a b \sin(\theta)$

somber coyoteBOT Mar 9, 2022, 8:01 AM

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Ann

vagrant ore Mar 9, 2022, 8:02 AM

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Is ab base × height?

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The formula I was thinking of is 1/2 base × height

dark sparrow Mar 9, 2022, 8:04 AM

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no

vagrant ore Mar 9, 2022, 8:04 AM

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Oh. Then what is it?

atomic tulip Mar 9, 2022, 8:05 AM

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a and b are the sides which have the included angle in them.

dark sparrow Mar 9, 2022, 8:05 AM

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vagrant ore Mar 9, 2022, 8:05 AM

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Oh ok

atomic tulip Mar 9, 2022, 8:06 AM

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This is essentially the same as 1/2bh.

vagrant ore Mar 9, 2022, 8:06 AM

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For my question I only know 1 side how would I use this formula?

atomic tulip Mar 9, 2022, 8:06 AM

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Well, there's something you could notice.

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That's a circle.

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I know you know that lol.

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So, which sides are we talking about in the figure do you know that?

atomic tulip Mar 9, 2022, 8:07 AM

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vagrant ore I need help with this

Let the centre be O, the other points on the circle be A and B.

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Now tell me which sides are the ones you should put in the formula?

vagrant ore Mar 9, 2022, 8:08 AM

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Ok

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27.8 for sure

atomic tulip Mar 9, 2022, 8:09 AM

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In terms of A B and O.

vagrant ore Mar 9, 2022, 8:09 AM

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How do I find the other side?

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Because if the center is o then let's say a = 27.8 then how would I get b?

dark sparrow Mar 9, 2022, 8:10 AM

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wym other side

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you've got a circle

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the two sides are both radii of said circle

atomic tulip Mar 9, 2022, 8:10 AM

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Exactly, that's what I've been implying.

dark sparrow Mar 9, 2022, 8:10 AM

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if you remember what a circle is, it should be obvious how long the other side is

vagrant ore Mar 9, 2022, 8:11 AM

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Like the diameter?

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Or the circumference?

dark sparrow Mar 9, 2022, 8:13 AM

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dark sparrow the two sides are both radii of said circle

.

vagrant ore Mar 9, 2022, 8:16 AM

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I don't think you guys understand how dumb I am

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See I thought that the diameter was the radius x 2

dark sparrow Mar 9, 2022, 8:17 AM

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the diameter is equal to twice the radius, you're right about that

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that's not the point

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there are no diameters in your picture anyway

vagrant ore Mar 9, 2022, 8:17 AM

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dark sparrow that's not the point

Is that because it's a circle..

vagrant ore Mar 9, 2022, 8:17 AM

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dark sparrow there are no diameters in your picture anyway

Yes I know. That's what makes it hard to find the other side

dark sparrow Mar 9, 2022, 8:17 AM

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no

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okay

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let's try this

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can you tell me the definition of a circle?

vagrant ore Mar 9, 2022, 8:18 AM

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No

dark sparrow Mar 9, 2022, 8:18 AM

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so you don't know what a circle is.

vagrant ore Mar 9, 2022, 8:18 AM

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It's round

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What is there to define about it?

dark sparrow Mar 9, 2022, 8:18 AM

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so you don't know that a circle is defined as the set of all points at a fixed distance (the radius) from a fixed point (the center)?

vagrant ore Mar 9, 2022, 8:19 AM

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Ya I know that

dark sparrow Mar 9, 2022, 8:19 AM

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but this never occurred to you?

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any point on a circle is by definition the exact same distance away from the center.

vagrant ore Mar 9, 2022, 8:19 AM

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I just need to know how to find the other side

dark sparrow Mar 9, 2022, 8:19 AM

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any point on a circle is by definition the exact same distance away from the center.

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and that distance is called the radius.

vagrant ore Mar 9, 2022, 8:19 AM

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I know

dark sparrow Mar 9, 2022, 8:19 AM

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i guess i need to say this even more explicitly

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any line segment joining a point on a circle to its center has the same length

vagrant ore Mar 9, 2022, 8:20 AM

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If the formula you said I should use is correct then just skip to telling me what I need to do to find the other side

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I know it's not the same as the radius

dark sparrow Mar 9, 2022, 8:20 AM

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YES IT IS

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IT IS

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IT IS THE RADIUS

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it is LITERALLY the radius

vagrant ore Mar 9, 2022, 8:21 AM

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27.8

dark sparrow Mar 9, 2022, 8:21 AM

#

look at the green side...

vagrant ore Mar 9, 2022, 8:21 AM

#

That side is unknown

dark sparrow Mar 9, 2022, 8:21 AM

#

is it not blindingly obvious that it joins a point on the circle to the center...

vagrant ore Mar 9, 2022, 8:21 AM

#

I see that

#

But the length could be anything

dark sparrow Mar 9, 2022, 8:22 AM

#

no it couldnt

vagrant ore Mar 9, 2022, 8:22 AM

#

It's not 27.8

dark sparrow Mar 9, 2022, 8:22 AM

#

YES IT IS!!!!!!!!!!!!!!!!!!!

#

the radius of the circle is 27.8!!!!

vagrant ore Mar 9, 2022, 8:22 AM

#

Ok calm down

dark sparrow Mar 9, 2022, 8:22 AM

#

and this green line is equal to the radius!!!!!!!!!!!!!!!!!

vagrant ore Mar 9, 2022, 8:23 AM

#

Ok got it sheesh

dark sparrow Mar 9, 2022, 8:24 AM

#

i mean like

#

you say you know that all points on a circle are by definition the same distance away from the center

#

but then you say that the green line could be anything

#

despite it being a line that joins the circle to its center

#

do you maybe have a mental disconnect between distance and length of a line segment

vagrant ore Mar 9, 2022, 8:25 AM

#

You know what. I'm going to find help somewhere else..

#

You're clearly not fit to teach

light grotto Mar 9, 2022, 8:26 AM

#

@dark sparrow where can I ask questions about basic math

#

I need second opinions

dark sparrow Mar 9, 2022, 8:26 AM

#

depending on how basic, anywhere in the pre-university category.

#

or you could post in a questions channel.

#

if you post in the wrong channel you'll get redirected anyway.

light grotto Mar 9, 2022, 8:26 AM

#

What is within 2 and 5

#

This is a trick question, it feels like a Trick

dark sparrow Mar 9, 2022, 8:27 AM

#

is that exactly what the question says, and nothing else?

#

"What is within 2 and 5?"

light grotto Mar 9, 2022, 8:27 AM

#

Yes

dark sparrow Mar 9, 2022, 8:27 AM

#

thonk

#

strange

light grotto Mar 9, 2022, 8:27 AM

#

IT IS

#

IT IS STRANGE

#

THE BOOK IS LYING TO ME

dark sparrow Mar 9, 2022, 8:28 AM

#

can you take a picture of the question in the book

#

and the answer key if you have it

light grotto Mar 9, 2022, 8:28 AM

#

Is between and within the same?

dark sparrow Mar 9, 2022, 8:29 AM

#

no, these aren't the same word

#

would have appreciated "no, i'm not able to take any pictures right now"...

light grotto Mar 9, 2022, 8:30 AM

#

You know what, thank you
Im gonna just ask the teacher

grave pond Mar 9, 2022, 2:38 PM

#

Unclick the checkmark in #get-advanced-access.

upper karma Mar 9, 2022, 6:38 PM

#

Can somebody help me with the intuition here? I feel like I can't remember why this makes sense. He solves the y function for x and somehow that represents the distance of the function from the y-axis?

#

(ignore the x=-2 line, that's for a further explanation)

#

I'm not sure what x represents here.

grave pond Mar 10, 2022, 12:08 AM

#

"distance from the y-axis" is what an x-coordinate is.

upper karma Mar 10, 2022, 3:11 AM

#

grave pond "distance from the y-axis" is what an x-coordinate _is_.

but isnt a coordinate a point

#

so how could a point also be a distance

crude niche Mar 10, 2022, 3:56 AM

#

its the x coordinate

#

or the first value

crude niche Mar 10, 2022, 4:40 AM

#

helop

#

what r very important theorems to know

#

in general

#

Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus.

#

acc just explain what these r

#

acc i can just search them up

#

does anyone know how to practice geometry problems

#

like a website or smth for that?

nocturne remnant Mar 10, 2022, 4:43 AM

#

are you looking for competition-like problems?

crude niche Mar 10, 2022, 4:43 AM

#

yea

nocturne remnant Mar 10, 2022, 4:43 AM

#

AoPS forum maybe

covert wyvern Mar 10, 2022, 4:48 AM

#

i've never heard of brahmagupta's formula

nocturne remnant Mar 10, 2022, 5:45 AM

#

covert wyvern i've never heard of brahmagupta's formula

I think it’s the formula for cyclic quad area given all sides

covert wyvern Mar 10, 2022, 6:59 AM

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huh, don't remember that one, but it seems plausible

unique flower Mar 10, 2022, 7:15 AM

#

have you heard of heron's formula?

covert wyvern Mar 10, 2022, 8:08 AM

#

yes, but i don't remember what it is

upper karma Mar 10, 2022, 2:23 PM

#

can someone help me with my trig work

#

please and thank you

#

you dont need to find the answers for me, i just need help writing down the formulas and i can punch it into my calculator lol

#

opal cargo Mar 10, 2022, 2:37 PM

#

draw diagram now

#

angle of elevation is the angle between the horizontal line and the line of sight

#

you're gonna form an orthogonal triangle

#

core trigonometry 😩

trim adder Mar 10, 2022, 4:53 PM

#

visual igloo Mar 10, 2022, 5:08 PM

#

What's cos sin and tan

#

What do you use it for what does it mean

#

In English pls

light axle Mar 10, 2022, 6:26 PM

#

spice coyote Mar 10, 2022, 6:53 PM

#

visual igloo What do you use it for what does it mean

Functions that form graphs when put with angles idk im not smart

rigid wadi Mar 10, 2022, 8:37 PM

#

How do I calculate the volume of tetrahedron if the sum of all edges is 72cm?

grave pond Mar 10, 2022, 8:40 PM

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Do you know the tetrahedron is regular? Otherwise I don't think you can.

rigid wadi Mar 10, 2022, 8:43 PM

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grave pond Do you know the tetrahedron is _regular_? Otherwise I don't think you can.

it is

grave pond Mar 10, 2022, 8:45 PM

#

So you should be able to compute the common side length. Figure out the area of an equilateral triangle with the side length (which will be your base), then compute the height from that base, and plug into the formula for the volume of a generic pyramid.

rigid wadi Mar 10, 2022, 8:46 PM

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Base is this

#

right?

grave pond Mar 10, 2022, 8:47 PM

#

Looks generally like a formula of the right shape, but I've not done the calculation myself.

finite cove Mar 11, 2022, 1:28 AM

#

Can anyone help me find the phase shift and period

storm portal Mar 11, 2022, 5:59 AM

#

finite cove Can anyone help me find the phase shift and period

You can probably look up resources that can explain this better than I can, but I can try:

Phase shift: The horizontal distance the graph is moved from the parent graph (with no phase shift). You can find this by figuring out how "offset" this is from the parent, and in what direction. Now you may not have a phase shift (sometimes phase shift = 0).

Period: The distance between two consecutive peaks = the distance between two consecutive troughs = twice the distance between a peak and the next trough

vagrant ore Mar 11, 2022, 9:58 AM

#

Does anybody know how to solve this?

steady spire Mar 11, 2022, 10:13 AM

#

TIL that we can't do modular arithmetic with real numbers or even rational numbers because, while addition and subtraction are well-defined, multiplication doesn't work: 2/3 is the same as −1/3 and 3/5 is the same as −2/5, but (2/3)⋅(3/5) doesn't end up being the same as (−1/3)⋅(−2/5).

But this raises another question: What kind of spaces are circles, cylinders or torus then? I can clearly do some geometry on them. On a circle, I can add and subtract (but not multiply) points (angles). On the surface of cylinders/torus/sphere, I can draw shapes like triangles and translate them around. But are operations like scaling a shape or rotating a shape on these surfaces not well-defined at all?

dark sparrow Mar 11, 2022, 10:14 AM

#

scaling is not well-defined yes

#

unless like, you consider it locally or something

#

and that only on flat surfaces like the torus or cylinder

upper karma Mar 11, 2022, 12:08 PM

#

vagrant ore Does anybody know how to solve this?

A=A circlesector- A triangle

torn meteor Mar 11, 2022, 12:58 PM

#

vagrant ore Does anybody know how to solve this?

First find the area of the arc:

A=80/360 ×π×5²=50π/9
Then find the area of the triangle:

A=5×5×sin80/2=12.5sin 80

Subtract the area of the arc from the area of the triangle:

(50π/9)-(12.5sin 80)≈5.1cm²

dark sparrow Mar 11, 2022, 1:16 PM

#

@torn meteor do not give out answers.

uneven bloom Mar 11, 2022, 6:11 PM

#

Can I solve for theta in this polygon given a,b,c?

alpine tartan Mar 11, 2022, 8:13 PM

#

yo, my friend and I are trying to find the length of the side of the octagon, on the following image:

#

#

the symbol that looks like an "empty set" is the diameter of the circle its pointing at

#

I'm really not sure what to do here

#

seems like the apothem of the octogon is 25, since Its the length 50 divided by 2

#

I'm really confused

grave pond Mar 11, 2022, 8:15 PM

#

Thus, 25·2sin(2pi/16)

alpine tartan Mar 11, 2022, 8:15 PM

#

Wait, I'm not sure If I got It

#

how did you get the 2sin(2pi/16)?

grave pond Mar 11, 2022, 8:16 PM

#

(Fixed a typo, sorry)

alpine tartan Mar 11, 2022, 8:16 PM

#

no no, I'm very thankful, actually

#

I'm just not sure how you got to this result

grave pond Mar 11, 2022, 8:17 PM

#

Cut the octagon in 16 little congruent triangles. Each of them is right-angled, and you have just computed that the long leg has length 25. The angle adjacent to that leg is such that 16 of them just fit together around the circle.

alpine tartan Mar 11, 2022, 8:17 PM

#

Ooooooooooh

#

Thanks, I think I got It

#

Wait, sorry to bother again, but woudn't I need tangent, instead of sine?

#

I don't have the hypothenuse

#

but I have both sides

torn meteor Mar 11, 2022, 8:30 PM

#

I'm working on multiplication of arctangents. What do you guys think?

#

grave pond Mar 11, 2022, 8:47 PM

#

alpine tartan Wait, sorry to bother again, but woudn't I need tangent, instead of sine?

Whoops yes, you're completely right. Always check the work of random people you meet on the internet before you believe it!

alpine tartan Mar 11, 2022, 8:48 PM

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Oooh, all right, thanks!!! :))

grave pond Mar 11, 2022, 9:17 PM

#

alpine tartan yo, my friend and I are trying to find the length of the side of the octagon, on...

A shortcut approach could be to write x/sqrt(2) + x + x/sqrt(2) = 50 (where each term corresponds to one of the sides of the octagon that is not perpendicular to the 50-mm diameter) and solve for x.

alpine tartan Mar 11, 2022, 9:53 PM

#

oh, thanks

#

Sorry, for some reason I only got the notification now :/

alpine mesa Mar 12, 2022, 4:05 AM

#

#

Number 17 b) is the trouble

#

This unit is on tangent ratio (trig)

mighty rune Mar 12, 2022, 5:58 AM

#

light axle

did anyone help you with this?

#

that should be just sqrt of the sum of 4^2 and 8^2

#

since 11-7 is 4 and 5-(-3) is 8

inland estuary Mar 12, 2022, 6:03 AM

#

Question: Let’s say you have f(x)=1/8(x-2)^2. On a graph, this is expressed as a parabola. If you remove the square, the shape of the line changes into a regular diagonal. Why does the square completely change the direction of the line?

The reason I used such a seemingly random equation is because this was the problem that brought the question to mind and I apologize if this is has a really obvious answer, I’ve just never been told why that is, only that that’s how it works.

mighty rune Mar 12, 2022, 6:04 AM

#

inland estuary Question: Let’s say you have f(x)=1/8(x-2)^2. On a graph, this is expressed as a...

is the slope 1/8 or is the (x-2)^2 in the denominator of the fraction?

inland estuary Mar 12, 2022, 6:05 AM

#

(X-2)^2 isn’t part of the denominator no

mighty rune Mar 12, 2022, 6:05 AM

#

also its because of how negatives don't exist in even exponents

inland estuary Mar 12, 2022, 6:05 AM

#

Should’ve put a space there probably

mighty rune Mar 12, 2022, 6:05 AM

#

and so the negative x value to y is the same as positive x value to y

#

the reason why absolute values dont work here because of how parabolas take on the curvature of an ln graph and absolute value takes the tendency of a linear graph since its a direct relationship

#

@inland estuary did you get it?

#

the curvature is also from the square itself

#

because now each y value from the x is squared too

#

making the rate of change non-linear

#

absolute values have no squares (unless the function itself has a square) and so they have a linear change in rate

light axle Mar 12, 2022, 6:10 AM

#

mighty rune did anyone help you with this?

so the answer is option 1

mighty rune Mar 12, 2022, 6:10 AM

#

light axle so the answer is option 1

yeah

#

you just have to think about the Pythagorean theorem

#

since AB, distance between x-values, and distance between y-values make a right angle triangle

#

and you can find the distance between y-values and distance between x-values

#

and your "C" is AB

#

so just do $$sqrt(A^2+B^2)$$

somber coyoteBOT Mar 12, 2022, 6:12 AM

#

Omega Warrior

mighty rune Mar 12, 2022, 6:12 AM

#

sqrt didnt work right lol

light axle Mar 12, 2022, 6:13 AM

#

yeah

mighty rune Mar 12, 2022, 6:13 AM

#

but you get what i mean

light axle Mar 12, 2022, 6:13 AM

#

yeah thanks alot

mighty rune Mar 12, 2022, 6:13 AM

#

yeah np

inland estuary Mar 12, 2022, 6:15 AM

#

mighty rune <@!887915194670526505> did you get it?

That makes sense, thank you!

mighty rune Mar 12, 2022, 6:15 AM

#

yeah np 🙂

dark sparrow Mar 12, 2022, 6:17 AM

#

mighty rune so just do $$sqrt(A^2+B^2)$$

$\sqrt{A^2 + B^2}$

somber coyoteBOT Mar 12, 2022, 6:17 AM

#

Ann

dark sparrow Mar 12, 2022, 6:18 AM

#

if you're going to use latex then use the things latex provides you

odd knoll Mar 12, 2022, 9:46 AM

#

tiny stirrup Mar 12, 2022, 10:18 AM

#

Hey, please read this question and tell me where I am going wrong.
According to me this question is wrong because they are asking for the locus of a point which is fixed.
Explaination- A FIXED CIRCLE is given and A FIXED PARABOLA is given. Now, since both of them are fixed, their points of intersection would also be fixed. Since their points of intersection are fixed, the chord between the points of intersection will also be fixed. Since the chord is fixed, its mid-point will also be fixed.
NOW IF THE MID-POINT IS FIXED, how can they ask for it's locus?
Btw, the answer is x^2+y^2-2x-2y=0

dark sparrow Mar 12, 2022, 10:30 AM

#

i mean if you really are right and theres only one possible place for this midpoint then its locus consists of one point

#

thats not really an egregious error or anything

#

but also lets graph this

#

Now, since both of them are fixed, their points of intersection would also be fixed.

#

sure, the points of intersection of the parabola and the circle are fixed. so what?

#

we're not interested in those

#

we're interested in the intersections between the chord (or rather the straight line containing it, presumably) and the parabola.

#

@tiny stirrup

unique fox Mar 12, 2022, 10:39 AM

#

Am hello

north willow Mar 12, 2022, 10:40 AM

#

just paste it

unique fox Mar 12, 2022, 10:40 AM

#

#

Need help

#

Here

north willow Mar 12, 2022, 10:42 AM

#

I mean... I haven't seen those angle pair names in a while, but it seems pretty self explanatory

#

I'm assuming interior means between the parallel lines and exterior means outside

tiny stirrup Mar 12, 2022, 10:43 AM

#

dark sparrow we're interested in the intersections between the _chord_ (or rather the straigh...

yeah, but the chord will be at the point of interesection right?

dark sparrow Mar 12, 2022, 10:44 AM

#

??

tiny stirrup Mar 12, 2022, 10:44 AM

#

https://www.desmos.com/calculator/tsbs4d0zry

Desmos

Desmos | Graphing Calculator

#

this is the graph

#

of the circle

#

tell me where would the chord be

dark sparrow Mar 12, 2022, 10:45 AM

#

something like this, except i didn't draw the chord (yet) but instead a segment on the line containing it

#

specifically, this is the segment intercepted by the chord

tiny stirrup Mar 12, 2022, 10:46 AM

#

where did that black line come from?

#

what do the green lines represent? x=y and x=-y???

#

you know what, maybe I am misunderstanding the question, could you please explain it to me?

dark sparrow Mar 12, 2022, 10:48 AM

#

no, the green lines represent the lines y = mx and y = (-1/m)x, i.e. a pair of perpendicular lines through the origin

#

where m is unknown and variable

#

they illustrate the 'subtend a right angle at the origin' condition

tiny stirrup Mar 12, 2022, 10:50 AM

#

dark sparrow they illustrate the 'subtend a right angle at the origin' condition

okay, then how does the circle play any role in this?

dark sparrow Mar 12, 2022, 10:50 AM

#

to say it very roughly we have this green cross that can rotate freely about the origin. it intersects the parabola in two points (not cutting the origin)

#

these two points define a straight line

tiny stirrup Mar 12, 2022, 10:51 AM

#

dark sparrow to say it very roughly we have this green _cross_ that can rotate freely about t...

and we have to determine the mid-point of the line segment between those two points??

dark sparrow Mar 12, 2022, 10:51 AM

#

no

#

we are supposed to look at the chord that is cut out of the circle (that's where it comes in) by the straight line which contains this segment

tiny stirrup Mar 12, 2022, 10:53 AM

#

chord that is cut out of the circle? are you talking about the chord of the circle or the chord of the parabola?
If it is the chord of circle, how can it cut out of the circle?

dark sparrow Mar 12, 2022, 10:53 AM

#

......

#

look

#

extend the black segment into a straight line

tiny stirrup Mar 12, 2022, 10:53 AM

#

chord of parabola right?

dark sparrow Mar 12, 2022, 10:53 AM

#

and consider THAT line and the circle

tiny stirrup Mar 12, 2022, 10:54 AM

#

okay, but i considered the common chord between the parabola and the circle.
how is that wrong?

dark sparrow Mar 12, 2022, 10:55 AM

#

it's wrong because it completely ignores what the question asks of you

tiny stirrup Mar 12, 2022, 10:56 AM

#

when the question mentions, "the chord of a circle x^2+y^2=4", what does it mean by "chord"? A line segment? or a straight Line???

dark sparrow Mar 12, 2022, 10:56 AM

#

PRESUMABLY it means the straight line

#

#

like this

tiny stirrup Mar 12, 2022, 10:57 AM

#

let me take a moment to let that sink into me!

dark sparrow Mar 12, 2022, 10:57 AM

#

dont bother

#

clearly im unable to explain it to you anyway

tiny stirrup Mar 12, 2022, 10:58 AM

#

no no, i get it

dark sparrow Mar 12, 2022, 10:58 AM

#

because i have no idea how the fuck to do any of this crap algebraically as youre expected to do

tiny stirrup Mar 12, 2022, 10:58 AM

#

somewhat

dark sparrow Mar 12, 2022, 10:58 AM

#

you dont get shit i dont get shit

#

dont pretend otherwise

tiny stirrup Mar 12, 2022, 10:58 AM

#

wanna take a look at the solution?

#

T=S1 is the formula for equation of the chord where T is the tangent and S1 is the power of midpoint of the chord.

#

to summarise, the circle has infinite chords. some of those chords also happen to be the chords to this parabola. And out of those some chords, some happen to form right angle at the origin. And we just calculated the midpoint of those some chords? right???

dark sparrow Mar 12, 2022, 11:05 AM

#

yes it appears so

tiny stirrup Mar 12, 2022, 11:06 AM

#

okay, thank you so much!

verbal coyote Mar 12, 2022, 12:10 PM

#

Hi

#

Can anyone help in my homework

atomic tulip Mar 12, 2022, 1:22 PM

#

JustAsk

reef merlin Mar 12, 2022, 1:29 PM

#

verbal coyote Can anyone help in my homework

It depends on what difficulty it is

#

What grade ?

verbal coyote Mar 12, 2022, 1:52 PM

#

reef merlin What grade ?

9th grade

reef merlin Mar 12, 2022, 1:52 PM

#

Ok

#

Let me see the problem

reef merlin Mar 12, 2022, 1:53 PM

#

verbal coyote 9th grade

I could be able to help you

verbal coyote Mar 12, 2022, 1:53 PM

#

reef merlin I could be able to help you

Thanks

verbal coyote Mar 12, 2022, 1:53 PM

#

reef merlin Let me see the problem

Ok wait

#

#

I need the second answer

reef merlin Mar 12, 2022, 1:54 PM

#

I can't see

#

Can you write it ?

#

@verbal coyote

verbal coyote Mar 12, 2022, 1:56 PM

#

Okay

#

In the figure angle aob=120° find angle acb

reef merlin Mar 12, 2022, 1:58 PM

#

I don't know how to solve that but Sakata here can help you

atomic tulip Mar 12, 2022, 2:06 PM

#

Sure I can.

#

Is O the centre?

#

@verbal coyote

verbal coyote Mar 12, 2022, 2:07 PM

#

atomic tulip <@473191304562606090>

Yes

atomic tulip Mar 12, 2022, 2:07 PM

#

So

#

Do you know any relation about the central angle subtended by an arc and an angle on the circumference on the circle?

verbal coyote Mar 12, 2022, 2:08 PM

#

No

robust garden Mar 12, 2022, 2:10 PM

#

verbal coyote I need the second answer

for question two ?

verbal coyote Mar 12, 2022, 2:10 PM

#

Yes

robust garden Mar 12, 2022, 2:10 PM

#

use this

verbal coyote Mar 12, 2022, 2:10 PM

#

Ok thx

atomic tulip Mar 12, 2022, 2:10 PM

#

Don't give away answers.

#

Just give the respective theorem and all.

robust garden Mar 12, 2022, 2:11 PM

#

mb oops

atomic tulip Mar 12, 2022, 2:11 PM

#

Or hints.

#

Right.

verbal coyote Mar 12, 2022, 2:11 PM

#

Ok thx guys

robust garden Mar 12, 2022, 2:11 PM

#

#

accidentally deleted this

verbal coyote Mar 12, 2022, 2:12 PM

#

Np thanks again

robust garden Mar 12, 2022, 2:12 PM

#

atomic tulip Don't give away answers.

i’ll keep that in mind next time :>

robust garden Mar 12, 2022, 2:12 PM

#

verbal coyote Np thanks again

nppp

atomic tulip Mar 12, 2022, 2:13 PM

#

In a triangle PQR angle P is 90°. PS is altitude. From S are drawn SA and SB respectively perpendicular to PQ and PR. C is an arbitrary point on line segment AB. The line perpendicular to SC meets PQ at L and PR at M.\
Prove that circumcircle of triangle PLM passes through S.\
If $C_1$ is another arbitrary point of line segment AB and the line perpendicular to $SC_1$ ,meets PQ at $L_1$ and PR at $M_1$. Prove that $\frac{LL_1}{MM_1}$ is a constant.

somber coyoteBOT Mar 12, 2022, 2:16 PM

#

Sakata Yaksha

hybrid yoke Mar 12, 2022, 4:14 PM

#

Need help

#

light axle Mar 12, 2022, 4:22 PM

#

can someone help me with this

upper karma Mar 12, 2022, 4:45 PM

#

light axle can someone help me with this

u know the standard eq. of a circle?

#

assume that h and k are 0 btw... tho it isnt mentioned in the questions.. the options make it obvious

light axle Mar 12, 2022, 5:57 PM

#

upper karma u know the standard eq. of a circle?

so the answer is option 1

upper karma Mar 12, 2022, 6:01 PM

#

Ur getting the idea... but ur not exactly right

#

Remember, the standard eq. Of a circle at the centre is x^2+y^2=r^2

#

Read the question one more time.. youll get it

light axle Mar 12, 2022, 6:04 PM

#

upper karma Read the question one more time.. youll get it

so it is option 3

upper karma Mar 12, 2022, 6:05 PM

#

Whats your resoning behind that?

light axle Mar 12, 2022, 6:07 PM

#

so the Diameter of a circle = d = 2r = 10 units

upper karma Mar 12, 2022, 6:07 PM

#

Right

#

Then?

light axle Mar 12, 2022, 6:08 PM

#

so the radius of a circle is 5 units

upper karma Mar 12, 2022, 6:09 PM

#

K.. youre right till here.. you made one tiny mistake after this. Read the standard eq of the circle again

torn meteor Mar 12, 2022, 6:10 PM

#

x²+y²=r²

torn meteor Mar 12, 2022, 6:10 PM

#

torn meteor x²+y²=r²

'r²'

light axle Mar 12, 2022, 6:10 PM

#

oh i got so the answer is 25

upper karma Mar 12, 2022, 6:10 PM

#

Thanks emanuel

#

And yep

#

Its option 4

light axle Mar 12, 2022, 6:11 PM

#

thanks

torn meteor Mar 12, 2022, 6:13 PM

#

Can you solve this?

sin-¹x+tan-¹x=45

#

I was solving it and found out there can be 4 answers.

#

I got x to be -1

#

But now I'm stuck

upper merlin Mar 12, 2022, 6:16 PM

#

atomic tulip In a triangle PQR angle P is 90°. PS is altitude. From S are drawn SA and SB res...

After some angle chasing you can prove that angle CLA=b which implies that SCAL is cyclic => angle SLC=a => MPLS is cyclic

upper karma Mar 12, 2022, 6:18 PM

#

Im sorry emanuel, but i havent leant inv trig yet.. so i cant help you

torn meteor Mar 12, 2022, 6:19 PM

#

But you know how to solve cubic equations right?

#

Well I have some formulae to solve it but it will give a quartic equation. I got x=-1 but the rest is still unknown.

upper karma Mar 12, 2022, 6:23 PM

#

Hnn, can we write tan-1x as sin-1x/cos-1x?

upper karma Mar 12, 2022, 6:24 PM

#

torn meteor Well I have some formulae to solve it but it will give a quartic equation. I got...

Z

torn meteor Mar 12, 2022, 6:24 PM

#

upper karma Hnn, can we write tan-1x as sin-1x/cos-1x?

No

#

But sin-¹x=tan-¹(x/√1-x²)

upper karma Mar 12, 2022, 6:28 PM

#

Idk what to do with that... tho if you coukd make the equation from a sum to a product... it would probs be easier

#

Nvm.. i guess that wont work

torn meteor Mar 12, 2022, 6:31 PM

#

Just use the formula to convert inverse sine to inverse tangent.

#

Then use this: tan-¹a+tan-¹b=tan-¹(a+b/1-ab)

upper karma Mar 12, 2022, 6:32 PM

#

Oh theres a formula like that huh

#

One sec

#

Im not gettin anythin

#

Im kinda tired rn, its 12 00 here. Mabye ill try again tmrw

#

Tho im curious... how did u get -1 as a solution?

serene iron Mar 12, 2022, 7:38 PM

#

#

How

#

Hi

quartz bough Mar 12, 2022, 7:43 PM

#

Surface area is
[ 4\pi\cdot r^2 ]
So
[ 4\pi\cdot r^2 = \frac{8788}{3}\pi \implies 4r^2=\frac{8788}{3}\implies r=\frac{13\sqrt{39}}{3} ]
And volume is
[ \frac{4}{3}\pi r^3 ]
So you just need to plug in the $r$ you found into $\frac{4}{3}r^3$

somber coyoteBOT Mar 12, 2022, 7:43 PM

#

serene iron Mar 12, 2022, 7:44 PM

#

Thanks @quartz bough

hybrid yoke Mar 12, 2022, 7:44 PM

#

YOU ALL ARE A FR MATH WIZARDS

quartz bough Mar 12, 2022, 7:44 PM

#

sully

serene iron Mar 12, 2022, 7:44 PM

#

I know right he is too smart

#

This guy is my go to mathigician

quartz bough Mar 12, 2022, 7:44 PM

#

yall gotta talk to someone who actually knows math, like someone with honorable or a mod

serene iron Mar 12, 2022, 7:45 PM

#

You're enough buddy

hybrid yoke Mar 12, 2022, 7:45 PM

#

What gradw are you all on?

serene iron Mar 12, 2022, 7:45 PM

#

10th

valid osprey Mar 12, 2022, 8:35 PM

#

quartz bough yall gotta talk to someone who actually knows math, like someone with honorable ...

or I

#

the one who taught Euler everything he knew

spare delta Mar 13, 2022, 8:29 AM

#

wrong screenshot

vagrant ore Mar 13, 2022, 8:46 AM

#

I need help finding the area of the Pentagon. I found the area of the circle is 50.24 and now I'm stuck

silent plank Mar 13, 2022, 8:48 AM

#

try splitting the pentagon into a few triangles

vagrant ore Mar 13, 2022, 9:04 AM

#

I'm not sure how to do that. Like by splitting the numbers too

silent plank Mar 13, 2022, 9:10 AM

#

draw lines from the centre to each vertex

vagrant ore Mar 13, 2022, 9:25 AM

#

Ok so I have 5 triangles so how do I find the area of one of them

#

I want to know what numbers to use because I know how to find the area of a triangle

silent plank Mar 13, 2022, 10:47 AM

#

if you know how to find the area of a triangle, you should be able to find the areas of those triangles

viral hamlet Mar 13, 2022, 12:58 PM

#

So tommorow I have an exam which include geometry ( Triangles, Quadrilateral and circles ), is there anyway I can finish all of this in 1 day? Cuz I know nothing

#

There is like 106 theory or smth

#

🤔

nocturne remnant Mar 13, 2022, 12:58 PM

#

What 106 theory catthonk

viral hamlet Mar 13, 2022, 12:58 PM

#

No like

#

Theories*

nocturne remnant Mar 13, 2022, 12:58 PM

#

Theorems

#

!

#

Very different things

viral hamlet Mar 13, 2022, 12:58 PM

#

Whatever English not my first language

#

😭

#

Is there any single chance ?

#

AAAAAAA

#

Looks like I won't waste time on it then

silent plank Mar 13, 2022, 1:21 PM

#

if its just basic 2d geometry then it should be doable

#

but you should've already building up that knowledge throughout the semester

nocturne remnant Mar 13, 2022, 1:29 PM

#

viral hamlet Looks like I won't waste time on it then

Also this is the wrong way to view exams in general

#

If you totally give up this time

#

Next time you’ll still face the same dilemma

#

Of not being able to catch up

#

Unless you’re deciding to drop the entire subject catthonk

limber ice Mar 13, 2022, 2:52 PM

#

Screen_Shot_2022-03-13_at_10.48.58_AM.png

#

can someone explain to me how this works?

#

Like, I don't understand the steps here

spare delta Mar 13, 2022, 2:57 PM

#

the first step uses the identity cos2x = cos^2(x) - sin^2(x)

#

does that sound familiar?

limber ice Mar 13, 2022, 3:10 PM

#

not really, not familiar with that identity

spare delta Mar 13, 2022, 3:12 PM

#

oh err
it's quite important

limber ice Mar 13, 2022, 3:13 PM

#

I mean, I haven't taken a trig heavy class in years, I am in calc 2 and we only run into the double angle identity maybe like a few times in the whole class?

spare delta Mar 13, 2022, 3:14 PM

#

important for trig stuff anyway

limber ice Mar 13, 2022, 3:14 PM

#

A lot of it is just other identities, to be honest

#

I get that it's a double angle

#

after reading about it more

#

But I don't understand how to factor it still

#

cosx =cosx^2x-sin^2x?

spare delta Mar 13, 2022, 3:15 PM

#

factoring 2cos^2x - cosx - 1 =0
let cosx = u
that gives 2u^2 - u -1 =0

#

which is just a simple quadratic that shouldn't be too difficuly

limber ice Mar 13, 2022, 3:15 PM

#

how did you get rid of the sin?

spare delta Mar 13, 2022, 3:15 PM

#

limber ice cosx =cosx^2x-sin^2x?

from here, sin^2(x) = 1 - cos^2(x)

#

\begin{align*}
\cos(x) &= \cos^2(x) - \sin^2(x) \
&= \cos^2(x) - (1 - \cos^2(x)) \
&= 2\cos^2(x) - 1
\end{align*}

somber coyoteBOT Mar 13, 2022, 3:20 PM

#

twiceshy

dark sparrow Mar 13, 2022, 5:55 PM

#

cos(2x) at the start

grim plank Mar 13, 2022, 6:01 PM

#

they're solving an equation

#

Perhaps if they wrote out the first line as the equation it would be better

vagrant ore Mar 13, 2022, 10:18 PM

#

How do I solve this one?

craggy river Mar 13, 2022, 10:27 PM

#

Find the area of the circle and the area of the triangle, then reason to find the type of proportion between them you want

#

So like if it was if it falls in the triangle, you'd do (area of triangle)/(area of full circle)

#

That's NOT the proportion you want but idk how else to explain that without an example

upper karma Mar 14, 2022, 12:09 AM

#

How do I solve this one?

idle wedge Mar 14, 2022, 12:45 AM

#

upper karma How do I solve this one?

first draw this on a piece of paper and then add the lengths you already know

woeful bobcat Mar 14, 2022, 1:16 AM

#

hey, does anybody know the steps from left to right? I tried rewriting the cosine part as sine and end up with sin(pi*(x-2)/x)/sin(pi/x)

upper karma Mar 14, 2022, 2:04 AM

#

woeful bobcat hey, does anybody know the steps from left to right? I tried rewriting the cosin...

I... really don't like here that x->(infinity)
Although I'm not a mathematician or planning to go for math major, I could suggest changing that x->infinity to x->0, right....?

#

Sorry, x->0+ to be precise

mighty rune Mar 14, 2022, 3:26 AM

#

dark sparrow $\sqrt{A^2 + B^2}$

thanks

upbeat helm Mar 14, 2022, 3:59 AM

#

woeful bobcat hey, does anybody know the steps from left to right? I tried rewriting the cosin...

this would go in #calculus

#

and it is in the form sin(0)/cos(pi/2) which you can use l'h on, so i would think that is what they did

inland mica Mar 14, 2022, 4:27 AM

#

fossil yacht Mar 14, 2022, 5:04 AM

#

inland mica

what have you tried?

inland mica Mar 14, 2022, 5:05 AM

#

I am stuck on this question

fossil yacht Mar 14, 2022, 5:05 AM

#

where are you stuck

inland mica Mar 14, 2022, 5:05 AM

#

idk what to do

fossil yacht Mar 14, 2022, 5:06 AM

#

start by trying to find the measure angle CFE

abstract saddle Mar 14, 2022, 6:40 AM

#

How would I go about solving this?

dark sparrow Mar 14, 2022, 7:23 AM

#

,rccw

somber coyoteBOT Mar 14, 2022, 7:23 AM

#

abstract saddle Mar 14, 2022, 7:40 AM

#

somber coyote

I got the answer (I think)

#

Is angle of elevation/depression always 90 degrees?

upper karma Mar 14, 2022, 7:43 AM

#

The angles of depression of two boats from the top of a cliff are 31° and 23° respectively. If the two boats are 150 m apart, find the height of the cliff above sea level, correct to the nearest m.

#

I have done something wrong I can feel it

mystic karma Mar 14, 2022, 11:09 AM

#

@dusky surge where you at bro

woeful bobcat Mar 14, 2022, 1:07 PM

#

upper karma I... really don't like here that x->(infinity) Although I'm not a mathematician ...

ty

woeful bobcat Mar 14, 2022, 1:07 PM

#

upbeat helm this would go in <#326138772477575180>

oh, sorry and thank you

urban vine Mar 14, 2022, 1:51 PM

#

Uhhhh

#

I think there’s supposed to be two triangles

idle wedge Mar 14, 2022, 1:54 PM

#

urban vine Uhhhh

grave nova Mar 14, 2022, 3:54 PM

#

urban vine Uhhhh

Previous question maybe???

past sonnet Mar 14, 2022, 5:16 PM

#

I want learn Euclidean syntheitic geometry any book you recommend

deft veldt Mar 14, 2022, 5:49 PM

#

might wanna delete this before a mod sees this

#

lol

idle wedge Mar 14, 2022, 5:58 PM

#

write it down on paper and fill in as many angles as you can

#

we're not here to do your homework, we're here to help you understand and guide you into the right direction

#

first figure out the ratio of the polygons' sizes

urban vine Mar 14, 2022, 6:18 PM

#

grave nova Previous question maybe???

No there was supposed to be a second triangle

#

But there wasn’t

grave nova Mar 14, 2022, 6:19 PM

#

I was thinking maybe the second triangle was on a previous question

wary zinc Mar 14, 2022, 6:50 PM

#

idle wedge Mar 14, 2022, 6:58 PM

#

wary zinc

what's the formula for calculating the slope of a line given two points?

wary zinc Mar 14, 2022, 6:59 PM

#

Subtract the make a fraction

idle wedge Mar 14, 2022, 7:13 PM

#

right, then you should be able to fill in the top 3

#

what about the length?

limber wing Mar 14, 2022, 10:19 PM

#

thats eacy

#

45 degrees

grizzled lichen Mar 14, 2022, 10:58 PM

#

I need help with a Geometry mapping issue

The goal is to create a hexagon from equilateral triangles generated in from the center in a clockwise motion
I have a functional loop that represents the current 'ring' and the current 'edge' being created

code:

int i = 0;
int r = 0;
Vector3 p = Vector3.zero;
for (int ring = 0; ring < gridSize; ring++)
{
    for (int edge = 0; edge <= ring * 6; edge++)
    {
        Verts.Add(new Vector3(
             p.x + 0.2f * (float)Math.Cos(ring * 60 * Math.PI / 180f),
             p.y + 0.2f * (float)Math.Sin(ring * 60 * Math.PI / 180f),
            p.z + 0));
        p = Verts[Verts.Count - 1];

        if (i >= 2)
        {
        int shift = ((ring - 1) * 6) + edge;
            if (shift % 2 == 0)
            {
                Tris.Add(i);
                Tris.Add(i - shift );
                Tris.Add(i - 1);
            }

            if (shift % 2 != 0)
            {
                Tris.Add(i);
                Tris.Add(i - shift );
                Tris.Add(i - shift - 1);
            }
            i++;
        }
        r += ring * 6;
}    }

grizzled lichen Mar 14, 2022, 11:16 PM

#

I fear my calculations and assumptions are wrong

R at the bottom is an accumulator so it should yield in order 0,6,18,36,60...

grizzled lichen Mar 14, 2022, 11:54 PM

#

this is the progress I've made

#

grave nova Mar 15, 2022, 12:38 AM

#

You’re probably better off asking in the Unity discord or some other h programming discord @grizzled lichen

quasi galleon Mar 15, 2022, 12:43 AM

#

can someone help me with this

sleek pecan Mar 15, 2022, 12:58 AM

#

I'm pretty sure mFGH = 90 because it goes to points F and H which is a semi-circle. So 180/2=90

thin leaf Mar 15, 2022, 1:06 AM

#

…uuhh

vagrant ore Mar 15, 2022, 2:22 AM

#

how do you do this?

sleek pecan Mar 15, 2022, 2:24 AM

#

if the diameter is 16.4. The radius is 8.2. And since it's a right 45-degree triangle, both sides are 8.2. Meaning the answer is 8sqrt2

vagrant ore Mar 15, 2022, 2:25 AM

#

that's wrong

#

I tried it

sleek pecan Mar 15, 2022, 2:26 AM

#

Oh I’m sorry. I’m not sure then

#

I realized my mistake. I calculated the length of JM, not the arc.

vital pike Mar 15, 2022, 2:33 AM

#

does anyone know the formula for this

Screen_Shot_2022-03-14_at_10.17.31_PM.png

sleek pecan Mar 15, 2022, 2:37 AM

#

vital pike Mar 15, 2022, 2:38 AM

#

tyyy

willow anvil Mar 15, 2022, 5:16 PM

#

Prove that the diagonal of the 3D parelelogram ( not a native english speaker ) ABCDA1B1C1D1 cuts through the center of the triangle BDA1

#

craggy river Mar 15, 2022, 8:19 PM

#

grizzled lichen I need help with a Geometry mapping issue The goal is to create a hexagon from ...

In Unity you should probably be using Mathf instead of Math, and there's also a Deg2Rad and Rad2Deg (just a little easier)

light axle Mar 15, 2022, 9:37 PM

#

can someone help me with

idle wedge Mar 15, 2022, 9:47 PM

#

light axle can someone help me with

what is the slope of y = mx + b?
if you know that, then you can rewrite the equation in that form and you're done

light axle Mar 15, 2022, 9:58 PM

#

idle wedge what is the slope of y = mx + b? if you know that, then you can rewrite the equa...

so the answer 2/3

idle wedge Mar 15, 2022, 9:58 PM

#

light axle so the answer 2/3

correct

light axle Mar 15, 2022, 9:59 PM

#

thanks

upper karma Mar 16, 2022, 2:56 AM

#

Can anyone help me on this question?

For a quadrangle ABCD inscribed in a circle O, two diagonal lines are perpendicular to each other. Define E as the point where the two diagonal lines meet, and F as the foot of a perpendicular line to line AB drawn from C. The radius of the circumcircles of triangle AEF and BCF are 1 and 2 each. Find the area of Circle O.
a)π
b)3π
c)4π
d)5π
e)7π
(Angle ABC is not 90°.)

#

Yes, this question did not give any drawings or whatsoever.....

crude niche Mar 16, 2022, 3:04 AM

#

then draw it urself, it would make it a lot easier yk

upper karma Mar 16, 2022, 3:07 AM

#

crude niche then draw it urself, it would make it a lot easier yk

Yeah, I've tried several times before asking this here.

#

How do I use the radius of circumcircle of triangle AEF?

#

You could draw a circumcircle of quadrangle ECBF- how do you use this advantage though

#

Or, does this question lack information?

#

<@&286206848099549185>

ripe skiff Mar 16, 2022, 3:26 AM

#

pls try not to ping helpers unless you're in a help channel.

upper karma Mar 16, 2022, 3:27 AM

#

Oh....I apologize

#

Should I have sent this in #help though?

upper karma Mar 16, 2022, 3:52 AM

#

Edit:Nobody solved this. Fine, I did it myself. Here's the solution:

#

#

||law of sine saves the day.||

near sand Mar 16, 2022, 3:54 AM

#

Could someone help explain what the construction of these two are?

tawdry pivot Mar 16, 2022, 10:37 AM

#

ruler and compass constructions of ab and a/b

karmic void Mar 16, 2022, 11:56 AM

#

I have a more etymological question. Does anyone know why the barycenter of a triangle got that name?

upper karma Mar 16, 2022, 12:24 PM

#

from Ancient Greek βαρύς (barús) 'heavy', and κέντρον (kéntron) 'center') (Wikipedia)

upper karma Mar 16, 2022, 12:24 PM

#

karmic void I have a more etymological question. Does anyone know why the barycenter of a tr...

you can just search anything online these days, you don't have to ask

karmic void Mar 16, 2022, 12:37 PM

#

i tried that but this is not what i am searching. i am trying to find the connection between the weight which in greek is βαρος βαρυκεντρο barycenter and the intercept point of the three medians of a triangle

idle wedge Mar 16, 2022, 1:43 PM

#

karmic void i tried that but this is not what i am searching. i am trying to find the connec...

because it is the center of mass

karmic void Mar 16, 2022, 1:43 PM

#

What exactly do you mean

idle wedge Mar 16, 2022, 1:45 PM

#

if you take a triangle and want to balance it on exactly one point the barycenter is that point at which it is balanced

#

like this (from here https://math.stackexchange.com/a/3454865)

karmic void Mar 16, 2022, 1:51 PM

#

Thank you very much

upper karma Mar 16, 2022, 4:38 PM

#

a) At the local ice rink, popcorn is sold in a square-based pyramid-shaped container with side lengths of 15 cm and a height of 21 cm. Calculate how much popcorn this container will hold.

b) After a hockey game at the local arena, a tired player gets a drink from the water cooler. The water cups provided have a conical shape with a diameter of 11 cm and a height of 12cm. How much water will fit into this cup?

c) A basketball has a diameter of 24.8 cm. How much air does it take to fill this basketball?

d) During the holiday season, a company packages their chocolates in a box shaped like a pyramid. The base of the box is a square with side lengths of 10 cm. The pyramid is 12 cm high. Calculate the amount of packaging needed for this pyramid-shaped box.

e) A new popsicle on the market has the shape of a cone with a radius of 1.5 cm and a height of 15 cm. Calculate the surface area of this popsicle so that the company will know at least how much packaging may be necessary.

f) A chocolate in the shape of a sphere is packaged by wrapping it in colored foil. If the chocolate has a radius of 1.8 cm, calculate the amount of foil needed to package the candy. Draw a diagram.

icy berry Mar 16, 2022, 11:04 PM

#

#

,rotate

somber coyoteBOT Mar 16, 2022, 11:04 PM

#

icy berry Mar 16, 2022, 11:04 PM

#

How does a link with b

#

Is my working out okay so far ?

fossil pier Mar 16, 2022, 11:35 PM

#

#

can someone check my proof?

#

statements and reasons?

sinful gyro Mar 17, 2022, 12:57 AM

#

@fossil pier I think, you second step is not necessary.

fossil pier Mar 17, 2022, 12:58 AM

#

yeah I just noticed that but ty

sinful gyro Mar 17, 2022, 12:58 AM

#

Ok ok. The rest is valid.

#

Good proof.

fossil pier Mar 17, 2022, 12:58 AM

#

bc the angle dB and angle ae are un the given already

#

and marked

#

so that's how I knew

#

#

could u check this one

#

@sinful gyro

sinful gyro Mar 17, 2022, 1:03 AM

#

Yup

#

Valid

#

#

@icy berry I think you forgot the sin(2theta) bro

cold totem Mar 17, 2022, 8:58 AM

#

how?

restive fiber Mar 17, 2022, 10:14 AM

#

Hello people I'm looking for a coordinate geometry course for computer vision underpinnings of mathematical and physical-based prerequisites are coordinate geometry, linear algebra
So, would someone mind helping me to recommend to take one..

#

restive fiber Mar 17, 2022, 10:15 AM

#

restive fiber

How come the 2nd question got an answer of 77mm. Can someone mind interpretin it?

grave pond Mar 17, 2022, 12:21 PM

#

It sounds pretty strange that an answer in millimeters can be produced for a question with only unitless numbers in it.

#

It makes some numeric sense that (400:600:1200) = (24:36:72), but how the 72 suddenly becomes millimeters is a mystery.

grave pond Mar 17, 2022, 12:40 PM

#

I think it is somewhat conventional for "focal length" for digital cameras to mean the focal length of an imagined lens that would give the same field of view with a 24×36 mm image sensor (that is, the standard frame size on chemical film). However, that doesn't help us here -- we still don't know the resolution the image coordinates are given in. (They can't be pixels; that would be ridiculously low resolution; they also can't be millimeters on the usually imagined 24×36 mm sensor because that would place the image point far outside the sensor; the origin of the coordinate system is in the center of the sensor).

nocturne remnant Mar 17, 2022, 2:02 PM

#

The numbers represent the surface areas?

#

You can set the surface areas of each different face to be p, q, r
Then obtain 3 linear equations in p,q,r

dark sparrow Mar 17, 2022, 2:34 PM

#

to clarify: we want the surface area of one block given the surface areas of each of those composite blocks, yes?

#

@upper karma

#

okay

#

let p be the area of the top/bottom face, q be the area of the front/back face and r be the area of the left/right face

#

then we have 2p+4q+4r = 72, 4p+2q+4r = 102 and 4p+4q+2r = 96

grave pond Mar 17, 2022, 2:39 PM

#

Add all the equations to get a value for 10(p+q+r).

dark sparrow Mar 17, 2022, 2:40 PM

#

^ there is a trick here

#

and also note the surface area of one block is 2p+2q+2r

grave pond Mar 17, 2022, 2:44 PM

#

The side lengths also work out nicely.

narrow urchin Mar 17, 2022, 2:45 PM

#

wow you are smart

wanton hamlet Mar 17, 2022, 5:33 PM

#

dont know much but i think the brackets around x-3 in the second problem refer to absolute value

#

so if x=-3 then [x-3] would be 6

dark sparrow Mar 17, 2022, 6:44 PM

#

those are not brackets those are absolute value bars

#

also best not to divulge any info when OP is choosing not to say anything beyond posting the questions

#

oh yeah that too

upper karma Mar 17, 2022, 8:05 PM

#

Guys i need help with this one

#

So i basically need to find radius R, radius r, angle v, and the area of the dark grey area

#

a) radius R.

#

b) radius r, as in Figure 5.

#

c) angle v, as in Figure 5.

#

d) the area og the "dark grey area", (Figue 5)

mild birch Mar 17, 2022, 8:37 PM

#

upper karma Guys i need help with this one

could you translate this please

upper karma Mar 17, 2022, 8:41 PM

#

The picture shows a vent hood on the roof of an HTX-Building engineering workshop. The upper part of the vent hood is designed as two frusto bumps. The one truncated cone with target is shown in Figure 4. The truncated cone is made of a thin plate and the unfolded truncated cone is shown as a "Grey" area in Figure 5.

#

At the calculations, the plate thickness is disregarded.

#

a) Determine radius R.

#

b) Determine radius r, which is shown in figure 5.

#

c) Determine the angle v, shown in figure 5.

#

d) Detmine the area of the "gray" area.

#

Hope you understand my translation...

tall python Mar 17, 2022, 11:12 PM

#

uh

#

does anyone know how to do dilations

#

i need help learning how to do this shit bro

#

my geometry teacher can't teach to save his life

#

if anyone knows how to explain it simply unlike some grown ass men with feather dusters as a mustace

#

please ping me

tall python Mar 18, 2022, 12:02 AM

#

bro it's been hours

#

seriously

#

💀

ripe skiff Mar 18, 2022, 2:50 AM

#

sin (90 deg + x deg)= sin 90 deg + sin x deg = sin x deg?

upbeat helm Mar 18, 2022, 2:51 AM

#

ripe skiff sin (90 deg + x deg)= sin 90 deg + sin x deg = sin x deg?

no

ripe skiff Mar 18, 2022, 2:51 AM

#

oop

upbeat helm Mar 18, 2022, 2:51 AM

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$\sin(\alpha+\beta) = \sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)$

somber coyoteBOT Mar 18, 2022, 2:51 AM

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Brontochad (Shuri for honorable)

uncut bronze Mar 18, 2022, 4:30 AM

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guys, how can i proof that 1/h²=1/b²+1/c²

grave pond Mar 18, 2022, 4:40 AM

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One way: Multiply through by h², and then 1=sin²+cos².

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Another way (at least superficially): The area of the large triangle is ah/2 = bc/2. Multiply the LHS of the equation by a²h² and the RHS by b²c². This yields a²=b²+c².

uncut bronze Mar 18, 2022, 4:47 AM

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Thanks man

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i will try to ask my teacher to allow me use this

upper merlin Mar 18, 2022, 6:45 AM

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why would you have doubt in all your 10 answers?

tall python Mar 18, 2022, 12:13 PM

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hm?

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wow

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so people were online

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i cant even ask for help on discord bro💀💀

limber goblet Mar 18, 2022, 1:55 PM

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Can any one can do it

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Pls

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All this

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Prob

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And answera

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Pls any one do it

idle wedge Mar 18, 2022, 2:37 PM

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we're not here to do your homework

runic zinc Mar 18, 2022, 3:27 PM

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I don't need the answer, but how do i go about working this out, obvs a is 86 because its parrellel but not im stuck lol

tall python Mar 18, 2022, 3:34 PM

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runic zinc I don't need the answer, but how do i go about working this out, obvs a is 86 be...

@runic zinc they're not gonna help you bro💀

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i done asked twice now

spare delta Mar 18, 2022, 3:59 PM

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tall python does anyone know how to do dilations

what part do you not understand

acoustic jungle Mar 18, 2022, 4:32 PM

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runic zinc I don't need the answer, but how do i go about working this out, obvs a is 86 be...

use triangles. Sum of angles add to 180.

tall python Mar 18, 2022, 4:36 PM

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spare delta what part do you not understand

literally everything brah

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that's why i've been asking somebody if they can simplify it for me cause my geometry teacher can't do that

spare delta Mar 18, 2022, 4:38 PM

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dilation is essentially
you have a centre of dilation and a scale factor
lets say your shape is called A
for each corner of your shape A, take the line between that corner and the centre of dilation
multiply the length of that line by the scale factor, and that will give you the new point after the transformation

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do that for each point and you will have the transformed shape

spare delta Mar 18, 2022, 4:48 PM

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runic zinc I don't need the answer, but how do i go about working this out, obvs a is 86 be...

hint: for two parallel lines you can draw a line between the two which meets both at 90°

upper merlin Mar 18, 2022, 6:39 PM

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still stone Mar 18, 2022, 6:50 PM

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upper merlin

You could try opening the cos(A+B) using the identity cos(A+B)=cosAcosB-sinAsinB

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Haven't done trigo identities in forever so nothing else comes to mind really

upper merlin Mar 18, 2022, 6:54 PM

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I did that and got $\frac{(1 - \cos A)(1 + \cos B) + \sin A \sin B}{(1 + \cos A)(1 - \cos B) + \sin A \sin B}$

somber coyoteBOT Mar 18, 2022, 6:54 PM

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LazyKnight

upper merlin Mar 18, 2022, 6:55 PM

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it seems like the right way to do

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but there's probably some identity I don't know about ):

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nvm finally got it lol

upper karma Mar 18, 2022, 7:23 PM

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Solve.

spare delta Mar 18, 2022, 7:30 PM

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is that a command? catThink

idle wedge Mar 18, 2022, 8:57 PM

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spare delta is that a command? <:catThink:526983414226747393>

\solve

spare delta Mar 18, 2022, 8:57 PM

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i meant 'are you commanding me to solve it' but thanks lol

idle wedge Mar 18, 2022, 8:58 PM

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spare delta i meant 'are you commanding me to solve it' but thanks lol

i know KEK

spare delta Mar 18, 2022, 8:58 PM

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wait
that's not a command is it bleakkekw

idle wedge Mar 18, 2022, 8:58 PM

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spare delta wait that's not a command is it <:bleakkekw:913344117981999125>

not sure, we could try it though 👀 edit: nope, lol

spare delta Mar 18, 2022, 8:59 PM

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well there's always wolfram

idle wedge Mar 18, 2022, 9:09 PM

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30 deg, trickyy

thin leaf Mar 18, 2022, 9:29 PM

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Bing-

idle wedge Mar 18, 2022, 9:30 PM

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thin leaf Bing-

-bong?

thin leaf Mar 18, 2022, 9:30 PM

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Bing….

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No loll

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Bing

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O

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Was his name Oh

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:).

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Hehe

shut granite Mar 18, 2022, 10:02 PM

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The law of Sines, does it have to follow the order of a = b = c? Or can it be a = c?

spare delta Mar 18, 2022, 10:04 PM

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equality is transitive
a = b = c implies that a = c yeah

shut granite Mar 18, 2022, 10:04 PM

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Okay thanks

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If an angle is 110°15’ would that make it 110.20°?

grave pond Mar 18, 2022, 10:24 PM

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110 + 15/60 is what?

shut granite Mar 18, 2022, 10:26 PM

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Ah, my bad. 110.25

grave pond Mar 18, 2022, 10:27 PM

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Yes.

thin leaf Mar 18, 2022, 11:51 PM

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Abcdefghijklmnopqrstuvwxyz

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What that’s English

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Dang

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Nvm

upper karma Mar 19, 2022, 4:41 AM

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Help pls?

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with solution

weary drift Mar 19, 2022, 7:41 AM

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@upper karma pls dont just give answers

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@upper karma pls dont just ask for answers, show what u tried

upper karma Mar 19, 2022, 7:43 AM

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tysm

upper karma Mar 19, 2022, 7:44 AM

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weary drift <@456226577798135808> pls dont just give answers

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I just want to know if im right

weary drift Mar 19, 2022, 7:46 AM

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u posted no work of ur own

pure hazel Mar 19, 2022, 2:40 PM

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Can someone help me with this
if a+b+c=π Then prove that Cot(a)+ cot(b)+ cot(c)=cot(a)cot(b)cot(c)

pallid drum Mar 19, 2022, 3:23 PM

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So I'm looking to include something in my plugin that causes two particles to go around in a spiral trailing behind a projectile in Minecraft, I can get a circle to spiral around easily enough horizontally, but I'm not too sure how to make it follow and change based on the yaw/pitch of the projectile (can't really set the velocity of a particle more than once, so it actually keeps spawning more in). Any ideas?

zenith elm Mar 19, 2022, 6:46 PM

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hey need a little help

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grave pond Mar 19, 2022, 6:52 PM

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If you draw a line parallel to the downward-sloping one, through the intersection where 36° is marked, you can move all the angle measures to that intersection.

zenith elm Mar 19, 2022, 6:53 PM

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well i really can't mesure it

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i have to somehow calculate it from the 36

grave pond Mar 19, 2022, 6:53 PM

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I mean, just move the indications of angle sizes down to that intersection.

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Or, perhaps slightly easier to argue, do it this way:

fossil sundial Mar 19, 2022, 7:11 PM

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yo

fleet flume Mar 19, 2022, 9:21 PM

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upper karma Solve.

it's 20 degrees

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cus 80 on 1 side and 80 on 1 side

fleet flume Mar 19, 2022, 9:28 PM

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zenith elm hey need a little help

a=48

fleet flume Mar 19, 2022, 9:28 PM

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zenith elm

a+2a+36=180

zenith elm Mar 19, 2022, 9:29 PM

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fleet flume a+2a+36=180

yup

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someone already typed me it in dms

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i was just too blind and didn't see it

fleet flume Mar 19, 2022, 9:29 PM

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oh ok

zenith elm Mar 19, 2022, 9:29 PM

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thank you for your effort tho

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feels good knowing that i am not stupid but only half stupid and half blind bleakkekw

sharp sigil Mar 19, 2022, 10:06 PM

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c and d

Screen_Shot_2022-03-19_at_6.00.51_PM.png

shut granite Mar 19, 2022, 11:24 PM

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So for this problem I’m solving for angle B. I used both law of cosine and sines to solve for B and they gave me similar answers. I put in the answer from law of cosine and it says my answer is wrong and counted my answer from law of sines correct. So my question is: is there a specific formula to use to find an angle?

grave pond Mar 19, 2022, 11:39 PM

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Are you sure it's not just rounding error?

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It looks like your law-of-cosines calculation is using intermediate results with a fairly low number of significant digits.

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I'm assuming that the "it" that declared the results wrong and correct is an auto-grading system that doesn't see your actual work.

shut granite Mar 19, 2022, 11:51 PM

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grave pond Are you sure it's not just rounding error?

I’ve checked my answer 3 times for law of cosine, I keep getting the same answer. So I assume that it just went for law of sines

grave pond Mar 19, 2022, 11:52 PM

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Do you also keep rouding your intermediate results to the same number of digits?

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For example the value for a you write as 12.20 is more precisely 12.198074809815519.

shut granite Mar 19, 2022, 11:54 PM

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The problem asked me to round my answer to the nearest hundredths, so I just rounded to the nearest hundredths for anything answer I get

grave pond Mar 19, 2022, 11:55 PM

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Your intermediate values are not "answers". They're intermediates.

shut granite Mar 19, 2022, 11:55 PM

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Ah okay

grave pond Mar 19, 2022, 11:56 PM

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One of your lines even seems to mix 12.19 with 12.20.

shut granite Mar 19, 2022, 11:56 PM

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Yes, I messed up there but I fixed it earlier. I still got the same answer after that

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The -335.24 was suppose to be -335.84. I still got 10.54 (rounded) as my answer

grave pond Mar 20, 2022, 12:01 AM

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I agree that 12.20²+14²-3² is 335.84. However, with the better approximation of a above, the value of a²+14²-3³ is closer to 335.7930290659.
You see that several hundredths of error have already crept in.

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The number you write as 341.6 should be closer to 341.5460946748.

shut granite Mar 20, 2022, 12:04 AM

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Let me check my work again

grave pond Mar 20, 2022, 12:06 AM

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These rounding errors make the input to the final arrcosine slightly different from what it ought to have been. The value is already pretty close to 1, which magnifies the effect errors in the input has. As a result of that error, the arccos gives you 10.53664° whereas with better approximations you would have gotten 10.53111°.

shut granite Mar 20, 2022, 12:09 AM

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So I shouldn’t round my intermediates and only round my final answer?

grave pond Mar 20, 2022, 12:10 AM

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Right. If possible keep them in computer/calculator memory, and if you have to write them down, write several more digits of them than you want your final result to have.

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When I try on my computer I get the same answer for the law-of-sines and law-of-cosines calculutions, up to the ~16 digits of precision my calculator program outputs.

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Though if I round a to 12.2 like you do, the arcsine only gives 10.52943°.

shut granite Mar 20, 2022, 12:13 AM

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The arcsine only gives 10.52943° if you only round a to 12.2?

grave pond Mar 20, 2022, 12:14 AM

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Yeah,

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; asin(sin(48*deg)*3/12.2)/deg
    ~10.52942884319477848251

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whereas

; asin(sin(48*deg)*3/a)/deg
    ~10.53110964429801571849

shut granite Mar 20, 2022, 12:15 AM

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Ooh

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Okay I see now

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Thank you so much

restive fiber Mar 20, 2022, 3:54 AM

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A point (2,3) is translated by (2,1) and scaled by (5,5). Find the new coordinates of the point.

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The Ans : 20,20
Its 2D transformation related to computer vision

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Can someone plz interprett how come the ans 20,20

ruby nacelle Mar 20, 2022, 9:37 AM

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can anyone please help me understand this?

grave pond Mar 20, 2022, 10:50 AM

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restive fiber Can someone plz interprett how come the ans 20,20

After the translation the point is at (4,4).

fresh sky Mar 20, 2022, 10:55 AM

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I need major help on a math question

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so uhh

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is this one

Screen_Shot_2022-03-20_at_3.55.50_AM.png

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Ive mirrored over the shape

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to get

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Screen_Shot_2022-03-20_at_3.56.39_AM.png

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but now I need to elaborate on why the line hits point z

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and why cant it go out of the semicircle

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like this

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Screen_Shot_2022-03-20_at_3.57.39_AM.png

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I suspect its something to do with the right angle

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and im trying to see what would happen if I extended the line out of the semicircle

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but still kept angle BDC at 90 degrees

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plz help

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oh also

restive fiber Mar 20, 2022, 11:03 AM

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grave pond After the translation the point is at (4,4).

Thank you for trying to solve but I did this way after adding those (2,3)+(2,1) in column and multiplying (scaled up) with (5,5)
Sol:(20,20)

fresh sky Mar 20, 2022, 11:03 AM

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I need to know why line DZ cant be inside the semicircle aswell

acoustic jungle Mar 20, 2022, 7:09 PM

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fresh sky

thales theorem.

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thales theorem says 2 points on a diameter and one point somewhere else means 90 degrees. I think you have to manipulate it and do some stuff to prove the thing you have there since thales theorem doesn't exact describe your situation.