#help-23 | Mathematics | Page 102

whole merlin Apr 30, 2023, 5:14 PM

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Oh alright

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So for example would the top row be [1 1 1 1] or [1 1 -1 1]

worthy hemlock Apr 30, 2023, 5:16 PM

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The sign goes with the number

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So if it's -z, then the number is -1, because +z and -z are two different values

whole merlin Apr 30, 2023, 5:19 PM

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Got it, thanks

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.close

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robust quiver Apr 30, 2023, 5:27 PM

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safe radishBOT Apr 30, 2023, 5:27 PM

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robust quiver

robust quiver Apr 30, 2023, 5:27 PM

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please help its a speed =d/t

hazy elbow Apr 30, 2023, 5:30 PM

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Find time taken to complete race in 2014 in terms of t

safe radishBOT Apr 30, 2023, 5:42 PM

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@robust quiver Has your question been resolved?

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robust quiver Apr 30, 2023, 5:47 PM

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safe radishBOT Apr 30, 2023, 5:47 PM

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robust quiver

robust quiver Apr 30, 2023, 5:47 PM

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so far

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#

#

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how?

safe radishBOT Apr 30, 2023, 6:03 PM

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@robust quiver Has your question been resolved?

robust quiver Apr 30, 2023, 6:04 PM

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<@&286206848099549185>

barren magnet Apr 30, 2023, 6:08 PM

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robust quiver <@&286206848099549185>

hi

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im imo particapiant

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so i can help u.

robust quiver Apr 30, 2023, 6:09 PM

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thx

safe radishBOT Apr 30, 2023, 6:39 PM

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@robust quiver Has your question been resolved?

robust quiver Apr 30, 2023, 6:39 PM

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.close

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safe radishBOT Apr 30, 2023, 7:17 PM

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exotic dawn Apr 30, 2023, 7:22 PM

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how would i find the radius and interval of convergence of this limit?

safe radishBOT Apr 30, 2023, 7:22 PM

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exotic dawn how would i find the radius and interval of convergence of this limit?

exotic dawn Apr 30, 2023, 7:23 PM

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ive tried using the ratio test but im getting messy algebra

empty gyro Apr 30, 2023, 7:25 PM

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!show

safe radishBOT Apr 30, 2023, 7:25 PM

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Show your work, and if possible, explain where you are stuck.

empty gyro Apr 30, 2023, 7:26 PM

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Looks like it may get a little messy, but algebra usually does

exotic dawn Apr 30, 2023, 7:26 PM

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empty gyro !show

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.flip

fast gazelle Apr 30, 2023, 7:27 PM

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,rccw

flat frigateBOT Apr 30, 2023, 7:27 PM

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empty gyro Apr 30, 2023, 7:29 PM

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You don't keep (x-1)

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Ratio test is of just the coefficients

exotic dawn Apr 30, 2023, 7:31 PM

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empty gyro You don't keep (x-1)

i think i meant to write the (x-1) as |x-1| outside of the limit

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but im still unsure on where to go from here

empty gyro Apr 30, 2023, 7:32 PM

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flat frigate

This is indeed kinda messy, but you can apply lhopital several times to get your final result

exotic dawn Apr 30, 2023, 7:33 PM

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so i'd take the derivative of [(k+1+2^(k+1))*(k^2+3^k)] and [((k+1)^2+3^(k+1))(k+2^k)] with respect to k?

empty gyro Apr 30, 2023, 7:34 PM

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Yes

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Tedious, but that's the best approach I have

empty gyro Apr 30, 2023, 7:34 PM

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exotic dawn so i'd take the derivative of [(k+1+2^(k+1))*(k^2+3^k)] and [((k+1)^2+3^(k+1))(k...

Multiplying it out first may make it easier

exotic dawn Apr 30, 2023, 7:34 PM

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ah right, ill go ahead and try that rn

empty gyro Apr 30, 2023, 7:36 PM

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Good luck

safe radishBOT Apr 30, 2023, 7:49 PM

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@exotic dawn Has your question been resolved?

exotic dawn Apr 30, 2023, 7:53 PM

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empty gyro Good luck

i honestly have no idea how l'hopital would help

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i used it once and got this

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[\frac{\left(3^k+k^2\right)\left(\ln\left(2\right){\cdot}2^{k+1}+1\right)+\left(\ln\left(3\right){\cdot}3^k+2k\right)\left(2^{k+1}+k+1\right)}{\left(2^k+k\right)\left(\ln\left(3\right){\cdot}3^{k+1}+2\left(k+1\right)\right)+\left(\ln\left(2\right){\cdot}2^k+1\right)\left(3^{k+1}+\left(k+1\right)^2\right)}]

flat frigateBOT Apr 30, 2023, 7:53 PM

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kyIe

empty gyro Apr 30, 2023, 7:53 PM

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hmmCat

exotic dawn Apr 30, 2023, 7:53 PM

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idk how that makes it any easier

empty gyro Apr 30, 2023, 7:53 PM

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Lemme take a look

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hold on

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@exotic dawn, I feel a little bad. I wasted your time there.

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I found an easier way to do your limit

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exotic dawn Apr 30, 2023, 8:08 PM

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empty gyro

how did you get the first line?

empty gyro Apr 30, 2023, 8:08 PM

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ratio test

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Oh I made a typo

exotic dawn Apr 30, 2023, 8:09 PM

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oh right

empty gyro Apr 30, 2023, 8:10 PM

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exotic dawn Apr 30, 2023, 8:10 PM

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and then you'd sub in infinity?

empty gyro Apr 30, 2023, 8:11 PM

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more or less

exotic dawn Apr 30, 2023, 8:12 PM

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wouldnt that just be 1 then?

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because both limits = 1 when you sub in infinity?

empty gyro Apr 30, 2023, 8:12 PM

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I gtg sorry

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<@&286206848099549185>

exotic dawn Apr 30, 2023, 8:13 PM

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because k^2 is infinity + 3^k which is infinity too over (infinity+infinity)

exotic dawn Apr 30, 2023, 8:13 PM

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empty gyro I gtg sorry

ah, all good. tysm for the help

safe radishBOT Apr 30, 2023, 8:43 PM

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@exotic dawn Has your question been resolved?

safe radishBOT Apr 30, 2023, 9:13 PM

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fiery cosmos Apr 30, 2023, 9:24 PM

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Why are the area of the parametric equation the same?

safe radishBOT Apr 30, 2023, 9:24 PM

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fiery cosmos Why are the area of the parametric equation the same?

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@fiery cosmos Has your question been resolved?

safe radishBOT Apr 30, 2023, 10:12 PM

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@fiery cosmos Has your question been resolved?

safe radishBOT Apr 30, 2023, 11:14 PM

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@fiery cosmos Has your question been resolved?

spiral bane May 1, 2023, 1:23 AM

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fiery cosmos Why are the area of the parametric equation the same?

give some more context

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ah you can just check itusing a double integral then

fiery cosmos May 1, 2023, 1:34 AM

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haven't learned double intergral yet

spiral bane May 1, 2023, 1:34 AM

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hm

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i have no idea what either of those things are

fiery cosmos May 1, 2023, 1:36 AM

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Its the unit calculus with parametric curves

spiral bane May 1, 2023, 1:36 AM

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as in I haven't learned it

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I just graphed it

fiery cosmos May 1, 2023, 1:36 AM

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ahh ic

spiral bane May 1, 2023, 1:36 AM

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area is approx 6-7

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so its not pi/2

fiery cosmos May 1, 2023, 1:37 AM

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ahh ty thats all I needed to know

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thanks for helping me

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.close

safe radishBOT May 1, 2023, 1:37 AM

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dusty talon May 1, 2023, 1:41 AM

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.

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Is there an "ultimate" guide to what you can do with a function?

safe radishBOT May 1, 2023, 1:41 AM

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dusty talon Is there an "ultimate" guide to what you can do with a function?

dusty talon May 1, 2023, 1:41 AM

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such as

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all x-values y-values

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min max

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inflection points

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i cant remember the other things but hopefully you get the idea

sour abyss May 1, 2023, 1:44 AM

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for specific functions?

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can you be more specific in phrasing maybe give an example of what you mean

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also no there probably isnt but wikipedia is out there and there are lots of videos on khan academy and youtube and stuff so you should be able to find whatever you need

dusty talon May 1, 2023, 1:45 AM

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my test tomorrow has me finding all of those and more from a single funtion

sour abyss May 1, 2023, 1:46 AM

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well do you know what the and more is

dusty talon May 1, 2023, 1:46 AM

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let me see

sour abyss May 1, 2023, 1:46 AM

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are you wanting to know how to solve for these things?

dusty talon May 1, 2023, 1:47 AM

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yes, I guess this is the best example

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sour abyss May 1, 2023, 1:48 AM

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yeah while there isnt some super guide you can definitely just look this stuff up and find resources

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its probably a waste of your time and other peoples if we try to explain it since guides online will do it better

dusty talon May 1, 2023, 1:48 AM

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ya I was having a hard time finding a function that looks like this

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with the x^2 in denom

sour abyss May 1, 2023, 1:49 AM

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solving for concave up or down and increasing/decreasing should be the same or at the very least a similar process for all functions

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just study how to solve for it and maybe what it means geometrically as sketching the graph loosely can help sometimes

dusty talon May 1, 2023, 1:52 AM

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.close

safe radishBOT May 1, 2023, 1:52 AM

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safe radishBOT May 1, 2023, 9:46 AM

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buoyant mural May 1, 2023, 10:02 AM

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safe radishBOT May 1, 2023, 10:02 AM

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buoyant mural

buoyant mural May 1, 2023, 10:03 AM

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help pls

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180

crimson locust May 1, 2023, 10:05 AM

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its 78?

buoyant mural May 1, 2023, 10:06 AM

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Yeah I tried solving it and got 78

crimson locust May 1, 2023, 10:06 AM

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is that the answer?

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i think its supplementry

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however u spell it

buoyant mural May 1, 2023, 10:06 AM

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i didn’t submit an answer yet

sonic spruce May 1, 2023, 10:06 AM

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Can you show your work?

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Angle BCD is not 78

buoyant mural May 1, 2023, 10:07 AM

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Add 67+ 35+ c= 180
102+c=180
180-102=78

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oh

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how can I solve it?

sonic spruce May 1, 2023, 10:09 AM

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Multiple ways

sonic spruce May 1, 2023, 10:10 AM

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buoyant mural Add 67+ 35+ c= 180 102+c=180 180-102=78

With the way you are doing this, realize that ‘c’ was angle ACB

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Angle ACB and DCB make a linear pair

buoyant mural May 1, 2023, 10:11 AM

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is the answer 145?

sonic spruce May 1, 2023, 10:11 AM

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So, what is angle ACB + DCB= ?

sonic spruce May 1, 2023, 10:11 AM

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buoyant mural is the answer 145?

… how did you get that?

sonic spruce May 1, 2023, 10:11 AM

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sonic spruce So, what is angle ACB + DCB= ?

…?

buoyant mural May 1, 2023, 10:11 AM

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180-35

sonic spruce May 1, 2023, 10:12 AM

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Why are you subtracting 35

buoyant mural May 1, 2023, 10:12 AM

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67+c+35 (ACB)

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=180

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D+C+35=180 (DCB)

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am I doing this correct?

sonic spruce May 1, 2023, 10:13 AM

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buoyant mural D+C+35=180 (DCB)

What? No

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What are you saying

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Write it out clearly

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Which angles are you talking about?

buoyant mural May 1, 2023, 10:16 AM

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<ACB= m<67 + m<c + m<35

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now how can I get to finding the angle <BCD

sonic spruce May 1, 2023, 10:17 AM

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Okay, let’s skip this method

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I can see you are getting two things mixed up

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Are you aware of that exterior angle is always equal to the sum of the interior opposite angle?

buoyant mural May 1, 2023, 10:18 AM

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yes

sonic spruce May 1, 2023, 10:18 AM

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This

sonic spruce May 1, 2023, 10:19 AM

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buoyant mural yes

So, Can you apply this in the problem on hand?

buoyant mural May 1, 2023, 10:19 AM

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<DCB= 67+35

sonic spruce May 1, 2023, 10:21 AM

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buoyant mural <DCB= 67+35

It would be wrong to call angle DCB angle d

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But yes, you applied it well

buoyant mural May 1, 2023, 10:21 AM

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ok

sonic spruce May 1, 2023, 10:22 AM

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Now do you want to go through the other way?

buoyant mural May 1, 2023, 10:22 AM

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i want the simplest method

sonic spruce May 1, 2023, 10:22 AM

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This is the least number of steps

buoyant mural May 1, 2023, 10:22 AM

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buoyant mural <DCB= 67+35

now how can i move on after this

sonic spruce May 1, 2023, 10:23 AM

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Just add em up

buoyant mural May 1, 2023, 10:23 AM

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Sure, let me finish knowing this method

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=102

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final answer?

sonic spruce May 1, 2023, 10:23 AM

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Yes

buoyant mural May 1, 2023, 10:23 AM

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ok introduce me to the next one

sonic spruce May 1, 2023, 10:24 AM

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Alr so, sum of interior angles of a triangle is 180 deg.
So, Angle CAB + ABC + BCA = 180

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You already know what CAB and ABC is

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So can you find BCA?

buoyant mural May 1, 2023, 10:26 AM

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They asked for BCD

sonic spruce May 1, 2023, 10:27 AM

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Yes, in this way we use BCA to find BCD

buoyant mural May 1, 2023, 10:28 AM

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yes you add 35 + c +67 =180 ?

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Hey can we skip this one

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sonic spruce May 1, 2023, 10:30 AM

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buoyant mural Hey can we skip this one

It’s your wish

sonic spruce May 1, 2023, 10:30 AM

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buoyant mural

You can use the same idea again

buoyant mural May 1, 2023, 10:40 AM

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What’s next

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sorry I was afk

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@sonic spruce

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<@&286206848099549185>

sonic spruce May 1, 2023, 10:51 AM

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It’s correct so far

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Now you have to find angle A

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A = 5x + 2

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Since you already know what x is, you can plug in the value for x into 5x+2

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To get the measure of angle A

buoyant mural May 1, 2023, 10:54 AM

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oh thx!

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67

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sonic spruce May 1, 2023, 10:56 AM

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Go through this one on your own

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What did you get?

buoyant mural May 1, 2023, 10:59 AM

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86

sonic spruce May 1, 2023, 11:00 AM

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buoyant mural 86

What? How?

buoyant mural May 1, 2023, 11:01 AM

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how can I get to the answer

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i tried multiple ways

sonic spruce May 1, 2023, 11:01 AM

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Can you show your working

buoyant mural May 1, 2023, 11:02 AM

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i’m quite in a hurry so i’m requesting to know the quickest way for the answer

sonic spruce May 1, 2023, 11:02 AM

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Why in such a hurry?

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But okay

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This one is no different from what you’ve been doing so far

buoyant mural May 1, 2023, 11:03 AM

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i’m in public

sonic spruce May 1, 2023, 11:03 AM

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In all the other questions

buoyant mural May 1, 2023, 11:03 AM

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ok

sonic spruce May 1, 2023, 11:03 AM

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MEF is exterior angle

buoyant mural May 1, 2023, 11:04 AM

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yes

sonic spruce May 1, 2023, 11:04 AM

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EFG and FGE are the interior angles opposite to MEF

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…

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What do you get?

buoyant mural May 1, 2023, 11:05 AM

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sonic spruce EFG and FGE are the interior angles opposite to MEF

yes so

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yeah how can I plug that

sonic spruce May 1, 2023, 11:07 AM

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sonic spruce This

You use exterior angle theorem

buoyant mural May 1, 2023, 11:14 AM

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94= F + 54

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40?

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@sonic spruce

sonic spruce May 1, 2023, 11:17 AM

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Yes

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Nice

buoyant mural May 1, 2023, 11:18 AM

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Yes

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Thank you

sonic spruce May 1, 2023, 11:18 AM

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No problem:)

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Have a good day

buoyant mural May 1, 2023, 11:18 AM

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The assignment’s complete now

buoyant mural May 1, 2023, 11:18 AM

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sonic spruce Have a good day

You too brother :))

sonic spruce May 1, 2023, 11:18 AM

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Good job happy

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Close the channel if you don’t have any other questions

buoyant mural May 1, 2023, 11:19 AM

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.close

safe radishBOT May 1, 2023, 11:19 AM

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safe radishBOT May 1, 2023, 11:35 AM

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sand ember May 1, 2023, 12:36 PM

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I'm trying to get the value of (-3/p). It equals 1 when p = 1 or 7 (mod 12) for instance

safe radishBOT May 1, 2023, 12:36 PM

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sand ember I'm trying to get the value of (-3/p). It equals 1 when p = 1 or 7 (mod 12) for ...

sand ember May 1, 2023, 12:36 PM

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this means p = 1 (mod 4), p = 1 (mod 3) OR p = 7 (mod 3), p = 7 (mod 4)

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so this means p = 1 (mod 3) AND (p = 1, 3 (mod 4))

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Now, apparently this simplifies to p = 1 (mod 3)

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I really don't understand why though

peak estuary May 1, 2023, 12:49 PM

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p=1,3 mod 4 just means that p is odd

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which assuming p is prime and not 2 is given

sand ember May 1, 2023, 12:51 PM

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peak estuary p=1,3 mod 4 just means that p is odd

Thank you, I get it now!

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.close

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trim peak May 1, 2023, 1:51 PM

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Pls help

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safe radishBOT May 1, 2023, 1:51 PM

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trim peak Pls help

safe radishBOT May 1, 2023, 2:06 PM

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@trim peak Has your question been resolved?

safe radishBOT May 1, 2023, 2:36 PM

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@trim peak Has your question been resolved?

safe radishBOT May 1, 2023, 3:06 PM

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real charm May 1, 2023, 3:08 PM

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Note that e^((-1+t)inf) and e^((1+t)(-inf)) are both equal to zero

safe radishBOT May 1, 2023, 3:08 PM

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real charm Note that e^((-1+t)inf) and e^((1+t)(-inf)) are both equal to zero

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Please don't occupy multiple help channels.

real charm May 1, 2023, 3:08 PM

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Is this statement true?

pseudo scroll May 1, 2023, 3:08 PM

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What's t

real charm May 1, 2023, 3:09 PM

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Some constant

pseudo scroll May 1, 2023, 3:09 PM

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Is it greater than 1 or lesser than 1

real charm May 1, 2023, 3:10 PM

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It can be any value

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Arbitrary constant

pseudo scroll May 1, 2023, 3:10 PM

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Then you can't say anything about those expressions

real charm May 1, 2023, 3:11 PM

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This is the context

pseudo scroll May 1, 2023, 3:13 PM

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It really depends on the value of t

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If t was -5, then the first one would be 0 but the second would be infinity

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Of t was 0, then both would be 0

safe radishBOT May 1, 2023, 3:26 PM

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@real charm Has your question been resolved?

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frosty granite May 1, 2023, 3:35 PM

#

do i need to algebraic division

safe radishBOT May 1, 2023, 3:35 PM

#

frosty granite do i need to algebraic division

frosty granite May 1, 2023, 3:35 PM

#

even then it doesnt look that clear

real charm May 1, 2023, 3:39 PM

#

Just simplify it

#

Then match up the coefficients on each side of the equation

frosty granite May 1, 2023, 3:44 PM

#

yh that works thanks

#

.close

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steep gust May 1, 2023, 3:59 PM

#

help

safe radishBOT May 1, 2023, 3:59 PM

#

steep gust help

steep gust May 1, 2023, 3:59 PM

#

with this

#

this is my expression

safe radishBOT May 1, 2023, 4:15 PM

#

@steep gust Has your question been resolved?

steep gust May 1, 2023, 4:18 PM

#

?

safe radishBOT May 1, 2023, 4:52 PM

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@steep gust Has your question been resolved?

safe radishBOT May 1, 2023, 6:10 PM

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tacit gyro May 1, 2023, 6:25 PM

#

I know the working is long but i’d be extremely grateful for someone to verify my answer

safe radishBOT May 1, 2023, 6:26 PM

#

tacit gyro I know the working is long but i’d be extremely grateful for someone to verify m...

restive creek May 1, 2023, 6:30 PM

#

Yeah, looks good to me

peak estuary May 1, 2023, 6:31 PM

#

just use online calculators to verify answers

restive creek May 1, 2023, 6:33 PM

#

Or just use adj(A)/det(A)

peak estuary May 1, 2023, 6:34 PM

#

dont use that. that scales horribly

#

somewhat doable for 3x3, sure. but anything bigger is a huge pain

safe radishBOT May 1, 2023, 6:40 PM

#

@tacit gyro Has your question been resolved?

tacit gyro May 1, 2023, 6:41 PM

#

peak estuary dont use that. that scales horribly

use what?

safe radishBOT May 1, 2023, 6:56 PM

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patent musk May 1, 2023, 7:00 PM

#

safe radishBOT May 1, 2023, 7:00 PM

#

patent musk

patent musk May 1, 2023, 7:00 PM

#

am i right wit C?

#

<@&286206848099549185>

modest field May 1, 2023, 7:20 PM

#

Did u use cosine rule

safe radishBOT May 1, 2023, 7:29 PM

#

@patent musk Has your question been resolved?

patent musk May 1, 2023, 7:39 PM

#

modest field Did u use cosine rule

wait is it wrong

modest field May 1, 2023, 7:40 PM

#

Yeah

#

$c^2=a^2+b^2-2ab\cos(C)$

flat frigateBOT May 1, 2023, 7:40 PM

#

Misachive

modest field May 1, 2023, 7:40 PM

#

Cosine rule ^

#

Use tgat

#

That*

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safe radishBOT May 1, 2023, 8:36 PM

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soft sail May 1, 2023, 8:37 PM

#

can someone please walk me through how to do this

safe radishBOT May 1, 2023, 8:37 PM

#

soft sail can someone please walk me through how to do this

junior basalt May 1, 2023, 8:40 PM

#

So basically you’re going to want to use the sin trig function

#

A good way to remember is Soh Cah Toa (sin Opposite over hyp) (cosine adjacent over hyp) (tan opposite over adjacent)

#

But you can’t put it in right away hold on let me get paper

soft sail May 1, 2023, 8:42 PM

#

sin = sin(51)?

plucky elk May 1, 2023, 8:43 PM

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,tex .sohcahtoa

flat frigateBOT May 1, 2023, 8:43 PM

#

riemann

junior basalt May 1, 2023, 8:45 PM

#

#

Put it in your calculator like that

soft sail May 1, 2023, 8:45 PM

#

11.66?

junior basalt May 1, 2023, 8:46 PM

#

Make sure to round to tenths place as asked by the question

#

So put it in as 11.7

soft sail May 1, 2023, 8:46 PM

#

tytyty

junior basalt May 1, 2023, 8:46 PM

#

Or else it’s confusing wording?

soft sail May 1, 2023, 8:47 PM

#

i wasnt sure how to do it

#

11.7 was wrong opencry

junior basalt May 1, 2023, 8:47 PM

#

💀 what

#

Does it tell you what it was?

#

OHH @soft sail I know what I did wrong I’m sorry

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When x is on the bottom you basically swap the trig function and x

#

So you would write it as 15/sin(51)

#

(For future reference)

soft sail May 1, 2023, 8:52 PM

#

ok ty

junior basalt May 1, 2023, 8:53 PM

#

Sorry we did that a few units ago and I forgot about that one part 💀

safe radishBOT May 1, 2023, 9:07 PM

#

@soft sail Has your question been resolved?

safe radishBOT May 1, 2023, 9:22 PM

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safe radishBOT May 1, 2023, 10:00 PM

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dreamy finch May 1, 2023, 10:04 PM

#

how many integer solutions are there to x1 + x2 + x3 + x4 = 12 where
x1 >= 2, x2 > -1, x3 >= -2, and x4 >= 0?

safe radishBOT May 1, 2023, 10:04 PM

#

dreamy finch how many integer solutions are there to x1 + x2 + x3 + x4 = 12 where x1 >= 2, x2...

dreamy finch May 1, 2023, 10:05 PM

#

do you make so all of them are greater than or equal to 1?

#

so (x1 -1) + (x2 + 1) + (x3 + 3) + (x4 + 1) = 4 + 12?

#

and then do 16-1 choose 4-1

#

final answer 455?

safe radishBOT May 1, 2023, 10:21 PM

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dreamy finch May 1, 2023, 10:21 PM

#

.reopen

safe radishBOT May 1, 2023, 10:21 PM

#

✅

dreamy finch May 1, 2023, 10:21 PM

#

<@&286206848099549185>

#

how many integer solutions are there to x1 + x2 + x3 + x4 = 12 where
x1 >= 2, x2 > -1, x3 >= -2, and x4 >= 0?

#

do you make so all of them are greater than or equal to 1?
so (x1 -1) + (x2 + 1) + (x3 + 3) + (x4 + 1) = 4 + 12?
and then do 16-1 choose 4-1
final answer 455?

empty gyro May 1, 2023, 10:25 PM

#

Do you mean $x_k$ or $x^k$?

flat frigateBOT May 1, 2023, 10:25 PM

#

SWR

dreamy finch May 1, 2023, 10:33 PM

#

empty gyro Do you mean $x_k$ or $x^k$?

x sub k

safe radishBOT May 1, 2023, 10:48 PM

#

@dreamy finch Has your question been resolved?

safe radishBOT May 1, 2023, 11:03 PM

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true frigate May 1, 2023, 11:05 PM

#

hey I have a question about graphing so if x axis is -4 and my y is 1/16 how would I graph that

safe radishBOT May 1, 2023, 11:05 PM

#

true frigate hey I have a question about graphing so if x axis is -4 and my y is 1/16 how wou...

safe radishBOT May 1, 2023, 11:22 PM

#

@true frigate Has your question been resolved?

safe radishBOT May 1, 2023, 11:37 PM

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safe radishBOT May 2, 2023, 2:38 AM

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valid mauve May 2, 2023, 3:00 AM

#

Prove that if X, Y are irrational numbers, X≠-Y, then X + Y is irrational

safe radishBOT May 2, 2023, 3:00 AM

#

valid mauve Prove that if X, Y are irrational numbers, X≠-Y, then X + Y is irrational

fast gazelle May 2, 2023, 3:04 AM

#

well that's false

buoyant shadow May 2, 2023, 3:04 AM

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that's false

valid mauve May 2, 2023, 3:05 AM

#

That might be the reason why I can't prove it

#

Why is it false?

fast gazelle May 2, 2023, 3:06 AM

#

consider something like $x=\sqrt{2}, y=1-\sqrt{2}$

flat frigateBOT May 2, 2023, 3:06 AM

#

bee

fast gazelle May 2, 2023, 3:06 AM

#

they're not negatives of each other, but they sum to 1, which is rational

valid mauve May 2, 2023, 3:09 AM

#

That is a counterexample right

fast gazelle May 2, 2023, 3:10 AM

#

yes

valid mauve May 2, 2023, 3:10 AM

#

my professor said we should consider X≠-Y

#

so that's false cause it is not true for the sum of every X irrational and Y irrational

safe radishBOT May 2, 2023, 3:31 AM

#

@valid mauve Has your question been resolved?

safe radishBOT May 2, 2023, 3:46 AM

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royal arch May 2, 2023, 4:16 AM

#

safe radishBOT May 2, 2023, 4:16 AM

#

royal arch

royal arch May 2, 2023, 4:16 AM

#

how did my teacher get that answer?

#

lavish remnant May 2, 2023, 4:18 AM

#

royal arch

Look

#

look here okay

#

you see

#

the range

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between 7 & 10 is what?

#

how far is 7 away from 0?

#

How much would you have to reduce to bottom and top to keep the same range

#

If you reduce the x value how does that affect the equation

#

It's been two minutes and not a single questions has been answered

#

good luck

safe radishBOT May 2, 2023, 4:31 AM

#

@royal arch Has your question been resolved?

safe radishBOT May 2, 2023, 4:46 AM

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lean otter May 2, 2023, 5:41 AM

#

safe radishBOT May 2, 2023, 5:41 AM

#

lean otter

obsidian hedge May 2, 2023, 5:41 AM

#

add 4 and 3 togeather

#

divide 28 by 7 (the answer to 1.)

hazy elbow May 2, 2023, 5:42 AM

#

lean otter

assume land given to them be 4x and 3x

obsidian hedge May 2, 2023, 5:42 AM

#

times the answer of 2. by 3

lean otter May 2, 2023, 5:53 AM

#

obsidian hedge 2. divide 28 by 7 (the answer to 1.)

Why 7 is being divided by 28 ??

hazy elbow May 2, 2023, 5:54 AM

#

lean otter Why 7 is being divided by 28 ??

because total land is 3x+4x=7x

lean otter May 2, 2023, 5:54 AM

#

Hmm ... Ok

lean otter May 2, 2023, 5:57 AM

#

obsidian hedge times the answer of 2. by 3

2 by 3 or 4/3??

hazy elbow May 2, 2023, 5:59 AM

#

lean otter 2 by 3 or 4/3??

NOO
we got value of X which is 4

obsidian hedge May 2, 2023, 5:59 AM

#

lean otter 2 by 3 or 4/3??

by 3

hazy elbow May 2, 2023, 5:59 AM

#

so 3X is 3x4=12 and 4x is 4x4=16

obsidian hedge May 2, 2023, 6:00 AM

#

beard im right not u

#

and then add ^2 after the answer

lean otter May 2, 2023, 6:00 AM

#

hazy elbow so 3X is 3x4=12 and 4x is 4x4=16

Yep ... Final answer is 12 , you are correct

#

.close

safe radishBOT May 2, 2023, 6:03 AM

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waxen moon May 2, 2023, 6:36 AM

#

Hi, I need help figuring out what scenario is taking place with this question

safe radishBOT May 2, 2023, 6:36 AM

#

waxen moon Hi, I need help figuring out what scenario is taking place with this question

empty gyro May 2, 2023, 6:50 AM

#

waxen moon Hi, I need help figuring out what scenario is taking place with this question

waxen moon May 2, 2023, 6:52 AM

#

empty gyro

How did u get that scenario?

empty gyro May 2, 2023, 6:53 AM

#

The height of the ladder is just a sample

#

But the setup is what matters

#

Here's a more agnostic image

safe radishBOT May 2, 2023, 7:07 AM

#

@waxen moon Has your question been resolved?

safe radishBOT May 2, 2023, 7:22 AM

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mystic timber May 2, 2023, 8:16 AM

#

safe radishBOT May 2, 2023, 8:16 AM

#

mystic timber

mystic timber May 2, 2023, 8:16 AM

#

Found two

#

Sinx = 1/✓7 so, it should have two solutions because other two would have negative sign

dusk wharf May 2, 2023, 8:20 AM

#

but sin can indeed have negative sign

#

but yeah there are 2 solutions

safe radishBOT May 2, 2023, 8:32 AM

#

@mystic timber Has your question been resolved?

dusk wharf May 2, 2023, 8:34 AM

#

talk

#

mate talk

maiden star May 2, 2023, 8:35 AM

#

there are four solutions

#

because of its periodic nature

#

observe the interval

dusk wharf May 2, 2023, 8:35 AM

#

yeah

maiden star May 2, 2023, 8:35 AM

#

for domain of x

dusk wharf May 2, 2023, 8:35 AM

#

im sorry

#

yeah

mystic timber May 2, 2023, 8:35 AM

#

No

dusk wharf May 2, 2023, 8:35 AM

#

okay

mystic timber May 2, 2023, 8:35 AM

#

No

dusk wharf May 2, 2023, 8:35 AM

#

No.

maiden star May 2, 2023, 8:36 AM

#

mystic timber No

huh ?

dusk wharf May 2, 2023, 8:37 AM

#

if youre not wiling to accept what youre told here you can could just stop asking

safe radishBOT May 2, 2023, 8:47 AM

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dreamy hornet May 2, 2023, 9:11 AM

#

a function is given at f(x) = pi * sin(x). One of the 3 graphs is the graph for f. which one is it

safe radishBOT May 2, 2023, 9:11 AM

#

dreamy hornet a function is given at f(x) = pi * sin(x). One of the 3 graphs is the graph for ...

dreamy hornet May 2, 2023, 9:11 AM

#

how can I see this ?

obsidian oracle May 2, 2023, 9:11 AM

#

Try to find f(0) and f(1)

#

You will have to process by elimination

dreamy hornet May 2, 2023, 9:16 AM

#

obsidian oracle Try to find f(0) and f(1)

I think it’s B but I don’t how to put it in words to explain it

lean otter May 2, 2023, 9:31 AM

#

not B

#

pi * sin(x) is just sin(x) which is upscaled by pi

#

so the curve will reach x-axis at points where sin(x) becomes 0 as usual..but the maxima and minima will be +pi and -pi respectively instead of +1 and -1

#

C curve seems to me the answer

safe radishBOT May 2, 2023, 9:38 AM

#

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patent lodge May 2, 2023, 11:04 AM

#

safe radishBOT May 2, 2023, 11:04 AM

#

patent lodge

patent lodge May 2, 2023, 11:04 AM

#

Hello i have two questions

#

First is i dont exactly understand what 2. c) is asking me to do (seems too easy) and i dont know how to do 3. c) ii)

#

I have done all of the other parts of the questions

#

is anyone here to help?

safe radishBOT May 2, 2023, 11:25 AM

#

@patent lodge Has your question been resolved?

patent lodge May 2, 2023, 11:27 AM

#

anyone here to help? itll only be quick ive already done most of it and have a vague idea of what to do

#

<@&286206848099549185>

#

:(

granite idol May 2, 2023, 11:38 AM

#

its asking you to express the vector v with its coordinates w.r.t. the eigenbasis

#

so if P is a matrix with its columns the eigenvectors of T, I think it'd just be P^{-1] v

patent lodge May 2, 2023, 11:40 AM

#

SOMEONE HERE THANK YUO

#

so i hbave three eigen vectors

#

i thought i could just do [x; y; z] = s [eigenvector one] + t[eigenvector 2] plus u[eigenvector 3] right?

granite idol May 2, 2023, 11:41 AM

#

should be the same thing

patent lodge May 2, 2023, 11:41 AM

#

granite idol its asking you to express the vector v with its coordinates w.r.t. the eigenbasi...

its asking for a linear combination to express [x; y; z]?

#

yah

#

but what notation does it want

patent lodge May 2, 2023, 11:42 AM

#

patent lodge i thought i could just do [x; y; z] = s [eigenvector one] + t[eigenvector 2] plu...

this seems too easy

granite idol May 2, 2023, 11:42 AM

#

well you'd need some expressions for [s, t, u]

patent lodge May 2, 2023, 11:42 AM

#

why they cant just be parameters?

granite idol May 2, 2023, 11:43 AM

#

I assume they want them to be in terms of [a, b, c] maybe

patent lodge May 2, 2023, 11:43 AM

#

but i cant do that

granite idol May 2, 2023, 11:44 AM

#

if you calculate the inverse of P, multiply it by [a, b, c] and see what you get

patent lodge May 2, 2023, 11:44 AM

#

what is P?

granite idol May 2, 2023, 11:44 AM

#

a 3x3 matrix, each column is an eigenvector of T

patent lodge May 2, 2023, 11:44 AM

#

why do i have to do that

granite idol May 2, 2023, 11:45 AM

#

you want to solve the system v = Pw, where w = [s, t, u] as you wrote it. the way to do that for P invertible is multiply on the left by P^{-1}

patent lodge May 2, 2023, 11:46 AM

#

granite idol you want to solve the system v = Pw, where w = [s, t, u] as you wrote it. the wa...

why is there a matrix now tho

#

its just a linear combination of three vectors making another vector

granite idol May 2, 2023, 11:47 AM

#

and that can be represented in terms of a matrix-vector product

patent lodge May 2, 2023, 11:47 AM

#

patent lodge i thought i could just do [x; y; z] = s [eigenvector one] + t[eigenvector 2] plu...

yeah but why cant i represent it like this

granite idol May 2, 2023, 11:48 AM

#

it's the same thing. call the eigenvectors of T v1, v2, v3. then [x, y, z] = sv1 + tv2 + uv3 is the same thing as [x, y, z] = P*[s, t, u]

patent lodge May 2, 2023, 11:49 AM

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yeah so if its the same thing why shouldnt i just write it like that

granite idol May 2, 2023, 11:49 AM

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as your answer? because that's not an answer, you haven't done anything when just writing it as that

patent lodge May 2, 2023, 11:50 AM

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i havent expressed v as a linear combination of other vectors?

granite idol May 2, 2023, 11:51 AM

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like I said, I assume they want the coordinates to be in terms of a, b, c

patent lodge May 2, 2023, 11:53 AM

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ahhh

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ok

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ok

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so

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how do i do that

granite idol May 2, 2023, 11:54 AM

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I have told you, either calculate the inverse of P and multiply by [a, b, c] or solve the system by row reduction/Gaussian elimination

patent lodge May 2, 2023, 11:54 AM

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and P is a matrix with eigenvector collumns?>

granite idol May 2, 2023, 11:54 AM

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yes

patent lodge May 2, 2023, 11:54 AM

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ok ill give it a go give me a few minutes

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ok i gave up and used symbolab to do the inverse and it is disgusting what next?

granite idol May 2, 2023, 11:59 AM

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multiply by [a, b, c]

patent lodge May 2, 2023, 12:00 PM

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and thats it?

granite idol May 2, 2023, 12:00 PM

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yes, that should be it

patent lodge May 2, 2023, 12:00 PM

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huh ok thanks

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is there a way i can check my answer?

granite idol May 2, 2023, 12:02 PM

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choose random values for a, b, c and see if you get the same thing on both sides

patent lodge May 2, 2023, 12:08 PM

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yeaa ok

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aight ill close this and if i have problems tomorrow ill get some more clarification

#

.close

safe radishBOT May 2, 2023, 12:08 PM

#

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sand ember May 2, 2023, 12:18 PM

#

I'm a bit lost of my old knowledge of Group Theory, what exactly is (Z/nZ)^x and (Z/nZ)*

safe radishBOT May 2, 2023, 12:18 PM

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sand ember I'm a bit lost of my old knowledge of Group Theory, what exactly is (Z/nZ)^x and...

lean otter May 2, 2023, 12:20 PM

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any context?

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they usually mean the same thing

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its the units of Z/nZ under multiplication

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which is precisely the numbers coprime to n

sand ember May 2, 2023, 12:21 PM

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lean otter any context?

Context is I want to show that assuming p is prime. That if p = 1 (mod 3) then a third of the elements in (Z/pZ)* are cubes and if p = 2 (mod 3) then all elements are cubes

lean otter May 2, 2023, 12:23 PM

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since n is prime, then every nonzero element is invertible (under multiplication)

sand ember May 2, 2023, 12:24 PM

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So (Z/pZ)* = {1,2,...,p-1} (assuming ig p > 3 here)

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Okay, any idea with the question btw?

lean otter May 2, 2023, 12:24 PM

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sand ember So (Z/pZ)* = {1,2,...,p-1} (assuming ig p > 3 here)

(Z/pZ)^*?

sand ember May 2, 2023, 12:24 PM

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lean otter (Z/pZ)^*?

Yeah

lean otter May 2, 2023, 12:24 PM

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sand ember Okay, any idea with the question btw?

let x be arbitrary in (Z/pZ)*

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consider the roots of (x^3-1) = 0 mod p

sand ember May 2, 2023, 12:25 PM

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lean otter consider the roots of (x^3-1) = 0 mod p

how could I infer to try this?

lean otter May 2, 2023, 12:25 PM

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how to get to that?

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or what to do with that?

sand ember May 2, 2023, 12:27 PM

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To get to that, like, obviously the x is arbitrary in (Z/pZ)* that makes sense since we want to show that such an x will be cubed for p = 2 (mod 3) and a third of them are cubes if p = 1 (mod 3), but like how could I figure out to consider that the roots of (x^3 - 1) = 0 mod p, if that makes sense? Like how would I think to myself; hm maybe I should try that

lean otter May 2, 2023, 12:28 PM

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ah sorry

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should be x^3=y lol

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wait

dreamy hornet May 2, 2023, 12:31 PM

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lean otter not B

could you explain why it’s not A

sand ember May 2, 2023, 12:32 PM

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dreamy hornet could you explain why it’s not A

restate your question and maybe tag them there, this channel is occupied

dreamy hornet May 2, 2023, 12:32 PM

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oh my bad

lean otter May 2, 2023, 12:32 PM

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sand ember To get to that, like, obviously the x is arbitrary in (Z/pZ)* that makes sense s...

forget what I said for now

#

do you know the fact that every finite field has a primitive element?

sand ember May 2, 2023, 12:34 PM

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Idk about finite field because this is all in a number theory context, but we've done "Let p be a prime. Then there exists a primitive element
g modulo p."

lean otter May 2, 2023, 12:34 PM

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oh wait, theres an easier way of doing it

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sorry lol

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thinking on the spot

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we can use euler's theorem

sand ember May 2, 2023, 12:35 PM

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Hang on, let me just look that up in my notes lol

lean otter May 2, 2023, 12:35 PM

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its the one that says we can look at powers mod p-1

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so the cubing map is the same as multiplying by 3 mod p-1

sand ember May 2, 2023, 12:38 PM

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So n is a positive integer, and a is an integer such that gcd(a,n) = 1 Then $a^{\phi(n)} \equiv 1$ (mod n)and obviously here we're working in mod p and p is a prime so $\phi(p) = p-1$ so for all a coprime to p we have $a^{p-1} \equiv 1$ (mod p)

flat frigateBOT May 2, 2023, 12:38 PM

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LeftySam

sand ember May 2, 2023, 12:38 PM

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So a here is just an arbitrary element in (Z/pZ)*

lean otter May 2, 2023, 12:38 PM

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yeah

sand ember May 2, 2023, 12:40 PM

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Okay, but what does this have to do with cubes?

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I feel like you're about to blow my mind lol

lean otter May 2, 2023, 12:40 PM

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calm lol

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we want to find all cubes

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so we want to find the set of a^3 for all a

sand ember May 2, 2023, 12:41 PM

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that's just going to be {1,8,27, 64, ..., (p-1)^3} no?

lean otter May 2, 2023, 12:41 PM

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yeah

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mod p

sand ember May 2, 2023, 12:41 PM

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Or am I not taking into account the mod p

lean otter May 2, 2023, 12:42 PM

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everything is mod p

sand ember May 2, 2023, 12:42 PM

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Okay

lean otter May 2, 2023, 12:42 PM

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we want to find out whether this set has p-1 elements or (p-1)/3 elements

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(or something else)

lean otter May 2, 2023, 12:43 PM

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flat frigate **LeftySam**

so we can use this, and we get that we want to find the set of all 3b mod p-1

sand ember May 2, 2023, 12:43 PM

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Wait hang on, we want to prove that each of these are cubes; so surely we can't just cube each element?

lean otter May 2, 2023, 12:43 PM

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we want to find the size of the image of the cubing map

sand ember May 2, 2023, 12:44 PM

#

Okay and we want to show the image is (Z/pZ)* if p = 2 (mod 3) and the image I guess is all contained in (Z/pZ)* with (p-1)/3 elements if p = 1 (mod 3)

lean otter May 2, 2023, 12:44 PM

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yeah

sand ember May 2, 2023, 12:45 PM

#

So how do we use Euler's Theorem here?

lean otter May 2, 2023, 12:45 PM

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the main step is to reduce it from cubing in (Z/pZ)^* to tripling in Z/(p-1)Z

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this is similar to taking logs

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and this follows from euler's theorem

sand ember May 2, 2023, 12:46 PM

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I don't get what ur saying ngl

lean otter May 2, 2023, 12:47 PM

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you know how log(x^y)=ylog(x)

sand ember May 2, 2023, 12:47 PM

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yes

lean otter May 2, 2023, 12:47 PM

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thats what we are trying to do here

sand ember May 2, 2023, 12:47 PM

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in what sense?

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We don't have logs no?

lean otter May 2, 2023, 12:47 PM

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a^3 in (Z/pZ)* becomes 3b in Z/(p-1)Z

sand ember May 2, 2023, 12:48 PM

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Why?

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Also is not presupposing our result?

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*this not

lean otter May 2, 2023, 12:49 PM

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sand ember Why?

maybe its useful to know about primitive elements

sand ember May 2, 2023, 12:49 PM

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I know a fair bit about them

lean otter May 2, 2023, 12:49 PM

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let x be primitive mod p

sand ember May 2, 2023, 12:49 PM

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then x^{p-1} = 1

lean otter May 2, 2023, 12:49 PM

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yeah

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and then (Z/pZ)* = {1, x, x^2,...}

#

then if we want to cube every element, then we have {1, x^3, x^6, x^9,...}

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and then we can use euler's theorem on the powers

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eg, if p=7. Then x^9 = x^3 since 9 = 3 mod 6

sand ember May 2, 2023, 12:51 PM

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But we wish to prove that every (Z/pZ)* is a cube no? Won't work by cubing any element in it I wouldn't have thought

lean otter May 2, 2023, 12:52 PM

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sand ember But we wish to prove that every (Z/pZ)* is a cube no? Won't work by cubing any e...

if every element is a cube, then cubing is bijective

#

(i gtg for now, bbl)

safe radishBOT May 2, 2023, 1:06 PM

#

@sand ember Has your question been resolved?

safe radishBOT May 2, 2023, 1:21 PM

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safe radishBOT May 2, 2023, 1:48 PM

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frosty granite May 2, 2023, 1:49 PM

#

stuck

safe radishBOT May 2, 2023, 1:49 PM

#

frosty granite stuck

frosty granite May 2, 2023, 1:49 PM

#

forget about hte vectors for a sec how do u even prove the diagonals bisect

safe radishBOT May 2, 2023, 2:04 PM

#

@frosty granite Has your question been resolved?

safe radishBOT May 2, 2023, 2:41 PM

#

@frosty granite Has your question been resolved?

frosty granite May 2, 2023, 2:58 PM

#

anyone?

safe radishBOT May 2, 2023, 4:09 PM

#

@frosty granite Has your question been resolved?

safe radishBOT May 2, 2023, 6:11 PM

#

@frosty granite Has your question been resolved?

naive arch May 2, 2023, 6:36 PM

#

safe radishBOT May 2, 2023, 8:11 PM

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fleet jay May 2, 2023, 8:14 PM

#

Need help with

safe radishBOT May 2, 2023, 8:14 PM

#

fleet jay Need help with

safe radishBOT May 2, 2023, 8:30 PM

#

@fleet jay Has your question been resolved?

safe radishBOT May 2, 2023, 8:45 PM

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somber void May 2, 2023, 8:55 PM

#

safe radishBOT May 2, 2023, 8:55 PM

#

somber void

somber void May 2, 2023, 8:55 PM

#

Any shortcuts for this kind of problem on exam?

light shoal May 2, 2023, 9:00 PM

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shorter than just doing a substitution (either mentally or on paper), say y = x/a ?

safe radishBOT May 2, 2023, 9:10 PM

#

@somber void Has your question been resolved?

safe radishBOT May 2, 2023, 9:25 PM

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lean otter May 2, 2023, 9:37 PM

#

yo

safe radishBOT May 2, 2023, 9:37 PM

#

lean otter yo

lean otter May 2, 2023, 9:37 PM

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this guy on youtube

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said

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23 mod 30

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is equal to -7

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and 23

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is he frp

hardy lion May 2, 2023, 9:38 PM

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yes

lean otter May 2, 2023, 9:38 PM

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oh bruh

#

the logic I guess

#

is if you add 30

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then you subtract 7 to get 23

#

bruh why did khan academy skip over these

#

got hard scammed

#

.close

safe radishBOT May 2, 2023, 9:38 PM

#

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fleet portal May 2, 2023, 10:40 PM

#

I got a question on a test in this format:

Sasha takes 10 minutes to paint 25 square feet

Ben takes 5 minutes to paint 25 feet

Sasha says that it takes 15 minutes to paint 50 square feet together explain why she is wrong.
—————————————————

Now the obvious anwser is 10 as it would take Ben 10 minutes to finish the wall but I was stumped thinking about what the real true anwser, this is because the 10 minutes is only is Ben is painting but I want to know how fast it is together in the sense of what would be the most efficient way to paint the wall together.

safe radishBOT May 2, 2023, 10:40 PM

#

fleet portal I got a question on a test in this format: Sasha takes 10 minutes to paint 25 s...

fleet portal May 2, 2023, 10:42 PM

#

And what would the formula be for finding the anwser

mint holly May 2, 2023, 10:43 PM

#

Does it say the square footage of 1 wall

dull sequoia May 2, 2023, 10:45 PM

#

You seemed to have assumed that 1 wall is 50 square feet

safe radishBOT May 2, 2023, 10:57 PM

#

@fleet portal Has your question been resolved?

fleet portal May 2, 2023, 10:58 PM

#

Sorry meant to say 50 square feet

#

Not one wall

#

I fixed it

buoyant shadow May 2, 2023, 11:00 PM

#

~~yuor obvious answer is wrong~~

#

or at least i dont get it

#

the obvious answer is that it would take ben 5 minutes, and then 5 minutes later Sasha finishes as well, so that's 10, not 15 and we even let Ben rest more than necessary

toxic stratus May 2, 2023, 11:03 PM

#

hmmCat

buoyant shadow May 2, 2023, 11:03 PM

#

your reasoning is wildly different and i don;t get it

toxic stratus May 2, 2023, 11:04 PM

#

it's just it'll take at most 10 because ben can do it alone and take 10

buoyant shadow May 2, 2023, 11:04 PM

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okay yeah

#

thanks

toxic stratus May 2, 2023, 11:05 PM

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the least time needed is gonna be like 50/(25/10 + 25/5)

buoyant shadow May 2, 2023, 11:06 PM

#

i explained it once, like you calculate the painting speed, and add it together

#

and someone flipped out and said it's not a physics problem, i should shut up

toxic stratus May 2, 2023, 11:06 PM

#

hmmCat

buoyant shadow May 2, 2023, 11:06 PM

#

like a different helper

toxic stratus May 2, 2023, 11:06 PM

#

that's a sully moment

buoyant shadow May 2, 2023, 11:07 PM

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thanks for ur compassion

fleet portal May 2, 2023, 11:08 PM

#

toxic stratus the least time needed is gonna be like 50/(25/10 + 25/5)

So that would be the equation in this case?

toxic stratus May 2, 2023, 11:09 PM

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buoyant shadow i explained it once, like you calculate the painting speed, and add it together

you do this

#

calc the speed of each person and add it together

fleet portal May 2, 2023, 11:16 PM

#

Thanks

#

.close

safe radishBOT May 2, 2023, 11:16 PM

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#

@lean otter Has your question been resolved?

plucky elk May 2, 2023, 11:44 PM

#

JustAsk

smoky hamlet May 2, 2023, 11:46 PM

#

whats the question?

#

what dont you understand

safe radishBOT May 3, 2023, 12:24 AM

#

@lean otter Has your question been resolved?

plucky elk May 3, 2023, 12:27 AM

#

Be more specific and pick a place to start

safe radishBOT May 3, 2023, 12:54 AM

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crude phoenix May 3, 2023, 12:55 AM

#

From the window of a building, the angle of depression of a parked car is 24 deg. From a
window 15m lower, the angle of depression of the same parked car is 19 deg. How far from the foot of the building is the parked car? Include A diagram and a full solution.

safe radishBOT May 3, 2023, 12:55 AM

#

crude phoenix From the window of a building, the angle of depression of a parked car is 24 deg...

crude phoenix May 3, 2023, 12:55 AM

#

crude phoenix From the window of a building, the angle of depression of a parked car is 24 deg...

What would be an efficient way to solve this?

#

safe radishBOT May 3, 2023, 1:11 AM

#

@crude phoenix Has your question been resolved?

crude phoenix May 3, 2023, 1:11 AM

#

<@&286206848099549185>

safe radishBOT May 3, 2023, 1:42 AM

#

@crude phoenix Has your question been resolved?

atomic jackal May 3, 2023, 2:10 AM

#

crude phoenix What would be an efficient way to solve this?

find x using trigonometric ratios. write y in terms of F using trigonometric ratios. now write x+y in terms of 15+F using trigonometric ratios, you have two equations and two unknowns and you can find the value of F and y to calculate the horizontal distance between the two objects. I’m not sure if this method is the most efficient though

#

in these kind of questions try to establish as many relations between different variables and see where that gets you ig

safe radishBOT May 3, 2023, 2:12 AM

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vapid knoll May 3, 2023, 6:44 AM

#

Just making sure, answer is 0 right?

safe radishBOT May 3, 2023, 6:44 AM

#

vapid knoll Just making sure, answer is 0 right?

vapid knoll May 3, 2023, 6:47 AM

#

.close

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royal elm May 3, 2023, 6:58 AM

#

Hi, trying this one more time.

safe radishBOT May 3, 2023, 6:58 AM

#

royal elm Hi, trying this one more time.

peak estuary May 3, 2023, 7:01 AM

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what are you looking for. t only appears twice so that's pretty nice already

royal elm May 3, 2023, 7:02 AM

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Thanks. I know that t* that solves that equation is related to relative x,y,z values, and to a & b relative values, and would like to express it as directly as possible.

peak estuary May 3, 2023, 7:03 AM

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ok so you want to solve this for t?

#

that will probably be some horrible expression

royal elm May 3, 2023, 7:03 AM

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The uglier the better honestly.

#

I’m just stuck on knocking the t’s out of the exponents, then I end up with a t’th root of (5xa-5y) and just can’t get a regular old t in there.

#

I guess: How would you start?

#

I’m willing to toil over it for a while longer, it’s just for personal interest & challenge, I’m just stuck and could use a big brain hint.

peak estuary May 3, 2023, 7:06 AM

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get all terms involving x on one side, the rest on the other

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take logs

royal elm May 3, 2023, 7:07 AM

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do you mean t in this example?

peak estuary May 3, 2023, 7:07 AM

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yeah sorry

royal elm May 3, 2023, 7:08 AM

#

#

So I’ll need two different logs, correct? One to base (1+b) and one to base (1+a)?

#

Is this like an absolute horror of an exercise?

peak estuary May 3, 2023, 7:10 AM

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I'm not even sure this has an analytical solution

#

also I made a mistake in my head

royal elm May 3, 2023, 7:11 AM

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I’ve been calculating it in Excel for various starting values and indeed they don’t always converge.

#

#

Under assumptions that a and b are inversely related, there are a range of values of x,y,z that lead to convergence though.

peak estuary May 3, 2023, 7:12 AM

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just let the computer calculate it

#

that's what they are good at. solving for t wont give you anything valuable

royal elm May 3, 2023, 7:14 AM

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No? It’s the time at which it takes the x + y term to converge with the z term. The comparative statics of that point are of interest.

#

Maybe this is an optimal growth problem? I remember we used a Hamiltonian for that but this was too long ago.

peak estuary May 3, 2023, 7:15 AM

#

the current form is probably better for all kinds of things you wanna say about the equation. the solved form (if it exists) will probably be impossible to analyze

royal elm May 3, 2023, 7:16 AM

#

It doesn’t exist for all values of (x,y,z,a,b), that’s for sure.

#

How would a mathematician deduce the values for which a solution does exist? Or is that a really hard problem in itself?

peak estuary May 3, 2023, 7:17 AM

#

well I dont know really hard

#

but definitely nontrivial

royal elm May 3, 2023, 7:19 AM

#

Is there a general term for solving this type of equation?

#

Like how would I even refer to it?

#

Actually I just realized there should be a term on the initial x too - does that make it any more or less tractable?

#

#

This is the conjecture:
Low rates on savings make capital accumulation slow. Do increases in interest rates make it easier for savers to acquire the down payment for a home?
I’ve been able to formulate the problem like this:

#

I’m getting the impression that this is a much harder math problem than I anticipated.

#

Thanks @peak estuary , I appreciate the guidance.

#

.close

safe radishBOT May 3, 2023, 7:38 AM

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safe radishBOT May 3, 2023, 8:46 AM

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midnight patio May 3, 2023, 9:24 AM

#

safe radishBOT May 3, 2023, 9:24 AM

#

midnight patio

midnight patio May 3, 2023, 9:24 AM

#

How do I do this question?

#

so I did |u|*|w|cos(theta) = -30

#

and |u|*|w|*sin(theta) = Norm(-9,18,-3)

#

,w sqrt(81+ 18^2 +9)

flat frigateBOT May 3, 2023, 9:25 AM

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midnight patio May 3, 2023, 9:25 AM

#

But I don't know why this is wrong?

#

,w sec(arctan(3*sqrt(46)/-30))

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safe radishBOT May 3, 2023, 9:41 AM

#

@midnight patio Has your question been resolved?

midnight patio May 3, 2023, 9:42 AM

#

@sonic wadi

#

<@&286206848099549185>

safe radishBOT May 3, 2023, 10:12 AM

#

@midnight patio Has your question been resolved?

midnight patio May 3, 2023, 10:19 AM

#

<@&286206848099549185>

midnight patio May 3, 2023, 10:59 AM

#

.close

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lean otter May 3, 2023, 11:03 AM

#

is it asking me to draw a graph?

safe radishBOT May 3, 2023, 11:03 AM

#

lean otter is it asking me to draw a graph?

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@lean otter Has your question been resolved?

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fleet current May 3, 2023, 11:35 AM

#

(a) Argue that if X and Y are independent and identically distributed random variables, then P(X ≤ Y ) ≥ 1/2.
(bonus) (b) Would the latter inequality still hold if we removed the independence assumption?

safe radishBOT May 3, 2023, 11:35 AM

#

fleet current (a) Argue that if X and Y are independent and identically distributed random var...

fleet current May 3, 2023, 11:35 AM

#

can anyone help me with part b

safe radishBOT May 3, 2023, 11:50 AM

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@fleet current Has your question been resolved?

fleet current May 3, 2023, 11:50 AM

#

<@&286206848099549185>

safe radishBOT May 3, 2023, 12:20 PM

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compact folio May 3, 2023, 12:24 PM

#

hmm im kinda stuck here

safe radishBOT May 3, 2023, 12:24 PM

#

compact folio hmm im kinda stuck here

elfin yew May 3, 2023, 12:25 PM

#

create two fractions

lost lodge May 3, 2023, 12:25 PM

#

compact folio hmm im kinda stuck here

If you can turn the ratio on the left into a ratio ending with 12, you can say that r - 1 = the left value

compact folio May 3, 2023, 12:27 PM

#

so i did is i put
(r-1)=[(2)(12)]/3
(r-1)=[24]/3
(r-1)=8?

#

do i need to simplify the 8 one btw or thats already the answer?

#

<@&286206848099549185>

grim plover May 3, 2023, 12:37 PM

#

compact folio do i need to simplify the 8 one btw or thats already the answer?

u dont need to

#

i think

strong tendon May 3, 2023, 12:39 PM

#

simple:
2:3 = (r-1):12
2/3=(r-1)/12
so putting 12 that side,
2*12 /3=r-1
hence, r-1 =8 and r=9

compact folio May 3, 2023, 12:40 PM

#

.close

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lean otter May 3, 2023, 12:43 PM

#

can i consider this as true?

safe radishBOT May 3, 2023, 12:43 PM

#

lean otter can i consider this as true?

lean otter May 3, 2023, 12:44 PM

#

.close

safe radishBOT May 3, 2023, 12:44 PM

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lucid charm May 3, 2023, 12:57 PM

#

can someone help me with this, i dont know if im graphing correctly or not

safe radishBOT May 3, 2023, 12:57 PM

#

lucid charm can someone help me with this, i dont know if im graphing correctly or not

lucid charm May 3, 2023, 12:57 PM

#

here is my work so far:

safe radishBOT May 3, 2023, 1:12 PM

#

@lucid charm Has your question been resolved?

safe radishBOT May 3, 2023, 1:43 PM

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@lucid charm Has your question been resolved?

safe radishBOT May 3, 2023, 2:13 PM

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lean otter May 3, 2023, 2:22 PM

#

c i made

safe radishBOT May 3, 2023, 2:22 PM

#

lean otter c i made

sonic spruce May 3, 2023, 2:23 PM

#

Damn that’s really cool

#

But do you have a question to ask?

lean otter May 3, 2023, 2:23 PM

#

ty

sonic spruce May 3, 2023, 2:24 PM

#

sonic spruce But do you have a question to ask?

If you dont, you should probably close the channel as help channels are for any math related questions you might have

sonic spruce May 3, 2023, 2:25 PM

#

lean otter c i made

Impressive though ngl

lean otter May 3, 2023, 2:25 PM

#

how will i close

sonic spruce May 3, 2023, 2:25 PM

#

“.close”

lean otter May 3, 2023, 2:26 PM

#

".close"

#

not close

sonic spruce May 3, 2023, 2:26 PM

#

.close

safe radishBOT May 3, 2023, 2:26 PM

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torpid flare May 3, 2023, 2:46 PM

#

safe radishBOT May 3, 2023, 2:46 PM

#

torpid flare

torpid flare May 3, 2023, 2:46 PM

#

Need help with this

safe radishBOT May 3, 2023, 3:01 PM

#

@torpid flare Has your question been resolved?

torpid flare May 3, 2023, 3:04 PM

#

No

torpid flare May 3, 2023, 3:04 PM

#

safe radish <@688853349306466324> Has your question been resolved?

No

#

<@&286206848099549185>

safe radishBOT May 3, 2023, 3:36 PM

#

@torpid flare Has your question been resolved?

safe radishBOT May 3, 2023, 4:06 PM

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vocal moth May 3, 2023, 4:10 PM

#

ordered pair un unordered pair?

safe radishBOT May 3, 2023, 4:10 PM

#

vocal moth ordered pair un unordered pair?

#

@vocal moth Has your question been resolved?

vocal moth May 3, 2023, 4:55 PM

#

.close

safe radishBOT May 3, 2023, 4:55 PM

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ruby oar May 3, 2023, 4:57 PM

#

!help

safe radishBOT May 3, 2023, 4:57 PM

#

ruby oar !help

ruby oar May 3, 2023, 4:58 PM

#

Calculate the perimeter of the following shape

#

this is my working

#

P1 = (pi * 100) / 2
P1 = 314.159265359 / 2
P1 = 157.07963268

P2 = 70 + 70 + 100
P2 = 240

Total Perimeter = 240+157.07963268
Total Perimeter = 397.08m

obtuse plover May 3, 2023, 5:05 PM

#

Ur P2 is incorrect

ruby oar May 3, 2023, 5:05 PM

#

How come

obtuse plover May 3, 2023, 5:06 PM

#

Label which sides are 50 and 70 then show me

ruby oar May 3, 2023, 5:06 PM

#

Ok

#

let me redo it

#

check that

obtuse plover May 3, 2023, 5:08 PM

#

Yea that looks good

ruby oar May 3, 2023, 5:09 PM

#

Yeah

#

Someone asked why

#

for the perimeter of the rectangle i only added 3 numbers

#

and not 4

#

thats because the perimeter of the semi circle took the other length of the rectangle

obtuse plover May 3, 2023, 5:09 PM

#

Yea

ruby oar May 3, 2023, 5:10 PM

#

👍

#

Can I try one more to see your opinion

obtuse plover May 3, 2023, 5:10 PM

#

It’s only the outside lengths that are measured for perimeter

obtuse plover May 3, 2023, 5:10 PM

#

ruby oar Can I try one more to see your opinion

Ok

ruby oar May 3, 2023, 5:14 PM

#

P1 = (pi * 28) / 4
P1 = 21.9911485751

P2 = 46 + 46 + 14
P2 = 106cm

Total P = 21.9911485751 + 106
Total P = 127.99cm (2dp)

obtuse plover May 3, 2023, 5:18 PM

#

Ur P1 is incorrect

ruby oar May 3, 2023, 5:19 PM

#

How

#

Oh wait

#

im so sorry

#

forgive me

#

ill change it

#

the circle is just complex and i make these mistakes

obtuse plover May 3, 2023, 5:20 PM

#

ruby oar forgive me

No worries

ruby oar May 3, 2023, 5:20 PM

#

there check

obtuse plover May 3, 2023, 5:21 PM

#

More incorrect

#

We want the external circumference, not area

#

Of a quarter circle

ruby oar May 3, 2023, 5:21 PM

#

what?

#

but that isnt area

#

ohh wait

#

so sorry

#

forgive again

#

its just so ddamn confusing

#

check agian

#

again*

obtuse plover May 3, 2023, 5:26 PM

#

Yea looks good

ruby oar May 3, 2023, 5:26 PM

#

Im scared for my test

#

because it has those questions

#

and u saw how i mixed up a lot

obtuse plover May 3, 2023, 5:26 PM

#

Double check ur work

#

Write out formulas

ruby oar May 3, 2023, 5:26 PM

#

Yeah

#

Yo

#

i got a few more quetions

#

this scares me

#

I have no clue how to do it

obtuse plover May 3, 2023, 5:30 PM

#

Just search it up on yt

#

Or google

#

Plenty of tutorials

ruby oar May 3, 2023, 5:30 PM

#

Wait is it like?

#

Ok ill try to learn it

safe radishBOT May 3, 2023, 5:45 PM

#

@ruby oar Has your question been resolved?

ruby oar May 3, 2023, 5:50 PM

#

Yooo

#

@obtuse plover

#

#

Mark it for me

#

@ruby oar

#

@obtuse plover

#

<@&286206848099549185>

#

<@&286206848099549185>

lean hound May 3, 2023, 6:16 PM

#

What’s the issue?

ruby oar May 3, 2023, 6:16 PM

#

can u mark my cumulative frequency table

lean hound May 3, 2023, 6:18 PM

#

It’s good

ruby oar May 3, 2023, 6:18 PM

#

Thanks

#

if i wanted to find median whatd i do

#

the median age

#

wait

#

ill learn it

#

then tell u answer

#

actually

#

No

#

I dont know

#

help me

#

ok

safe radishBOT May 3, 2023, 7:08 PM

#

@ruby oar Has your question been resolved?

safe radishBOT May 3, 2023, 7:38 PM

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#

safe radishBOT May 3, 2023, 8:09 PM

#

@full yacht Has your question been resolved?

plucky elk May 3, 2023, 8:22 PM

#

"linear projection on the plane" means $\vp : P \to P$

flat frigateBOT May 3, 2023, 8:23 PM

#

riemann

plucky elk May 3, 2023, 8:23 PM

#

or actually $\vp : \ell_1^3 \to P$

flat frigateBOT May 3, 2023, 8:23 PM

#

riemann

plucky elk May 3, 2023, 8:40 PM

#

if you can prove the problem for one projection, it's probably then simpler to prove it for an arbitrary projection

#

i don't know what computations you're doing

#

what in your image is in P and what is in ell_1^3 ?

safe radishBOT May 3, 2023, 9:08 PM

#

@full yacht Has your question been resolved?

safe radishBOT May 3, 2023, 9:31 PM

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Channel closed

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cold cradle May 3, 2023, 9:41 PM

#

hey um I was given a 'Special triangle' and I dont know how to do any of it but I do know is that I was given a 45, 45, 90 triangle :/

safe radishBOT May 3, 2023, 9:41 PM

#

cold cradle hey um I was given a 'Special triangle' and I dont know how to do any of it but ...

plucky elk May 3, 2023, 9:41 PM

#

45-45-90 triangles are iscocoles

#

does that help?

cold cradle May 3, 2023, 9:41 PM

#

i dont know :/

#

wait does that mean the other angle is 45 too

plucky elk May 3, 2023, 9:42 PM

#

yes it does

cold cradle May 3, 2023, 9:42 PM

#

oh ok

plucky elk May 3, 2023, 9:42 PM

#

180 - 90 - 45 = 45

cold cradle May 3, 2023, 9:42 PM

#

yea sorry i suck at geometry

#

do you know the steps to find the variables?

#

it seems so confusing

mortal sandal May 3, 2023, 9:44 PM

#

What do you know about isosceles triangles

cold cradle May 3, 2023, 9:45 PM

#

well the two angles are congruent ofc

#

ig thats all i know

#

and in this case its a right isosceles so that box means its 90 degrees

#

.close

safe radishBOT May 3, 2023, 9:49 PM

#

Channel closed

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formal crest May 3, 2023, 10:02 PM

#

safe radishBOT May 3, 2023, 10:02 PM

#

formal crest

formal crest May 3, 2023, 10:03 PM

#

why can't I square both sides of the equation? Why is it no longer an equivalent equation?

#

I get a diffrent result if I do so

mint holly May 3, 2023, 10:07 PM

#

(a+b)^2 isn’t a^2+b^2

empty gyro May 3, 2023, 10:09 PM

#

https://en.wikipedia.org/wiki/Freshman's_dream

final halo May 3, 2023, 10:09 PM

#

Also 75² isn't 225

mint holly May 3, 2023, 10:10 PM

#

I think that’s a 15

formal crest May 3, 2023, 10:13 PM

#

mint holly May 3, 2023, 10:14 PM

#

Using a comma as a period is crazy

formal crest May 3, 2023, 10:15 PM

#

ok; that worked! but how do I decide now which value is valid from the two?

mint holly May 3, 2023, 10:15 PM

#

Plug each of them into the original one

formal crest May 3, 2023, 10:15 PM

#

mint holly Using a comma as a period is crazy

Im european

mint holly May 3, 2023, 10:15 PM

#

Yeah sorry im@not used to that

formal crest May 3, 2023, 10:19 PM

#

#

ok, thanks y'all, you have answered all of my questions

#

how to I end this?

mint holly May 3, 2023, 10:21 PM

#

Np

#

.close

formal crest May 3, 2023, 10:21 PM

#

oh

#

.cloase

#

.close

safe radishBOT May 3, 2023, 10:21 PM

#

Channel closed

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gilded fiber May 3, 2023, 10:24 PM

#

safe radishBOT May 3, 2023, 10:24 PM

#

gilded fiber

gilded fiber May 3, 2023, 10:24 PM

#

How do I turn this into a series

#

(2x)/(1+x^2)

#

safe radishBOT May 3, 2023, 10:40 PM

#

@gilded fiber Has your question been resolved?

safe radishBOT May 3, 2023, 11:14 PM

#

@gilded fiber Has your question been resolved?

gilded fiber May 3, 2023, 11:35 PM

#

.close

safe radishBOT May 3, 2023, 11:35 PM

#

Channel closed

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safe radishBOT May 4, 2023, 5:06 AM

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verbal adder May 4, 2023, 5:06 AM

#

hi!

safe radishBOT May 4, 2023, 5:06 AM

#

verbal adder hi!

verbal adder May 4, 2023, 5:06 AM

#

really quick question: Is the limit comparison test true if you take the inverse?

#

((: Σan / Σbn = C > 0, they either both converge or diverge. Is this true for Σbn / Σan too?