#help-0 | Mathematics | Page 914

alpine sable Dec 31, 2021, 9:07 PM

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sheaf, prismatic, single intersection, 2 parallel and 1 cutting, none of them touching each other.

knotty sleet Dec 31, 2021, 9:08 PM

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Because the two lines are each only the intersections of two of the three planes

alpine sable Dec 31, 2021, 9:08 PM

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oh yes thats right

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whoops

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so 3 different ways for a solution

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2 other ways they can be

knotty sleet Dec 31, 2021, 9:08 PM

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alpine sable sheaf, prismatic, single intersection, 2 parallel and 1 cutting, none of them to...

Ye

alpine sable Dec 31, 2021, 9:08 PM

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thanks :))

knotty sleet Dec 31, 2021, 9:09 PM

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Only sheaf and single intersection for solutions

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If 2 parallel or 3 parallel or prism then no solutions

alpine sable Dec 31, 2021, 9:09 PM

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oh whooops yep i did it again

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prismatic dont count as solution yh

knotty sleet Dec 31, 2021, 9:10 PM

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You can maybe draw a few diagrams on a page and keep it with your notes

alpine sable Dec 31, 2021, 9:10 PM

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yea im gonna do that now, thank you :)) happy new year.

knotty sleet Dec 31, 2021, 9:11 PM

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No worries, happy new year to you too 👍 😄

alpine sable Dec 31, 2021, 9:11 PM

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.close

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lavish monolith Dec 31, 2021, 9:26 PM

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why dim of subspace W = {(x,y): x + y = 0; of R^2 isn't 2 ?

lone heartBOT Dec 31, 2021, 9:26 PM

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lavish monolith why dim of subspace W = {(x,y): x + y = 0; of R^2 isn't 2 ?

lavish monolith Dec 31, 2021, 9:27 PM

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since it's R^2 shouldn't be 2 as dimension

robust geode Dec 31, 2021, 9:29 PM

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Not really

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The concept of dimension is mostly about the indépendance of the variables

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(each ones representing values on different axis)

lavish monolith Dec 31, 2021, 9:31 PM

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but we don't have matrix here how can I determine the dim

robust geode Dec 31, 2021, 9:31 PM

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Because R² is a matrix? 🤔

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Since in this set W, x and y are linked together by the equation x+y=0, then if you have x, you have y (and it would be the same if you set a value for y first, too)

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You can also see that x+y=0 is exactly the same as y=-x

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Which is... A line in R²

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And a line is of dimension what?

lavish monolith Dec 31, 2021, 9:34 PM

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oh thank you

lavish monolith Dec 31, 2021, 9:34 PM

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robust geode And a line is of dimension what?

1

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thank you have a good day

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.close

lone heartBOT Dec 31, 2021, 9:35 PM

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robust geode Dec 31, 2021, 9:35 PM

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Please don't ignore what I said above @lavish monolith

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The independance of x, y, z,... Is the core of the concept of dimensions

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The fact that a line is of dimension 1 in R^n (n>=1) comes from that

lone heartBOT Dec 31, 2021, 9:36 PM

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indigo tapir Dec 31, 2021, 9:37 PM

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can i get help here

lone heartBOT Dec 31, 2021, 9:37 PM

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indigo tapir can i get help here

indigo tapir Dec 31, 2021, 9:37 PM

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i need to find out how to do a question

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do i subtract x^3 by x^-3?

lavish monolith Dec 31, 2021, 9:41 PM

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robust geode The independance of x, y, z,... Is the core of the concept of dimensions

no no i didn't ignore it in fact i wrote it as note

robust geode Dec 31, 2021, 9:42 PM

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I just wanted to emphasize since it is the most important thing to understand in order for dimensions to make sense

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So not only graphically, but mostly algebraically

robust geode Dec 31, 2021, 9:42 PM

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indigo tapir

Handle the problem step by step

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The difficulty I would say is to figure out the order

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Are you beginning to be used at using fractions?

indigo tapir Dec 31, 2021, 9:44 PM

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well no

robust geode Dec 31, 2021, 9:44 PM

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Have you seen them?

indigo tapir Dec 31, 2021, 9:44 PM

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i have seen fraction before

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well i think which answer it is

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.close

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indigo tapir Dec 31, 2021, 10:28 PM

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so how do i do this?

lone heartBOT Dec 31, 2021, 10:28 PM

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indigo tapir so how do i do this?

indigo tapir Dec 31, 2021, 10:28 PM

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since all of the angle add up to 180

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should it be 180-3x

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wait it should be 2x

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bruh im confused

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because it should be either 2 or 4

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heck it could be 3

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i think to find it

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you have to do 180 minus the other 2 angles

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but then why is the other y+2x

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nvm ill figure it out

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.close

lone heartBOT Dec 31, 2021, 10:33 PM

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lone heartBOT Dec 31, 2021, 11:30 PM

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shadow wadi Dec 31, 2021, 11:41 PM

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hi, can someone explain this to me?

lone heartBOT Dec 31, 2021, 11:41 PM

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shadow wadi hi, can someone explain this to me?

elfin snow Dec 31, 2021, 11:50 PM

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it's just factored

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you can use the quadratic formula to arrive there

lone heartBOT Dec 31, 2021, 11:56 PM

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undone agate Jan 1, 2022, 12:12 AM

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lone heartBOT Jan 1, 2022, 12:12 AM

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undone agate

undone agate Jan 1, 2022, 12:13 AM

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I understand that im using FTOC, but why is the answer negative? If we graph out the function

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The function is always above the xaxis

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So the integral would measure the area between the xaxis and f(x) so why isnt the answer positive?

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It's negative according to FTOC but graphically i dont understand how it is negative

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boreal drum Jan 1, 2022, 12:18 AM

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You're integrating f(x) not F(x)

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And f(x) is the derivative of F(X) which will be negative for x less than 5

lone heartBOT Jan 1, 2022, 12:29 AM

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@undone agate Has your question been resolved?

undone agate Jan 1, 2022, 12:29 AM

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Thanks

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lone heartBOT Jan 1, 2022, 2:13 AM

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sturdy fog Jan 1, 2022, 2:51 AM

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can someone tell me how i can find the radius of the smaller cone

Screen_Shot_2022-01-01_at_1.56.54_pm.png

lone heartBOT Jan 1, 2022, 2:51 AM

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sturdy fog can someone tell me how i can find the radius of the smaller cone

severe sluice Jan 1, 2022, 2:52 AM

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sturdy fog can someone tell me how i can find the radius of the smaller cone

distance from the vertex is proportional to radius

sturdy fog Jan 1, 2022, 2:54 AM

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im still confused could you please show it step by step?

glass lichen Jan 1, 2022, 3:00 AM

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sturdy fog can someone tell me how i can find the radius of the smaller cone

What's the formula for volume of a cone?

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That's an obvious place to start.

sturdy fog Jan 1, 2022, 3:00 AM

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v= 1/3Ah

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1/3pir^2h

glass lichen Jan 1, 2022, 3:01 AM

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sure... more usefully is $V=\frac{\pi}{3}r^2h$

ocean sealBOT Jan 1, 2022, 3:01 AM

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Mosh

glass lichen Jan 1, 2022, 3:01 AM

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Find the volume of the cone, find the volume of the ice cream, then set up the appropriate eqn

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noting as bob pointed out, radius and height (for the ice cream specifically) are related through similar triangles

sturdy fog Jan 1, 2022, 3:02 AM

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sorry im still really confused could you walk it thru w me

glass lichen Jan 1, 2022, 3:02 AM

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No, about to log off.

sturdy fog Jan 1, 2022, 3:02 AM

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ah okay

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thanks

lone heartBOT Jan 1, 2022, 3:17 AM

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elder quartz Jan 1, 2022, 5:51 AM

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My son wants to know what other maths you need to know for trigonometry and I have forgot. Can someone help

lone heartBOT Jan 1, 2022, 5:51 AM

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elder quartz My son wants to know what other maths you need to know for trigonometry and I ha...

gray isle Jan 1, 2022, 5:53 AM

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basic geometry and algebra

lone heartBOT Jan 1, 2022, 6:06 AM

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@elder quartz Has your question been resolved?

elder quartz Jan 1, 2022, 6:06 AM

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Yes

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lone heartBOT Jan 1, 2022, 7:37 AM

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tawny fable Jan 1, 2022, 8:08 AM

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Heyo

lone heartBOT Jan 1, 2022, 8:08 AM

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tawny fable Heyo

tawny fable Jan 1, 2022, 8:08 AM

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I am back with the same question as before

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4.(c) if f is diff Df(x_0) = Df(x_0)

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I managed to prove that M(delta) = m(delta) for a specific delta, but I can't seem to prove that the limits are equal since we talk about a range of deltas as delta --> 0+

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<@&286206848099549185>

lone heartBOT Jan 1, 2022, 8:38 AM

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@tawny fable Has your question been resolved?

tawny fable Jan 1, 2022, 8:38 AM

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<@&286206848099549185>

lone heartBOT Jan 1, 2022, 9:08 AM

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@tawny fable Has your question been resolved?

tawny fable Jan 1, 2022, 9:16 AM

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<@&286206848099549185>

tawny fable Jan 1, 2022, 9:37 AM

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anyone?

knotty sleet Jan 1, 2022, 10:14 AM

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tawny fable anyone?

Was there something wrong with the method I showed you yesterday?

tawny fable Jan 1, 2022, 10:15 AM

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I am sorry. I might have missed what you said.

knotty sleet Jan 1, 2022, 10:15 AM

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knotty sleet Jan 1, 2022, 10:16 AM

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tawny fable I am sorry. I might have missed what you said.

Oh. Nw

tawny fable Jan 1, 2022, 10:18 AM

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So thats using the squeeze rule isnt it?

knotty sleet Jan 1, 2022, 10:19 AM

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Not really

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It's the same idea

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But not using the theorem per se

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It's really just definition of limits and manipulating inequalities

tawny fable Jan 1, 2022, 10:28 AM

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but eventually as I undestand it

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you proved it for a specific delta

knotty sleet Jan 1, 2022, 10:30 AM

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How do you mean?

tawny fable Jan 1, 2022, 10:30 AM

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I mean

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As I understand it

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Df(x_0)

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means lim delta -- > 0+ of M(delta)

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thus it has to work for all deltas

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in the range of 0<delta<something

knotty sleet Jan 1, 2022, 10:31 AM

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Yeah

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I've shown it works for 0<delta<delta'

tawny fable Jan 1, 2022, 10:34 AM

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Could you look at the inequality m >= D - epsilon

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and change sides

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and then add the 2 inequalities?

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M(delta) + (-m(delta)) <= 2epsilon ?

knotty sleet Jan 1, 2022, 10:36 AM

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Sure that's fine

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I don't see your point tho

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Oh

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If it's easier to understand that way then yh write it like that

tawny fable Jan 1, 2022, 10:40 AM

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I think I need to write it down to understand it more clearly

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If you would work with the defenition of x - x_0

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without h = x - x_0

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would it be the same?

knotty sleet Jan 1, 2022, 10:41 AM

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Yeah

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More or less

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Change up a few bits of notation but the idea won't be affected

lone heartBOT Jan 1, 2022, 11:41 AM

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@tawny fable Has your question been resolved?

orchid bane Jan 1, 2022, 12:10 PM

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can anyone solve my physics query

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if yes then ping me please

lone heartBOT Jan 1, 2022, 2:06 PM

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lone heartBOT Jan 1, 2022, 2:59 PM

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rain canyon Jan 1, 2022, 3:00 PM

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Let xyz = 1
Calculate
X/xy+x+1 +y/yz+z+1 + z/xz+z+1

lone heartBOT Jan 1, 2022, 3:00 PM

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rain canyon Let xyz = 1 Calculate X/xy+x+1 +y/yz+z+1 + z/xz+z+1

rain canyon Jan 1, 2022, 3:01 PM

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I Will use xy = 1/z?

tawdry saffron Jan 1, 2022, 3:02 PM

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$\frac{x}{xy}+x+1 + \frac{y}{yz}+z+1 + \frac{z}{xz}+z+1$

rain canyon Jan 1, 2022, 3:03 PM

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Nah

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Not that

rocky atlas Jan 1, 2022, 3:04 PM

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$\frac{x}{xy}+x+1 + \frac{y}{yz}+y+1 + \frac{z}{xz}+z+1$

ocean sealBOT Jan 1, 2022, 3:04 PM

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Ruffy🎄

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Ujju

rain canyon Jan 1, 2022, 3:04 PM

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Like that

tawdry saffron Jan 1, 2022, 3:04 PM

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oh

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parentheses exist

rain canyon Jan 1, 2022, 3:05 PM

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No

rocky atlas Jan 1, 2022, 3:07 PM

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Try substitutions with xy=1/z, yz=1/x and zx=1/y

vale wigeon Jan 1, 2022, 3:17 PM

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thonk

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so you explicitly refuse to write $\frac{x}{xy+x+1}$ as \texttt{x/(xy+x+1)} in plaintext? is that what you're saying? @rain canyon

ocean sealBOT Jan 1, 2022, 3:17 PM

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Ann

lone heartBOT Jan 1, 2022, 3:22 PM

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@rain canyon Has your question been resolved?

lone heartBOT Jan 1, 2022, 3:37 PM

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tawdry saffron Jan 1, 2022, 3:42 PM

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lone heartBOT Jan 1, 2022, 3:42 PM

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tawdry saffron

tawdry saffron Jan 1, 2022, 3:42 PM

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Can someone help me

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Simplify this

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And need a 1/k^2 in front

lone heartBOT Jan 1, 2022, 3:57 PM

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@tawdry saffron Has your question been resolved?

lone heartBOT Jan 1, 2022, 4:28 PM

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@tawdry saffron Has your question been resolved?

lone heartBOT Jan 1, 2022, 5:29 PM

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@tawdry saffron Has your question been resolved?

harsh swallow Jan 1, 2022, 6:23 PM

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does that say $e^{-i k \pi}$?

ocean sealBOT Jan 1, 2022, 6:23 PM

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Katharine

tawdry saffron Jan 1, 2022, 6:30 PM

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Yep

harsh swallow Jan 1, 2022, 6:49 PM

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is k an integer?

elfin snow Jan 1, 2022, 7:26 PM

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yes

tawdry saffron Jan 1, 2022, 7:48 PM

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Sadge

lone heartBOT Jan 1, 2022, 9:48 PM

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@tawdry saffron Has your question been resolved?

tawdry saffron Jan 1, 2022, 9:48 PM

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eh well

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.close I guess

lone heartBOT Jan 1, 2022, 9:48 PM

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bleak hearth Jan 1, 2022, 10:20 PM

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can someone help me with 8b pls

lone heartBOT Jan 1, 2022, 10:21 PM

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bleak hearth can someone help me with 8b pls

ancient saddle Jan 1, 2022, 10:33 PM

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bleak hearth can someone help me with 8b pls

Hello, take the derivative with respect to y on both sides of y = f(x)

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vocal slate Jan 1, 2022, 11:07 PM

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How do I prove/disprove $\lim _{x\to \infty }\left(\frac{\frac{2^x}{:x}}{\left(1.99\right)^x:}\right) = 0$

lone heartBOT Jan 1, 2022, 11:07 PM

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vocal slate How do I prove/disprove $\lim _{x\to \infty }\left(\frac{\frac{2^x}{\:x}}{\left(...

vocal slate Jan 1, 2022, 11:08 PM

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Plugging in values it seems to get closer and closer to 0, but wolfram alpha says it converges to infinity

ocean sealBOT Jan 1, 2022, 11:08 PM

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miku

vocal slate Jan 1, 2022, 11:19 PM

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I have gotten to here:
$\lim_{x\to \infty} \left( \frac{\frac{2^x}{x}}{\frac{199^x}{100^x}} \right)$ so
$\lim_{x\to \infty} \left( \frac{2^x}{x} \times \frac{100^x}{199^x} \right)$

surreal meadow Jan 1, 2022, 11:19 PM

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i think ratio test should work

ocean sealBOT Jan 1, 2022, 11:19 PM

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miku

vocal slate Jan 1, 2022, 11:20 PM

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ocean seal **miku**

with this, the problem I have is the 2^x/x tends towards infinity but the 100^x/199^x tends to 0

surreal meadow Jan 1, 2022, 11:20 PM

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have you tried a ratio test?

vocal slate Jan 1, 2022, 11:21 PM

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i will try it, thanks

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ill look up what it is

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i am bit confused, searching online is only coming up with stuff to do with series

copper stone Jan 1, 2022, 11:24 PM

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its weird wolfram says infinity

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the graph looks like this

vocal slate Jan 1, 2022, 11:26 PM

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the graph looks like it tends towards 0 too yeah

surreal meadow Jan 1, 2022, 11:26 PM

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oh sorry, this is for a sequence

vocal slate Jan 1, 2022, 11:26 PM

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,w lim x->infinity ((2^x/x)/((1.99)^x))

surreal meadow Jan 1, 2022, 11:26 PM

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this definitely diverges though

ocean sealBOT Jan 1, 2022, 11:26 PM

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Results provided by WolframAlpha

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surreal meadow Jan 1, 2022, 11:27 PM

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2^x will grow much more rapidly than 1.99^x * x at large numbers

vocal slate Jan 1, 2022, 11:27 PM

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this is quite confusing

copper stone Jan 1, 2022, 11:28 PM

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but x grows much more rapidly than (2/1.99)^x

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as 2/1.99 is very close to 1

surreal meadow Jan 1, 2022, 11:28 PM

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a^x / x diverges for a > 1

copper stone Jan 1, 2022, 11:28 PM

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the graph is confusing

surreal meadow Jan 1, 2022, 11:29 PM

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kind of, it’s just too small a scale to see the behavior at infinity

vocal slate Jan 1, 2022, 11:29 PM

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surreal meadow a^x / x diverges for a > 1

ok so 2^x / x -> inf as x -> inf

vocal slate Jan 1, 2022, 11:29 PM

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ocean seal **miku**

but then here we get a inf * 0 situation

surreal meadow Jan 1, 2022, 11:30 PM

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you can use lhopital if you’ve heard of it

copper stone Jan 1, 2022, 11:30 PM

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vocal slate ok so 2^x / x -> inf as x -> inf

yeah but the whole thing too

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as 2/1.99 > 1

vocal slate Jan 1, 2022, 11:31 PM

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copper stone yeah but the whole thing too

I dont understand what you mean

vocal slate Jan 1, 2022, 11:31 PM

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surreal meadow you can use lhopital if you’ve heard of it

I have heard of lopital yes

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it isn't a very nice one for this

copper stone Jan 1, 2022, 11:31 PM

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(2/1.99)^x / x -> inf

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as 2/1.99 > 1

copper stone Jan 1, 2022, 11:31 PM

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surreal meadow a^x / x diverges for a > 1

.

vocal slate Jan 1, 2022, 11:33 PM

#

Wait how do you go from $\frac{\frac{2^x}{x}}{1.99^x}$ to $\frac{\left(\frac{2}{1.99}\right)^x}{x}$

ocean sealBOT Jan 1, 2022, 11:33 PM

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miku

copper stone Jan 1, 2022, 11:34 PM

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its the same

surreal meadow Jan 1, 2022, 11:34 PM

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keep change flip

copper stone Jan 1, 2022, 11:34 PM

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$\frac{\frac{2^x}{x}}{1.99^x} = \frac{2^x}{x1.99^x}$

ocean sealBOT Jan 1, 2022, 11:34 PM

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nisrine

vocal slate Jan 1, 2022, 11:35 PM

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OH! Thank you ahahah sorry

#

I think that answers my question

#

thank you for your help @surreal meadow and @copper stone

#

.close

lone heartBOT Jan 1, 2022, 11:36 PM

#

Channel closed

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lone heartBOT Jan 2, 2022, 12:42 AM

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white sphinx Jan 2, 2022, 1:04 AM

#

3 and 4 are confusing me. I believe they are the same concept. how do I find the rate of change from what is given?

lone heartBOT Jan 2, 2022, 1:04 AM

#

white sphinx 3 and 4 are confusing me. I believe they are the same concept. how do I find the...

surreal meadow Jan 2, 2022, 1:07 AM

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do you know what a derivative is?

white sphinx Jan 2, 2022, 1:08 AM

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Yes

surreal meadow Jan 2, 2022, 1:08 AM

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that’s the instantaneous rate of change

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so f’(2) is the rate of change at x = 2

white sphinx Jan 2, 2022, 1:09 AM

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so do I just take the derivative and then plug in?

surreal meadow Jan 2, 2022, 1:09 AM

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yes

white sphinx Jan 2, 2022, 1:10 AM

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I thought so but I was going through the beginning of my textbook bc my prof skipped over it and this part was supposed to be only abt limits so I didn’t know how to find w/o just taking the derivative

#

thank you

surreal meadow Jan 2, 2022, 1:11 AM

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the definition of a derivative is a limit

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so it kind of is about limits, especially if you find the derivative through first principles instead of the power rule

white sphinx Jan 2, 2022, 1:15 AM

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#

that’s what I did

#

I still don’t rly know how to take a derivative

surreal meadow Jan 2, 2022, 1:16 AM

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derivative of x^2 is 2x

white sphinx Jan 2, 2022, 1:16 AM

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but I know I did it wrong be the answer is different in the book

surreal meadow Jan 2, 2022, 1:18 AM

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so instead of .04(8-x) it should be .04(8-2x)

white sphinx Jan 2, 2022, 1:19 AM

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alpine sable Jan 2, 2022, 1:20 AM

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Product rule looks incorrectly used and note that product rule is superfluous here

white sphinx Jan 2, 2022, 1:21 AM

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I’m not sure how to solve to get the derivative then

glass lichen Jan 2, 2022, 1:23 AM

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$f'(x)=0.04\dv{x}(8x-x^2)$

ocean sealBOT Jan 2, 2022, 1:23 AM

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Mosh

white sphinx Jan 2, 2022, 1:30 AM

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why don’t you take the derivative of the whole thing?

lone heartBOT Jan 2, 2022, 1:45 AM

#

@white sphinx Has your question been resolved?

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cinder sundial Jan 2, 2022, 2:11 AM

#

lone heartBOT Jan 2, 2022, 2:11 AM

#

cinder sundial

cinder sundial Jan 2, 2022, 2:13 AM

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the y-axis stands for people by cumulative frequency, x-axis is the grade.

#

well, it ask for the median

#

so we got (50th+51th)/2= median
and 50th and 51th falls in the area between grade 60 and grade 70

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so the interval is 10/25=0.4

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then i got the median= (64+64.4)/2=64.2

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Here’s the process tho

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somehow its wrong, the answer on the book said the median is just 64

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can someone check this out for me

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is there anything wrong in the process

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<@&286206848099549185>

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SOS

#

help me

wary stream Jan 2, 2022, 2:37 AM

#

cinder sundial so we got (50th+51th)/2= median and 50th and 51th falls in the area between gra...

Why exactly are you doing that for the median? Because if the median is the halfway point between 0 - 100, then should just be 50

cinder sundial Jan 2, 2022, 2:38 AM

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wary stream Why exactly are you doing that for the median? Because if the median is the half...

but the y-axis stands for ppl

cinder sundial Jan 2, 2022, 2:38 AM

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wary stream Why exactly are you doing that for the median? Because if the median is the half...

the 0th is non-existent

cinder sundial Jan 2, 2022, 2:40 AM

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wary stream Why exactly are you doing that for the median? Because if the median is the half...

why would you considerin the 0th? shouldn't the median be 50.5

#

or i have misinterpreted the chart?

lone heartBOT Jan 2, 2022, 2:58 AM

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@cinder sundial Has your question been resolved?

lone heartBOT Jan 2, 2022, 3:31 AM

#

@cinder sundial Has your question been resolved?

lone heartBOT Jan 2, 2022, 4:01 AM

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Channel closed

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cinder sundial Jan 2, 2022, 4:07 AM

#

lone heartBOT Jan 2, 2022, 4:07 AM

#

cinder sundial

cinder sundial Jan 2, 2022, 4:08 AM

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Can someone check the value of sin 15 degree for me

#

I’m not sure if it’s correct or not

#

also i got lineAB=sqrt6+sqrt2

#

<@&286206848099549185>

severe sluice Jan 2, 2022, 4:21 AM

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cinder sundial Can someone check the value of sin 15 degree for me

sin 15deg = sin(half of 30deg)

#

roketto's sheet is useful

cinder sundial Jan 2, 2022, 4:22 AM

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severe sluice sin 15deg = sin(half of 30deg)

"half", u mean 1/2(sin 30deg)

cinder sundial Jan 2, 2022, 4:23 AM

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severe sluice roketto's sheet is useful

no, i haven't learmed about that

severe sluice Jan 2, 2022, 4:23 AM

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wait a sec half-angle isn't in roketto's trig

ocean sealBOT Jan 2, 2022, 4:25 AM

#

bob ✓

$\sin\left(\frac{x}{2}\right) = \pm\sqrt{\frac{1-\cos(x)}{2}$
```Compilation error:```! Missing } inserted.
<inserted text> 
                }
l.55 ...{2}\right) = \pm\sqrt{\frac{1-\cos(x)}{2}$
                                                  
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```

lone heartBOT Jan 2, 2022, 4:38 AM

#

@cinder sundial Has your question been resolved?

lone heartBOT Jan 2, 2022, 4:53 AM

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cinder sundial Jan 2, 2022, 5:04 AM

#

lone heartBOT Jan 2, 2022, 5:04 AM

#

cinder sundial

cinder sundial Jan 2, 2022, 5:04 AM

#

That blue underlined part seems wrong

#

it should be b*c right

vale wigeon Jan 2, 2022, 5:05 AM

#

yes

cinder sundial Jan 2, 2022, 5:05 AM

#

thank you

lone heartBOT Jan 2, 2022, 5:20 AM

#

@cinder sundial Has your question been resolved?

lone heartBOT Jan 2, 2022, 5:35 AM

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Channel closed

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vestal aspen Jan 2, 2022, 6:11 AM

#

Conic sections problem

lone heartBOT Jan 2, 2022, 6:11 AM

#

vestal aspen Conic sections problem

vestal aspen Jan 2, 2022, 6:12 AM

#

Solution of this problem:

#

I didn't understood why option d is wrong? I mean why b=0 implies that x+3=0?

remote heron Jan 2, 2022, 6:13 AM

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you lose y, right?

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so you just have points

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it becomes a(x+3)^2=0

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a parabola would be a(x+3)^2=y

vestal aspen Jan 2, 2022, 6:15 AM

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oh, yes, thanks

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.close

lone heartBOT Jan 2, 2022, 6:15 AM

#

Channel closed

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lone heartBOT Jan 2, 2022, 9:14 AM

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misty bobcat Jan 2, 2022, 9:41 AM

#

Snimka_obrazovky_2022-01-02_o_10.41.11.png

lone heartBOT Jan 2, 2022, 9:41 AM

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misty bobcat

misty bobcat Jan 2, 2022, 9:41 AM

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,rotate

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Is my solution correct ?

ocean sealBOT Jan 2, 2022, 9:42 AM

#

misty bobcat Jan 2, 2022, 9:50 AM

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im changing my answer its a tautology

lone heartBOT Jan 2, 2022, 10:05 AM

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@misty bobcat Has your question been resolved?

lone heartBOT Jan 2, 2022, 10:38 AM

#

@misty bobcat Has your question been resolved?

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Channel closed

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lone heartBOT Jan 2, 2022, 11:11 AM

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worldly cove Jan 2, 2022, 11:48 AM

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Do i ask for help here?

lone heartBOT Jan 2, 2022, 11:48 AM

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worldly cove Do i ask for help here?

raw shard Jan 2, 2022, 11:49 AM

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yes

worldly cove Jan 2, 2022, 11:49 AM

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Ok

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Let me take a sc and show what i dont understand and what i think i did correct give 10min

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The questions from hegarty mayhs

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Maths*

void solar Jan 2, 2022, 11:50 AM

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Just post your question in any open help channel and it will be pinned by the bot

worldly cove Jan 2, 2022, 11:50 AM

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Is this not open

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Sorry

worldly cove Jan 2, 2022, 11:51 AM

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void solar Just post your question in any open help channel and it will be pinned by the bo...

Do i go where it says available

void solar Jan 2, 2022, 11:52 AM

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no this is open

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Go for it

worldly cove Jan 2, 2022, 11:52 AM

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Oh ok

void solar Jan 2, 2022, 11:52 AM

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Just trying to help clarify

worldly cove Jan 2, 2022, 11:52 AM

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Thanks

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Sorry im taking long just logging in

#

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Let me show you were i went wrong / didn't understand cause i attempted it before a similar question but i got mixed up

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Im in year 9 btw

void solar Jan 2, 2022, 12:01 PM

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Awesome, if you could show what you did we can help alot more

worldly cove Jan 2, 2022, 12:01 PM

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Ok just looking through my notes to see if i can find it

#

#

Should take a closer photo then ill describe the thought process of what is going on and what i thought

void solar Jan 2, 2022, 12:05 PM

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Yeah describe the thought process

worldly cove Jan 2, 2022, 12:05 PM

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So on the left hand side underneath where it says the shape of end face it says different shapes triangle rectangle etc

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And when i watched the video on how to disect this question it wrote the shape end face of the different shapes e.g triangle 3 rectangle 4 etc

pulsar aspen Jan 2, 2022, 12:08 PM

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It seems that you already got the idea. You just have to prove it with more rigor.

void solar Jan 2, 2022, 12:11 PM

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You understand that the question is asking for you to right a formula to link the number of edges with the total faces right

worldly cove Jan 2, 2022, 12:11 PM

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And where it said edeges it said we times by 3 so from 3( triangle)we times by 3 for the number of edges etc for each one as you can see thats the pattern as you times 3 from the shape end face to get the number of edges which is why at the bottom of the screen it says 3s

worldly cove Jan 2, 2022, 12:12 PM

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void solar You understand that the question is asking for you to right a formula to link th...

Yes

void solar Jan 2, 2022, 12:13 PM

#

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Ok so we always know theres two faces at both ends right

worldly cove Jan 2, 2022, 12:13 PM

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Yes

void solar Jan 2, 2022, 12:14 PM

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Then each side of the shape will make a rectangle right

worldly cove Jan 2, 2022, 12:14 PM

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Yes?

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Oh ok yh

void solar Jan 2, 2022, 12:14 PM

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So to get the total number of faces

worldly cove Jan 2, 2022, 12:15 PM

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Yep

void solar Jan 2, 2022, 12:15 PM

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It would be the two end faces plus the number of faces in the middle

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We can right it as
2 + x = y
x = number of sides of the base shape
y = total faces

worldly cove Jan 2, 2022, 12:15 PM

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Ok

void solar Jan 2, 2022, 12:16 PM

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Do you get how that equation works?

worldly cove Jan 2, 2022, 12:16 PM

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Im trying to understand it

void solar Jan 2, 2022, 12:16 PM

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maybe i read the question wrong

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let me double check

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Looks like i did read it wrong, my bad

worldly cove Jan 2, 2022, 12:18 PM

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It was asking for the formula that connects it thats how he got 3s cause you times by 3

worldly cove Jan 2, 2022, 12:18 PM

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void solar Looks like i did read it wrong, my bad

Np

void solar Jan 2, 2022, 12:18 PM

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If we take x as the number of sides

worldly cove Jan 2, 2022, 12:18 PM

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worldly cove It was asking for the formula that connects it thats how he got 3s cause you tim...

Yep

void solar Jan 2, 2022, 12:18 PM

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Then 2x will cover the edges for both ends

#

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So all we need is the middle right

worldly cove Jan 2, 2022, 12:19 PM

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void solar

What shape is that

void solar Jan 2, 2022, 12:19 PM

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triangle prism

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You ok using this shape to figure out the general formual

worldly cove Jan 2, 2022, 12:20 PM

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void solar If we take x as the number of sides

I understand

worldly cove Jan 2, 2022, 12:20 PM

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void solar You ok using this shape to figure out the general formual

Ill try

void solar Jan 2, 2022, 12:20 PM

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Since each edge makes a rectangle it means four edges. But it shares 2 edges with the base shape

#

#

It also shares an edge with adjacent faces

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So really each rectangle only makes one new edge

worldly cove Jan 2, 2022, 12:22 PM

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Ok

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Could you go a bit slower sorry

void solar Jan 2, 2022, 12:22 PM

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no thats fine

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Im probably explaining this badly

worldly cove Jan 2, 2022, 12:22 PM

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I do understand a bit

void solar Jan 2, 2022, 12:22 PM

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Since we already counted the edges of the base shape

worldly cove Jan 2, 2022, 12:22 PM

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Yep

void solar Jan 2, 2022, 12:22 PM

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We dont want to recount it

worldly cove Jan 2, 2022, 12:22 PM

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Ok

void solar Jan 2, 2022, 12:23 PM

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so really the only edges we will count are these

#

worldly cove Jan 2, 2022, 12:23 PM

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Yep

void solar Jan 2, 2022, 12:23 PM

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Cand you see the pattern between the faces and edges?

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3 faces

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3 edges

worldly cove Jan 2, 2022, 12:23 PM

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Yes

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Wait

void solar Jan 2, 2022, 12:24 PM

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Yes?

worldly cove Jan 2, 2022, 12:24 PM

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5 faces no?

void solar Jan 2, 2022, 12:24 PM

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Im only talking about the middle part

worldly cove Jan 2, 2022, 12:24 PM

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Or do we only count the faces of the edges

worldly cove Jan 2, 2022, 12:24 PM

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void solar Im only talking about the middle part

Ok

void solar Jan 2, 2022, 12:24 PM

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Not counting the base shapes (triangle faces)

worldly cove Jan 2, 2022, 12:24 PM

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Ok i see

void solar Jan 2, 2022, 12:25 PM

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Since each reactangle face is made by the edge of the triangle

worldly cove Jan 2, 2022, 12:25 PM

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Yep

void solar Jan 2, 2022, 12:25 PM

#

number of triangle edges = number of rectangle faces
Number of rectangle faces = Number of new edges

worldly cove Jan 2, 2022, 12:26 PM

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Ok

void solar Jan 2, 2022, 12:26 PM

#

So number of edges on the base shape = number of edges in the middle section

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So for the total edges

worldly cove Jan 2, 2022, 12:27 PM

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Yep

void solar Jan 2, 2022, 12:27 PM

#

x = number of sides of base shape
y= total edges
x + x = y

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Or in words

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Sides of the base shape + Edges in the middle part = Total edges

#

We can try it with a square prism if you want

worldly cove Jan 2, 2022, 12:28 PM

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void solar Sides of the base shape + Edges in the middle part = Total edges

Wait

void solar Jan 2, 2022, 12:28 PM

#

worldly cove Jan 2, 2022, 12:28 PM

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Can i just clarify something

void solar Jan 2, 2022, 12:28 PM

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yeah go for it

tight locust Jan 2, 2022, 12:29 PM

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What's the confusion

worldly cove Jan 2, 2022, 12:29 PM

#

worldly cove Jan 2, 2022, 12:29 PM

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void solar yeah go for it

E would still = 3s

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Right

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If the edges are represented as E

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Or im being stupid

void solar Jan 2, 2022, 12:30 PM

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yep

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No no your right

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I forgot something in my equation

worldly cove Jan 2, 2022, 12:31 PM

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Oh ok

#

Give me a sec ill be back

void solar Jan 2, 2022, 12:31 PM

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void solar x = number of sides of base shape y= total edges x + x = y

It was 2x, for two base faces
so 2x + x = y

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Which is jsut 3x = y

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What you were doing was right

#

and now that you have the formula, just apply it to the second half of the question

worldly cove Jan 2, 2022, 12:43 PM

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Ok thanks

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Sorry i took long to reply

#

My mum made look fro the remote for the tv

worldly cove Jan 2, 2022, 12:45 PM

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worldly cove

So in conclusion the E50 = 150 because they timesed the 50 sided polygon by 3 which was the pattern

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Close

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+close

void solar Jan 2, 2022, 12:46 PM

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.close

worldly cove Jan 2, 2022, 12:46 PM

#

. Close

void solar Jan 2, 2022, 12:46 PM

#

no space

worldly cove Jan 2, 2022, 12:46 PM

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.close

lone heartBOT Jan 2, 2022, 12:46 PM

#

Channel closed

Closed by @worldly cove

Use .reopen if this was a mistake.

worldly cove Jan 2, 2022, 12:47 PM

#

void solar .close

Thanks man

void solar Jan 2, 2022, 12:47 PM

#

Turns out you were right from the start

lone heartBOT Jan 2, 2022, 12:47 PM

#

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alpine sable Jan 2, 2022, 12:49 PM

#

f:[0,1]->R
f(x)= { x , if x is rational
x^2, if x is irrational }
is f integrable?

lone heartBOT Jan 2, 2022, 12:49 PM

#

alpine sable f:[0,1]->R f(x)= { x , if x is rational x^2, if x is irrational } i...

alpine sable Jan 2, 2022, 12:49 PM

#

ping me pls

pulsar aspen Jan 2, 2022, 1:01 PM

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Does not look to be even continuous

#

@alpine sable

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Let's find out lim f(x) as x getting close to c.

#

First, we consider squarefree rational sequence to x^2.

alpine sable Jan 2, 2022, 1:04 PM

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pulsar aspen Does not look to be even continuous

Arkos integrable functions are supposed to be continuous?

pulsar aspen Jan 2, 2022, 1:05 PM

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Yes. All integrable functions are continuous, but the reverse is not guaranteed.

alpine sable Jan 2, 2022, 1:06 PM

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Arkos isnt that the opposite

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or im tripping

pulsar aspen Jan 2, 2022, 1:07 PM

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In mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere

alpine sable Jan 2, 2022, 1:08 PM

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but thats differentiability

vale wigeon Jan 2, 2022, 1:09 PM

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@pulsar aspen continuity is a sufficient but not necessary condition for integrability

pulsar aspen Jan 2, 2022, 1:09 PM

#

Another quote:

If f is differentiable at a point x0, then f must also be continuous at x0

#

Oh. I misread the question, sorry.

#

Then, is this Riemann integrability or Lebesque integrability?

vale wigeon Jan 2, 2022, 1:12 PM

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riemann probably

alpine sable Jan 2, 2022, 1:12 PM

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riemann

pulsar aspen Jan 2, 2022, 1:12 PM

#

If it's Riemann integrability, then showing that the function is not continuous anywhere is enough.

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Whoops. Some grammatical mistakes.

#

It's Lebesgue-Vitali theorem

alpine sable Jan 2, 2022, 1:14 PM

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swagthink havent read that yet sry

#

we just read upper,lower integral, and that to be riemann integrable: L(f)=U(f)

pulsar aspen Jan 2, 2022, 1:17 PM

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Is this homework or just for fun?

#

If it's just for fun, I recommended reading that theorem.

alpine sable Jan 2, 2022, 1:18 PM

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homework

pulsar aspen Jan 2, 2022, 1:19 PM

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Oh, so you are not allowed to use that theorem then.

alpine sable Jan 2, 2022, 1:19 PM

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cant use it if sir didnt teach it MiiShrug

#

ASsadcat whys analysis so hard

echo socket Jan 2, 2022, 1:28 PM

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Cuz it's rigor at its purest

pulsar aspen Jan 2, 2022, 1:28 PM

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Well, I found it at last.

#

For any subrange of [0,1], you should find the sup{f(x)}, and inf{f(x)}.

#

Hint, (use the rational and irrational approximation of a real number)

#

||Note that for 0<=x<=1, x^2<=x, so for supremum, we can ignore the irrational number (we can replace it with the rational approximation to that irrational number), and for infinum, we can ignore the rational number.||

#

||Then, sup{f(x)| x element of subrange, x rational} is sup{x| x element of subrange, x rational}, or more simply the supremum of the subrange itself||

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||You can also do the same to the infinum. getting the infinum of the subrange itself, but squared.||

alpine sable Jan 2, 2022, 1:40 PM

#

dan why r u censoring it, i cant do anything by myself

pulsar aspen Jan 2, 2022, 1:40 PM

#

You can then plug it in into the formula of the upper and the lower integral, and you are done.

pulsar aspen Jan 2, 2022, 1:41 PM

#

alpine sable <:dan:665714487977836569> why r u censoring it, i cant do anything by myself

Maybe you want to find it by yourself. You can click it if you get stuck.

alpine sable Jan 2, 2022, 1:42 PM

#

pulsar aspen ||You can also do the same to the infinum. getting the infinum of the subrange i...

catthumbsup it'll take some time before i can respond to this

pulsar aspen Jan 2, 2022, 1:43 PM

#

But yeah, the easiest way to solve is by proving that the function is nowhere continuous, and then invokes Lebesque-Vitali theorem.

alpine sable Jan 2, 2022, 1:45 PM

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pulsar aspen Hint, (use the rational and irrational approximation of a real number)

and idk abt that

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I'll read that then

pulsar aspen Jan 2, 2022, 1:47 PM

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I mean, a sequence converging to x. The former means that every element is rational, and the latter means that every element is irrational.

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The easiest way to get irrational approximation is by getting a squarefree rational approximation to x^2

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And then you take a square root on each element.

lone heartBOT Jan 2, 2022, 2:01 PM

#

@alpine sable Has your question been resolved?

alpine sable Jan 2, 2022, 2:01 PM

#

Arkos well i need some time before i could respond so do i keep this channel occupied?

pulsar aspen Jan 2, 2022, 2:02 PM

#

Then react with X

lone heartBOT Jan 2, 2022, 2:34 PM

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@alpine sable Has your question been resolved?

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Channel closed

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rocky atlas Jan 2, 2022, 2:38 PM

#

lone heartBOT Jan 2, 2022, 2:38 PM

#

rocky atlas

rocky atlas Jan 2, 2022, 2:38 PM

#

What the answer is A instead of D

#

8, 6 and 10 exists too

silver marsh Jan 2, 2022, 2:39 PM

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Yeah but it’s asking you to write “a” Pythagorean triplet with 8 as the smallest number

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Not the smallest Pythagorean triplet with 8 as the smallest number

rocky atlas Jan 2, 2022, 2:39 PM

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oooh

severe sluice Jan 2, 2022, 2:39 PM

#

rocky atlas 8, 6 and 10 exists too

8 isn't the smallest

silver marsh Jan 2, 2022, 2:39 PM

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Oh yeah that too

rocky atlas Jan 2, 2022, 2:39 PM

#

Ok

severe sluice Jan 2, 2022, 2:39 PM

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~~oops~~

silver marsh Jan 2, 2022, 2:40 PM

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@.@

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Lol

rocky atlas Jan 2, 2022, 2:40 PM

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If there was no option given how would you find the answer?

silver marsh Jan 2, 2022, 2:41 PM

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Do you have questions like that?

rocky atlas Jan 2, 2022, 2:42 PM

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No but to make sure if there is a method other than making sure of the options

silver marsh Jan 2, 2022, 2:43 PM

#

There’s an algorithm to generate Pythagorean triples, but I’m not sure if it does what you want (generates one with an input smallest number)

rocky atlas Jan 2, 2022, 2:43 PM

#

is it something like m+n or m-n

silver marsh Jan 2, 2022, 2:43 PM

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3b1b has a video on it

rocky atlas Jan 2, 2022, 2:43 PM

#

Oh

silver marsh Jan 2, 2022, 2:43 PM

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Idk I forgot

rocky atlas Jan 2, 2022, 2:44 PM

#

Ok I'll check on youtube then

#

Thx

#

.close

lone heartBOT Jan 2, 2022, 2:44 PM

#

Channel closed

Closed by @rocky atlas

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rocky atlas Jan 2, 2022, 2:44 PM

#

.reopen

lone heartBOT Jan 2, 2022, 2:44 PM

#

✅

rocky atlas Jan 2, 2022, 2:44 PM

#

If you got anything to add, if not I'll close

silver marsh Jan 2, 2022, 2:44 PM

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O no, you’re good

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Gl!

rocky atlas Jan 2, 2022, 2:44 PM

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ok

#

Ty!

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. close

#

.close

lone heartBOT Jan 2, 2022, 2:44 PM

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final summit Jan 2, 2022, 2:58 PM

#

99% sure I'm right but you can't simplify ln(x)/ln(y) by just crossing out the ln, right? Since it's not a multiplication. Like you can't rewrite ln(x)/ln(y) as x/y.

lone heartBOT Jan 2, 2022, 2:58 PM

#

final summit 99% sure I'm right but you can't simplify ln(x)/ln(y) by just crossing out the l...

final summit Jan 2, 2022, 2:58 PM

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Friend asked and I don't remember much about logs

#

I know the quotient rule but I haven't seen anything about this.

silver marsh Jan 2, 2022, 2:59 PM

#

Yeah… you’re right

#

But you can simplify it

#

$\dfrac{\log_c(a)}{\log_c(b)} = \log_b(a)$

ocean sealBOT Jan 2, 2022, 2:59 PM

#

Slurp

final summit Jan 2, 2022, 3:00 PM

#

Thanks

silver marsh Jan 2, 2022, 3:00 PM

#

Np

final summit Jan 2, 2022, 3:01 PM

#

.close

lone heartBOT Jan 2, 2022, 3:01 PM

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Channel closed

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lone heartBOT Jan 2, 2022, 5:55 PM

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eternal fox Jan 2, 2022, 6:00 PM

#

I am trying to (create?) a function that is basically a logit; but "wider"

lone heartBOT Jan 2, 2022, 6:00 PM

#

eternal fox I am trying to (create?) a function that is basically a logit; but "wider"

eternal fox Jan 2, 2022, 6:02 PM

#

something like this. f(0) = +inf; f(10^7) = 0. and a sigmoid like pattern between the two

#

f[n] == -20000000 Log[x/(1 - x)]

seems kinda on the right path; but it goes to negative infinity instead of zero

#

,close

#

, close

#

.close

lone heartBOT Jan 2, 2022, 6:13 PM

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hasty grail Jan 2, 2022, 6:28 PM

#

Does someone know how to solve this?

lone heartBOT Jan 2, 2022, 6:28 PM

#

hasty grail Does someone know how to solve this?

gray isle Jan 2, 2022, 6:31 PM

#

you could try doing some factotisation

hasty grail Jan 2, 2022, 6:33 PM

#

The thing is, you can factorise but some factorisations return you a false value

gray isle Jan 2, 2022, 6:44 PM

#

wdym by return a false value

hasty grail Jan 2, 2022, 6:44 PM

#

nvm I got it

#

Thx

lone heartBOT Jan 2, 2022, 6:59 PM

#

@hasty grail Has your question been resolved?

lone heartBOT Jan 2, 2022, 7:14 PM

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#

alpine sable Jan 2, 2022, 7:27 PM

#

I really need help please 😢

#

Ask me If u don’t understand smth, i translated from French

lone heartBOT Jan 2, 2022, 7:42 PM

#

@alpine sable Has your question been resolved?

alpine sable Jan 2, 2022, 8:05 PM

#

#

I have to represent this function (f(x)) on [-4;4[

#

How can I do that

alpine sable Jan 2, 2022, 8:34 PM

#

Is this the study of sequences?

#

@alpine sable

#

No , I’m done with that actually @alpine sable

lone heartBOT Jan 2, 2022, 8:36 PM

#

Channel closed

Closed due to the original message being deleted

alpine sable Jan 2, 2022, 8:36 PM

#

.reopen

lone heartBOT Jan 2, 2022, 10:28 PM

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alpine sable Jan 2, 2022, 10:48 PM

#

lone heartBOT Jan 2, 2022, 10:48 PM

#

alpine sable

alpine sable Jan 2, 2022, 10:49 PM

#

I have to determine the left and right limit of f(x) as x approaches p ∈ Z , help please I’m so lost

lone heartBOT Jan 2, 2022, 11:04 PM

#

@alpine sable Has your question been resolved?

alpine sable Jan 2, 2022, 11:08 PM

#

<@&286206848099549185>

lone heartBOT Jan 2, 2022, 11:38 PM

#

@alpine sable Has your question been resolved?

alpine sable Jan 2, 2022, 11:38 PM

#

<@&286206848099549185>

lone heartBOT Jan 3, 2022, 12:38 AM

#

@alpine sable Has your question been resolved?

lone heartBOT Jan 3, 2022, 1:38 AM

#

Channel closed

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median mauve Jan 3, 2022, 2:01 AM

#

can a arithmetic sequence be only contain one element

lone heartBOT Jan 3, 2022, 2:01 AM

#

median mauve can a arithmetic sequence be only contain one element

wheat zenith Jan 3, 2022, 2:09 AM

#

median mauve can a arithmetic sequence be only contain one element

i think so yea

median mauve Jan 3, 2022, 2:09 AM

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I am trying to find an artical

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that proof this

wheat zenith Jan 3, 2022, 2:10 AM

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why do you need a proof

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ig it depends how you define it but i think one would conventionally define it such that sucessive elements have a constant difference and one element would satisfy that

median mauve Jan 3, 2022, 2:10 AM

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can't 1 be a ap

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arr = 1

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I can say that

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arr[0] and arr[0] have common different 0

wheat zenith Jan 3, 2022, 2:12 AM

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what do you need this for

#

it depends on your definition of arithmetic sequence/progression

median mauve Jan 3, 2022, 2:13 AM

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i am create an problem with AP

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should I assume it have at least 2 elements

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or I need to say that

wheat zenith Jan 3, 2022, 2:13 AM

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you should probably clarify to avoid ambiguity if it hasn't already been clarified

median mauve Jan 3, 2022, 2:14 AM

#

oh ok

wheat zenith Jan 3, 2022, 2:14 AM

#

if one element would make the solution trivial, you should specify that you don't consider it to be an arithmetic sequence, if one element would make the solution elegant and considering it not an arithmetic sequence would be annoying to deal with, specify that you do

median mauve Jan 3, 2022, 2:16 AM

#

ok ty

#

.close

lone heartBOT Jan 3, 2022, 2:16 AM

#

Channel closed

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alpine sable Jan 3, 2022, 2:19 AM

#

$\frac{a\cdot r^{n-1}}{(r-1)}+d\left(\frac{2\cdot r^{n} +(n-1) \cdot r^{n+1}-1-n\cdot r^{n}}{(r-1)(1-r)}\right)$

Does this work for Arithmetico-geometric prograssion sum

lone heartBOT Jan 3, 2022, 2:19 AM

#

alpine sable $\frac{a\cdot r^{n-1}}{(r-1)}+d\left(\frac{2\cdot r^{n} +(n-1) \cdot r^{n+1}-1-n...

ocean sealBOT Jan 3, 2022, 2:21 AM

#

IDrinkWine

alpine sable Jan 3, 2022, 2:30 AM

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Does it?

#

Mosh

glass lichen Jan 3, 2022, 2:31 AM

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I was just gonna tell you why .close fucked up.

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message needs to be just .close

alpine sable Jan 3, 2022, 2:31 AM

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Oh

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Well anyways does it work

glass lichen Jan 3, 2022, 2:32 AM

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no clue.

alpine sable Jan 3, 2022, 2:32 AM

#

Ah well I will verify it myself.

#

.close

lone heartBOT Jan 3, 2022, 2:32 AM

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Channel closed

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wanton kernel Jan 3, 2022, 2:40 AM

#

Algebra

lone heartBOT Jan 3, 2022, 2:40 AM

#

wanton kernel Algebra

wanton kernel Jan 3, 2022, 2:40 AM

#

what is it?

#

Like how does it work?

pine kettle Jan 3, 2022, 2:41 AM

#

the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

glass lichen Jan 3, 2022, 2:41 AM

#

https://en.wikipedia.org/wiki/Algebra

Algebra

Algebra (from Arabic: الجبر, romanized: al-jabr, lit. 'reunion of broken parts, bonesetting') is one of the broad areas of mathematics. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary e...

#

You too, can google

wanton kernel Jan 3, 2022, 2:41 AM

#

Thank you

wheat zenith Jan 3, 2022, 2:41 AM

#

the mathematical study of symmetry

glass lichen Jan 3, 2022, 2:41 AM

#

wanton kernel Thank you

next time: Put some effort in before asking here btw

severe sluice Jan 3, 2022, 2:42 AM

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wheat zenith the mathematical study of symmetry

that probably better suits group theory?

wheat zenith Jan 3, 2022, 2:42 AM

#

group theory \subset algebra

bleak ridge Jan 3, 2022, 2:43 AM

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The mathematical study of mathematics

wanton kernel Jan 3, 2022, 2:45 AM

#

Hi

#

I now have a more appropiate name

glass lichen Jan 3, 2022, 2:46 AM

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Cool, if you have a question get a help channel.

pine kettle Jan 3, 2022, 2:46 AM

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@wanton kernel please open a new channel if you're about to aska a question

#

Bruh

wanton kernel Jan 3, 2022, 2:46 AM

#

I'm not

glass lichen Jan 3, 2022, 2:46 AM

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So... why did you type here?

wanton kernel Jan 3, 2022, 2:46 AM

#

I'm just stating that I have changed my name

glass lichen Jan 3, 2022, 2:46 AM

#

#discussion

wanton kernel Jan 3, 2022, 2:46 AM

#

Ok

lone heartBOT Jan 3, 2022, 3:01 AM

#

@wanton kernel Has your question been resolved?

severe sluice Jan 3, 2022, 3:02 AM

#

lone heart <@926699019424653353> Has your question been resolved?

why did the bot ping him and not ultracoolduck

glass lichen Jan 3, 2022, 3:02 AM

#

same user

severe sluice Jan 3, 2022, 3:02 AM

#

ohh-

#

okay

#

didn't notice that

glass lichen Jan 3, 2022, 3:03 AM

#

Yeah... weird new users catshrug

#

<@&268886789983436800> this

lone heartBOT Jan 3, 2022, 3:16 AM

#

Channel closed

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alpine sable Jan 3, 2022, 3:38 AM

#

25x^2 + 10x - 3 = B^2 + 2B - 3

lone heartBOT Jan 3, 2022, 3:38 AM

#

alpine sable 25x^2 + 10x - 3 = B^2 + 2B - 3

alpine sable Jan 3, 2022, 3:38 AM

#

whats the value of B in terms of X

#

im p sure the answer is 5x but im not sure if its right or how to solve

raw shard Jan 3, 2022, 3:42 AM

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add 3 to both sides

#

then equate like terms

lone heartBOT Jan 3, 2022, 3:54 AM

#

@alpine sable Has your question been resolved?

alpine sable Jan 3, 2022, 3:54 AM

#

raw shard then equate like terms

can you show me how

#

i tried doing this

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but got caught up at what the next step is

raw shard Jan 3, 2022, 3:55 AM

#

so you have 25x^2+10x = B^2+2B

#

which term on the right would be similar looking to 10x?

alpine sable Jan 3, 2022, 3:56 AM

#

raw shard which term on the right would be similar looking to 10x?

2B

raw shard Jan 3, 2022, 3:56 AM

#

yeah

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so you’re assuming that 10x = 2B

#

solve for what B is

#

then see if that works for the whole thing

alpine sable Jan 3, 2022, 3:57 AM

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wait

#

u automatically would assume 10x = 2B

raw shard Jan 3, 2022, 3:57 AM

#

yeah

alpine sable Jan 3, 2022, 3:57 AM

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so that would work for any equation

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assume like terms r equivalent

raw shard Jan 3, 2022, 3:57 AM

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what do you mean

#

oh

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i guess

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i haven’t done many problems like this

alpine sable Jan 3, 2022, 3:58 AM

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oh i never knew that

raw shard Jan 3, 2022, 3:58 AM

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but that’s always how it seems to be

alpine sable Jan 3, 2022, 3:58 AM

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right thanks

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have a g1

#

and happy new year

raw shard Jan 3, 2022, 3:58 AM

#

thanks you too

alpine sable Jan 3, 2022, 3:58 AM

#

.close

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limber shard Jan 3, 2022, 4:09 AM

#

$$\begin{equation*}
A_{3,4} =
\begin{pmatrix}
1 & 3 & 4 & 8 \
0 & 0 & 8 & 0 \
0 & 0 & 0 & 21
\end{pmatrix} \end{equation*}$$

lone heartBOT Jan 3, 2022, 4:09 AM

#

limber shard $$\begin{equation*} A_{3,4} = \begin{pmatrix} 1 & 3 & 4 & 8 \\ 0 & 0 & 8 & 0 \\...

ocean sealBOT Jan 3, 2022, 4:10 AM

#

Aarjav
Compile Error! Click the errors reaction for more information.
(You may edit your message to recompile.)

limber shard Jan 3, 2022, 4:10 AM

#

is the answer to this question correct?

#

<@&286206848099549185>

lone heartBOT Jan 3, 2022, 4:38 AM

#

@limber shard Has your question been resolved?

lone heartBOT Jan 3, 2022, 5:08 AM

#

@limber shard Has your question been resolved?

lone heartBOT Jan 3, 2022, 6:19 AM

#

@limber shard Has your question been resolved?

small stag Jan 3, 2022, 6:20 AM

#

you might get help in a more tailored channel like #linear-algebra or #calculus

#

sorry I can't help you

raw shard Jan 3, 2022, 6:24 AM

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definitely #linear-algebra

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don’t go to #calculus

limber shard Jan 3, 2022, 6:32 AM

#

Alright. Thank you!

#

.close

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tidal crest Jan 3, 2022, 6:47 AM

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I need help with this, I’m really sorry.

lone heartBOT Jan 3, 2022, 6:47 AM

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tidal crest I need help with this, I’m really sorry.

tidal crest Jan 3, 2022, 6:47 AM

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(I’m an online student for my school so no one explains it to me )

echo socket Jan 3, 2022, 6:48 AM

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What are you asked to do here?

tidal crest Jan 3, 2022, 6:49 AM

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how to Graph it.

echo socket Jan 3, 2022, 6:50 AM

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Oh, to graph a line it's enough know know 2 points that it crosses and then just connect those lines with an line (make sure the line goes beyond the points as well)

tidal crest Jan 3, 2022, 6:50 AM

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Ah ok.

echo socket Jan 3, 2022, 6:50 AM

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In this case what you could do is choose any value of x or y and then solve for the other unknown

tidal crest Jan 3, 2022, 6:51 AM

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How do I solve for it?

echo socket Jan 3, 2022, 6:51 AM

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As I said first choose any value that you want for x or y

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Let's say we picked x=0

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Then what we have is -5y = -25

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Therefore y = 5

tidal crest Jan 3, 2022, 6:52 AM

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OOOOOOOHHHHHH

echo socket Jan 3, 2022, 6:52 AM

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So when x =0, then y = 5

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And it means that

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The line

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Crosses the point (0, 5)

tidal crest Jan 3, 2022, 6:52 AM

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That makes a lot more sense lol

echo socket Jan 3, 2022, 6:52 AM

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Now you need 2 points to graph a line, so now you need to make a different choice

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To find the other piint

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Point*

tidal crest Jan 3, 2022, 6:53 AM

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Ok tysm ❤️

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.close

lone heartBOT Jan 3, 2022, 6:53 AM

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Channel closed

Closed by @tidal crest

Use .reopen if this was a mistake.

#

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

surreal badger Jan 3, 2022, 7:00 AM

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if perimeter of rectangle is 68cm

and diagonal is 26 cm

how to find the dimensions of the rectangle ( length and breadth)

lone heartBOT Jan 3, 2022, 7:00 AM

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surreal badger if perimeter of rectangle is 68cm and diagonal is 26 cm how to find the dimen...

remote heron Jan 3, 2022, 7:04 AM

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surreal badger if perimeter of rectangle is 68cm and diagonal is 26 cm how to find the dimen...

draw a triangle

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use pythagorean thm

surreal badger Jan 3, 2022, 7:04 AM

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remote heron draw a triangle

nvm man

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found it

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lol

remote heron Jan 3, 2022, 7:04 AM

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oh

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nice

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hype

surreal badger Jan 3, 2022, 7:04 AM

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i didnt think deep

remote heron Jan 3, 2022, 7:04 AM

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u get 10/24

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ur good

surreal badger Jan 3, 2022, 7:04 AM

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its about triplets

remote heron Jan 3, 2022, 7:04 AM

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ah yea

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it is isnt it

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5 12 13

surreal badger Jan 3, 2022, 7:04 AM

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yh

remote heron Jan 3, 2022, 7:04 AM

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i didnt even think about that

surreal badger Jan 3, 2022, 7:05 AM

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lol

remote heron Jan 3, 2022, 7:05 AM

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i just did the algebra

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like a dope

surreal badger Jan 3, 2022, 7:05 AM

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i mean pythogoras works

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lol

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its just too much time

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guessing numbers

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then making

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lol

remote heron Jan 3, 2022, 7:05 AM

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not guessing

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just 2a+2b=68

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so (34-a)^2+a^2=26^2

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then 240-34a+a^2=0

surreal badger Jan 3, 2022, 7:06 AM

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quadratic?

remote heron Jan 3, 2022, 7:06 AM

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gives a,b are 10,24 interchangably

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yea

surreal badger Jan 3, 2022, 7:06 AM

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ah frick

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that works too

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lmao

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wait that might be the q

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cause the first q was about simultaneous

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shit

thorny patio Jan 3, 2022, 7:07 AM

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That's definitely the way youre supposed to do a prob like that

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Simultaneous equation with perimeter and area

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Err

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Not area

surreal badger Jan 3, 2022, 7:07 AM

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no like

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part a was to make a simultaneous and solve x and y

thorny patio Jan 3, 2022, 7:07 AM

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The pythagorean relationship

surreal badger Jan 3, 2022, 7:07 AM

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part b find length breadth

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i did using pytho

surreal badger Jan 3, 2022, 7:08 AM

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remote heron just 2a+2b=68

but i think the q is supposed to be donelike this

thorny patio Jan 3, 2022, 7:08 AM

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Yes becauseeeeee

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If the numbers were not nice

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You could not figure it out by intuitively checking right triangles

surreal badger Jan 3, 2022, 7:08 AM

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yh

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true

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examiners are smart

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lmao

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and also thinks about everyone too

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lol

thorny patio Jan 3, 2022, 7:09 AM

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With the algebraic way you can figure it out for any rectangle

surreal badger Jan 3, 2022, 7:09 AM

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yh

surreal badger Jan 3, 2022, 7:15 AM

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thorny patio With the algebraic way you can figure it out for any rectangle

whats the most efficient way to do maths

thorny patio Jan 3, 2022, 7:16 AM

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Practice the problems as many times as you can first xD

remote heron Jan 3, 2022, 7:16 AM

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surreal badger whats the most efficient way to do maths

generalize immediately

echo socket Jan 3, 2022, 7:16 AM

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thorny patio Practice the problems as many times as you can first xD

Especially the ones that you're not so comfortable with

surreal badger Jan 3, 2022, 7:16 AM

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remote heron so (34-a)^2+a^2=26^2

could u elaborate this a bit more
a bit confusing

thorny patio Jan 3, 2022, 7:16 AM

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Practice a wide variety of problems if you can but mostly practice

remote heron Jan 3, 2022, 7:17 AM

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surreal badger could u elaborate this a bit more a bit confusing

sure

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so you have this formula from perimeter

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2a+2b=68

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just name some side a

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some side b

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of the rectangle

surreal badger Jan 3, 2022, 7:17 AM

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yh

remote heron Jan 3, 2022, 7:17 AM

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it follows that a+b=34

surreal badger Jan 3, 2022, 7:17 AM

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yes

remote heron Jan 3, 2022, 7:17 AM

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then anywhere we see b, we can substitute 34-a

surreal badger Jan 3, 2022, 7:18 AM

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yes

remote heron Jan 3, 2022, 7:18 AM

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pyth gives that a^2+b^2 = 26^2

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sides of the rectangle and the diagonal

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we substitute

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and you get to what you had quoted

surreal badger Jan 3, 2022, 7:18 AM

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oh great it works

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thing is the main thing i hate about the maths im doing

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we arent supposed to use any calculators

remote heron Jan 3, 2022, 7:19 AM

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memorize some prime squares

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and factor

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if thats what youre worried about

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what sort of math are you struggling with?

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if it were me and i were on a test or something and you run into something you cant do without a calculator

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give it 5 min maybe then just make a note like

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im gonna call this number M

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or something

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honestly

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idk how your class is for partial credit

surreal badger Jan 3, 2022, 7:23 AM

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oh

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no like im doing OLs

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i have my mocks next week

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doing some past papers

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also school papers are actually harder than

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the the actual OL papers

surreal badger Jan 3, 2022, 7:24 AM

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remote heron memorize some prime squares

no like 34^2

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its just inefficent multiplaying

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takes time

remote heron Jan 3, 2022, 7:25 AM

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so thats

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yea thats not an easy one

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maybe you could use difference of squares here

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thonk

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idk how much time it saves

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theyre nicer numbers though

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60 and 8

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instead of 34^2 and 26^2

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you could probably do 60*8 in your head

surreal badger Jan 3, 2022, 7:26 AM

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yh

remote heron Jan 3, 2022, 7:26 AM

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since you have like

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$34^2 - 26^2 - 68a + 2 a^2 = (34+26)(34-26) - 68a + 2a^2 = 2 \left( (17+13)(17-13) - 34a + a^2 \right)$

ocean sealBOT Jan 3, 2022, 7:28 AM

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jan Niku

remote heron Jan 3, 2022, 7:28 AM

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this works great

surreal badger Jan 3, 2022, 7:28 AM

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it does

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also i think they will reduce marks if i did the triplet way

surreal badger Jan 3, 2022, 7:42 AM

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remote heron this works great

what thes best way u use to solve a fractional quadratic

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normal way

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equation

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or

remote heron Jan 3, 2022, 7:42 AM

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best?

surreal badger Jan 3, 2022, 7:42 AM

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completing the square

surreal badger Jan 3, 2022, 7:43 AM

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remote heron best?

like most efficient

remote heron Jan 3, 2022, 7:43 AM

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i mean there are a lot of ways

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it depends on what looks easiest

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that you do need some experience

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you should have a lot of methods at hand right

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you just have to recognize which one seems like it will work best

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it depends

surreal badger Jan 3, 2022, 7:47 AM

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then gotta study all

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ig mods can close this

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channel then

surreal badger Jan 3, 2022, 7:48 AM

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remote heron it depends

anyways thanks for ur help everyone
much appreciated

remote heron Jan 3, 2022, 7:48 AM

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catthumbsup

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you can close the channel if u want

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@surreal badger

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use .close

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ur the last one

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then ima go to bed

surreal badger Jan 3, 2022, 7:54 AM

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remote heron you can close the channel if u want

ah ok

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thanks!

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gn

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.close

lone heartBOT Jan 3, 2022, 7:54 AM

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Channel closed

Closed by @surreal badger

Use .reopen if this was a mistake.

#

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

tawny fable Jan 3, 2022, 8:15 AM

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Hi there

lone heartBOT Jan 3, 2022, 8:15 AM

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tawny fable Hi there

tawny fable Jan 3, 2022, 8:15 AM

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I need some help with this question

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Someone can help?

lone heartBOT Jan 3, 2022, 8:31 AM

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@tawny fable Has your question been resolved?

tawny fable Jan 3, 2022, 8:33 AM

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<@&286206848099549185>

vale wigeon Jan 3, 2022, 8:49 AM

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consider: A and B are row-equivalent iff there exists an invertible n by n matrix R such that RA = B

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this, and some thought, should let you do a, b and c

tawny fable Jan 3, 2022, 8:50 AM

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Yup

vale wigeon Jan 3, 2022, 8:50 AM

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d is a matter of thinking about the definition of nullspace and proving two sets are equal by element-chasing

tawny fable Jan 3, 2022, 8:51 AM

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vale wigeon consider: A and B are row-equivalent iff there exists an invertible n by n matri...

I mean, that is actually a matrix that came out of elementry row operations?

vale wigeon Jan 3, 2022, 8:51 AM

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sure

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row operations are just left-multiplications by particular matrices

tawny fable Jan 3, 2022, 8:52 AM

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yeah

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But the thing is, I am getting confused by the difference between row operations and column operations

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and how do the affect the column space

vale wigeon Jan 3, 2022, 8:53 AM

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row operations operate on rows. column operations operate on columns

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column operations preserve column spaces while row operations do not

tawny fable Jan 3, 2022, 8:56 AM

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On the one hand I feel like a is true, because trying to throw some examples I see that the basis stays the same

vale wigeon Jan 3, 2022, 8:56 AM

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it is not true

tawny fable Jan 3, 2022, 8:56 AM

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Because anyways, I need to get to REF

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Mhmm

vale wigeon Jan 3, 2022, 8:57 AM

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consider: row operations do not preserve column space

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and you are acting as if they do

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it is only natural that you arrive at a bullshit answer

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consider: $\bmqty{1&0\0&0}$ vs. $\bmqty{0&0\1&0}$

ocean sealBOT Jan 3, 2022, 8:57 AM

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Ann

vale wigeon Jan 3, 2022, 8:58 AM

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row equivalent? yes. same column space? no.

tawny fable Jan 3, 2022, 8:59 AM

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ocean seal **Ann**

But shouldn't the REF matrix be with the zero row on the bottom

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like shouldn't all the pivots be on top?

vale wigeon Jan 3, 2022, 8:59 AM

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who gives a shit about REF?

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you think a matrix does not deserve to exist unless it is immediately REF'd?

tawny fable Jan 3, 2022, 9:00 AM

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That is how we learned to find the basis of the column space

tawny fable Jan 3, 2022, 9:00 AM

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vale wigeon you think a matrix does not deserve to exist unless it is immediately REF'd?

lol

vale wigeon Jan 3, 2022, 9:00 AM

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setting aside the fact that there's no such thing as "the" basis,

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even if you use row ops to find a basis for the col space, you go back to the original matrix you started with

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you do not read the columns of the REF'd matrix directly to view them as making up your basis

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but still, what just came from you sounds like matrixbashing at its finest: clearly you only view matrices as something to put in REF and nothing else.

tawny fable Jan 3, 2022, 9:03 AM

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I think my misunderstanding is what exactly is the column space equal to

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for example in you're example

tawny fable Jan 3, 2022, 9:03 AM

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ocean seal **Ann**

here

vale wigeon Jan 3, 2022, 9:03 AM

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the column space is the span of the columns

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it could not be simpler as far as definitions go

tawny fable Jan 3, 2022, 9:05 AM

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So the column space = span{[0,1]} on the right one

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and span{[1,0]} on the left one

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?

vale wigeon Jan 3, 2022, 9:05 AM

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yes

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and it should be clear as day to you that these are not the same in the slightest

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sometimes it helps instead to view Col(A) as the set of all vectors of the form Ax, where x is an appropriately-sized but otherwise arbitrary column vector

tawny fable Jan 3, 2022, 9:11 AM

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vale wigeon sometimes it helps instead to view Col(A) as the set of all vectors of the form ...

When you say appropiately-sized you mean, you mean sized as the size of the column of the matrix?

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in that example you said:
Col(A) = {[a,0] | a in F}

vale wigeon Jan 3, 2022, 9:13 AM

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tawny fable When you say appropiately-sized you mean, you mean sized as the size of the colu...

yes. when i say "appropriately-sized" i mean "sized in a way that makes the product exist"

tawny fable Jan 3, 2022, 9:14 AM

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And about 6.(b). when they say F^n

tawny fable Jan 3, 2022, 9:14 AM

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vale wigeon yes. when i say "appropriately-sized" i mean "sized in a way that makes the prod...

I see

tawny fable Jan 3, 2022, 9:15 AM

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tawny fable And about 6.(b). when they say F^n

Can the column space be somethis else other than F^n?

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I mean doesn't that mean that the vectors that span the space are sized n?

vale wigeon Jan 3, 2022, 9:17 AM

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"This says the column space is F^n. Can the column space be something other than F^n?"

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do you hear yourself

tawny fable Jan 3, 2022, 9:21 AM

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Is that totally wrong?

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I meant when they say in the question that Col(A) = F^n

vale wigeon Jan 3, 2022, 9:23 AM

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yes, they say Col(A) = F^n so they mean Col(A) is all of F^n