#help-10 | Mathematics | Page 181

obtuse pebbleBOT May 15, 2023, 3:55 AM

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royal basin May 15, 2023, 3:57 AM

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vieta & careful manipulations to get that thing in terms of symmetric polys

wanton dagger May 15, 2023, 3:58 AM

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So how do I use vietas formula in this question

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Formulas*

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So I expanded the brackets

astral ivy May 15, 2023, 4:02 AM

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Unnecessary

wanton dagger May 15, 2023, 4:02 AM

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Why?

royal basin May 15, 2023, 4:07 AM

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this is fine as is though

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the numerator is (αβγ)^2 + αβγ(α+β+γ) + (αβ + βγ + γα) + 1

royal basin May 15, 2023, 4:08 AM

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astral ivy Unnecessary

you got something better?

wanton dagger May 15, 2023, 4:08 AM

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royal basin the numerator is (αβγ)^2 + αβγ(α+β+γ) + (αβ + βγ + γα) + 1

Right I see

wanton dagger May 15, 2023, 4:09 AM

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wanton dagger So I expanded the brackets

Oh so I just apply vietas formulae on this thing

obtuse pebbleBOT May 15, 2023, 4:24 AM

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@wanton dagger Has your question been resolved?

obtuse pebbleBOT May 15, 2023, 4:39 AM

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obtuse pebbleBOT May 15, 2023, 5:10 AM

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wooden needle May 15, 2023, 5:22 AM

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Let the set T = { 2 ; 3 ; 4 ; 5; 6 ; 7 ; 8 ; 9 } . Let B be the set of 3-digit natural numbers formed from the digits of the set T . Randomly select a number from set B . Find the probability to choose a number from set B such that the preceding digit is always less than or equal to the next digit

obtuse pebbleBOT May 15, 2023, 5:22 AM

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wooden needle Let the set T = { 2 ; 3 ; 4 ; 5; 6 ; 7 ; 8 ; 9 } . Let B be the set of 3-digit n...

hybrid gull May 15, 2023, 5:24 AM

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

drifting wraith May 15, 2023, 5:26 AM

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it's stars and bars

wooden needle May 15, 2023, 5:30 AM

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I'm not sure how to find a 3-digit number in the set B such that the preceding digit is less than or equal to the next digit

drifting wraith May 15, 2023, 5:30 AM

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you can also do cases, the number has two different digits (in one of two ways) or 3, or 1 (one case each)

wooden needle May 15, 2023, 5:37 AM

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thx, I found the answer from your suggestion

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.close

obtuse pebbleBOT May 15, 2023, 5:37 AM

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strong nebula May 15, 2023, 6:00 AM

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im confused why on the first step he switch signs

obtuse pebbleBOT May 15, 2023, 6:00 AM

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strong nebula im confused why on the first step he switch signs

tardy epoch May 15, 2023, 6:02 AM

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Plot it

strong nebula May 15, 2023, 6:02 AM

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ok

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and then rotating it around the x axis I use the formula pi*r^2

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I dont really get why we need to change the signs @tardy epoch

obtuse pebbleBOT May 15, 2023, 6:21 AM

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@strong nebula Has your question been resolved?

obtuse pebbleBOT May 15, 2023, 6:36 AM

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verbal atlas May 15, 2023, 7:03 AM

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Message attached as I dont have nitro, so I cant send long messages lol <@&286206848099549185>

📎 message.txt

obtuse pebbleBOT May 15, 2023, 7:03 AM

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verbal atlas Message attached as I dont have nitro, so I cant send long messages lol <@&28620...

obtuse pebbleBOT May 15, 2023, 7:22 AM

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@verbal atlas Has your question been resolved?

fervent nexus May 15, 2023, 7:24 AM

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!help

obtuse pebbleBOT May 15, 2023, 7:24 AM

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Please read #❓how-to-get-help

obtuse pebbleBOT May 15, 2023, 7:54 AM

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@verbal atlas Has your question been resolved?

obtuse pebbleBOT May 15, 2023, 8:54 AM

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@verbal atlas Has your question been resolved?

obtuse pebbleBOT May 15, 2023, 11:00 AM

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@verbal atlas Has your question been resolved?

obtuse pebbleBOT May 15, 2023, 3:00 PM

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@verbal atlas Has your question been resolved?

forest sinew May 15, 2023, 10:23 PM

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verbal atlas Message attached as I dont have nitro, so I cant send long messages lol <@&28620...

so wait you need to make a point rotate around a circle?

obtuse pebbleBOT May 16, 2023, 1:03 AM

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@verbal atlas Has your question been resolved?

scarlet pendant May 16, 2023, 4:39 AM

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Use parameteric equations

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Idk how to use calculator sites, but that could help

obtuse pebbleBOT May 16, 2023, 9:03 AM

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feral siren May 16, 2023, 9:07 AM

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If AB = 0 what can we conclude from this statement ?

obtuse pebbleBOT May 16, 2023, 9:07 AM

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feral siren If AB = 0 what can we conclude from this statement ?

feral siren May 16, 2023, 9:07 AM

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If A,B both are matrix

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I asked one of my seniors but he said this doesn't mean that One of A B is a null matrix

haughty coyote May 16, 2023, 9:09 AM

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It doesn't

feral siren May 16, 2023, 9:09 AM

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haughty coyote It doesn't

Why not ?

haughty coyote May 16, 2023, 9:09 AM

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((1,0),(0,0)) x ((0,0),(0,1)) = 0

feral siren May 16, 2023, 9:10 AM

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Oh. So we can conclude nothing from this statement?

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AB=0

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A ,B can be anything

kind hawk May 16, 2023, 9:10 AM

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well depends on what kind of information you want to conclude

haughty coyote May 16, 2023, 9:10 AM

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You can however say that im(B) is included in Ker(A)

kind hawk May 16, 2023, 9:10 AM

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you can for example conclude something about the rank or nullity of these matrices

feral siren May 16, 2023, 9:11 AM

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Ohh got it so one more question

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If A^2 = I
Why cant we say that A = I

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I is unit matrix

kind hawk May 16, 2023, 9:12 AM

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even for numbers this wouldnt be true

haughty coyote May 16, 2023, 9:12 AM

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A = ((-1,0), (0,-1)) is a counter example

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And there are much more complicated ones

feral siren May 16, 2023, 9:12 AM

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kind hawk even for numbers this wouldnt be true

Ohh A = -I too?

haughty coyote May 16, 2023, 9:12 AM

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And many more

kind hawk May 16, 2023, 9:12 AM

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but -I is the easiest other option

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you could also have ((-1, 0), (0, 1))

haughty coyote May 16, 2023, 9:13 AM

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Like ((0,1),(1,0))

kind hawk May 16, 2023, 9:13 AM

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and that's just for 2x2 and staying diagonal

feral siren May 16, 2023, 9:13 AM

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Okay So in this statement A^2 = I
We can although conculde that detA is either 1 or -1

kind hawk May 16, 2023, 9:13 AM

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yes

haughty coyote May 16, 2023, 9:13 AM

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Yes

feral siren May 16, 2023, 9:13 AM

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So that means all matrix whose det is 1 or -1

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Will satisfy

kind hawk May 16, 2023, 9:14 AM

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no

haughty coyote May 16, 2023, 9:14 AM

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Most certainly not

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Every rotation matrix for instance has determinant 1

feral siren May 16, 2023, 9:15 AM

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haughty coyote And there are much more complicated ones

Soo you gave me one simple example, what do you mean by complicated here?

haughty coyote May 16, 2023, 9:15 AM

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Ones that are less simple to check or obvious to come up with

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Ofc 2x2 can't get that complicated, but nxn can

feral siren May 16, 2023, 9:16 AM

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Yessir got it , i am getting so much confused as this is related to algebra

haughty coyote May 16, 2023, 9:16 AM

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Matrices aren't numbers. Nothing is true unless proved

feral siren May 16, 2023, 9:17 AM

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Here is another one
If AB = AC we cant say B = C
Likee broo how does that even make sense

haughty coyote May 16, 2023, 9:17 AM

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Not every matrix is invertible

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That's your problem

kind hawk May 16, 2023, 9:17 AM

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again, not even true for numbers. if A=0 for example

haughty coyote May 16, 2023, 9:18 AM

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As opposed to real numbers, where everything is either 0 or invertible

kind hawk May 16, 2023, 9:18 AM

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(although granted for numbers thats the only counterexample)

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but the point is even for numbers stuff can go wrong. that's nothing new

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just that now for matrices stuff can be even worse

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AB=AC is equivalent to A(B-C)=0 which is again of the form "AB=0" which we had earlier

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from which you cannot include B-C=0, aka B=C

feral siren May 16, 2023, 9:19 AM

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Oh true
I am new to this chapter so it will definitely take me some time to digest the concepts

kind hawk May 16, 2023, 9:19 AM

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yes thats normal

feral siren May 16, 2023, 9:20 AM

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Thank you both KEK

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.close

obtuse pebbleBOT May 16, 2023, 9:20 AM

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Channel closed

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kind hawk May 16, 2023, 9:20 AM

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do lots of examples

feral siren May 16, 2023, 9:20 AM

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Yeee will make sure

obtuse pebbleBOT May 16, 2023, 9:21 AM

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timid silo May 16, 2023, 9:22 AM

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obtuse pebbleBOT May 16, 2023, 9:22 AM

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timid silo

timid silo May 16, 2023, 9:22 AM

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I wrote the derivative I got in red

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Can someone please explain why the answer in blue is -sec^2xsinx

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I used chain rule and multiplied the negative at the front, subtracted 1 from the power then multiplied by the derivative of the inside cosx-> -sinx

hollow river May 16, 2023, 9:25 AM

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Ok

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So

timid silo May 16, 2023, 9:31 AM

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Yeah

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@hollow river

fervent nexus May 16, 2023, 9:33 AM

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Do you want solve it using integration or differentiation

timid silo May 16, 2023, 9:35 AM

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Differentiation

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Is the solution wrong?

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It’s the writing in blue

fervent nexus May 16, 2023, 9:36 AM

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It is sec^2(x)sin(x)

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You took the derivative of cosx as just sinx whereas it is -sinx

timid silo May 16, 2023, 9:37 AM

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I didn’t do that

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My writing is in red

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I’m asking if the blue writing is wrong?

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Or maybe I missed something idk

fervent nexus May 16, 2023, 9:38 AM

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The blue part's differentiation is incorrect

timid silo May 16, 2023, 9:38 AM

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Also for this

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This integration is incorrect?

fervent nexus May 16, 2023, 9:40 AM

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What have they integrated

timid silo May 16, 2023, 9:40 AM

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@fervent nexus

fervent nexus May 16, 2023, 9:40 AM

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4xcosx^2?

timid silo May 16, 2023, 9:40 AM

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Yeah

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These are solutions but it’s written weirdly

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It shouldn’t be negative right?

fervent nexus May 16, 2023, 9:42 AM

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No it should not be negative, and also the term should be 2sin(x^2) + c not 2sin^2(x) +c

timid silo May 16, 2023, 9:43 AM

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fervent nexus No it should not be negative, and also the term should be 2sin(x^2) + c not 2sin...

That’s what I thought too

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Thank you

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Could I ask you 1 more last thing if you don’t mind?

fervent nexus May 16, 2023, 9:44 AM

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No issue

timid silo May 16, 2023, 9:44 AM

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Could you please explain these steps, I’m a bit confused

fervent nexus May 16, 2023, 9:44 AM

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What is the question

timid silo May 16, 2023, 9:44 AM

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I don’t get what happens after the y’ part

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I’ll send it one sec

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4b

fervent nexus May 16, 2023, 9:47 AM

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After you found the derivative as y' = 2x,
You are substituting y = x^2 -1 and y' = 2x.

timid silo May 16, 2023, 9:47 AM

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I don’t get the third line

fervent nexus May 16, 2023, 9:48 AM

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The third line is the differential equation given in the problem

timid silo May 16, 2023, 9:49 AM

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OHHHHHHH

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I was sooo confused

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I didn’t even see that

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Thank you so much 😊

fervent nexus May 16, 2023, 10:04 AM

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If you are done, you can close this channel

obtuse pebbleBOT May 16, 2023, 10:09 AM

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@timid silo Has your question been resolved?

fervent nexus May 16, 2023, 10:09 AM

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.close

obtuse pebbleBOT May 16, 2023, 10:09 AM

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tulip anvil May 16, 2023, 10:17 AM

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What method am I suppose to use for this question? I can't get my head around it

rn_image_picker_lib_temp_15a0b82a-8719-415b-9642-89079a3066eb.jpg

obtuse pebbleBOT May 16, 2023, 10:17 AM

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tulip anvil What method am I suppose to use for this question? I can't get my head around it

obtuse pebbleBOT May 16, 2023, 10:40 AM

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@tulip anvil Has your question been resolved?

vast musk May 16, 2023, 10:55 AM

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the question is essentially asking what is the length of the curve for x [0,1]

obtuse pebbleBOT May 16, 2023, 11:12 AM

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@tulip anvil Has your question been resolved?

obtuse pebbleBOT May 16, 2023, 11:42 AM

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crimson orbit May 16, 2023, 11:50 AM

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obtuse pebbleBOT May 16, 2023, 11:50 AM

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crimson orbit

crimson orbit May 16, 2023, 11:50 AM

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i just started related rates

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can someone guide me through this q?

obtuse pebbleBOT May 16, 2023, 12:05 PM

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@crimson orbit Has your question been resolved?

crimson orbit May 16, 2023, 12:05 PM

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<@&286206848099549185>

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can you guys check tis out

fiery olive May 16, 2023, 12:05 PM

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Hey, what have you tried?

crimson orbit May 16, 2023, 12:06 PM

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uhhh let me send

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crimson orbit May 16, 2023, 12:07 PM

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fiery olive Hey, what have you tried?

i dont think this get me anywhere tho

fiery olive May 16, 2023, 12:08 PM

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What do you mean by dr/dt? What is r?

crimson orbit May 16, 2023, 12:09 PM

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dr/dt is the rate of change

south oracle May 16, 2023, 12:09 PM

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crimson orbit

Rate of change of what

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The angle? The area?

crimson orbit May 16, 2023, 12:10 PM

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i got that from the q, angle from two equal sides decreasing at rate of 0.1pi rad/sec

crimson orbit May 16, 2023, 12:10 PM

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south oracle The angle? The area?

angle

south oracle May 16, 2023, 12:10 PM

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Then shouldn't it be d(theta)/dt = -0.1 pi rad/s
Edit: pi

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You already have seemed to have drawn the pic and marked your angle as theta

fiery olive May 16, 2023, 12:11 PM

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south oracle Then shouldn't it be d(theta)/dt = -0.1 pi rad/s Edit: pi

Don't forget pi though 😼

crimson orbit May 16, 2023, 12:11 PM

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oh yeah

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ill change that

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but idk what to do next

south oracle May 16, 2023, 12:12 PM

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Represent the area as a function of theta

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Then differentiate it with t

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I believe you know how chain rule works

crimson orbit May 16, 2023, 12:13 PM

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south oracle Represent the area as a function of theta

so basically just..

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Area = 1/2(10)(10)sin(theta)

south oracle May 16, 2023, 12:13 PM

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The reason why we express the area with theta

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S because we have too much to think of when we represent it as t

south oracle May 16, 2023, 12:14 PM

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crimson orbit Area = 1/2(10)(10)sin(theta)

Great, which is 50sin(theta)

crimson orbit May 16, 2023, 12:14 PM

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and then you differentiate it?

south oracle May 16, 2023, 12:15 PM

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With t

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Not theta

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Note that

crimson orbit May 16, 2023, 12:15 PM

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so its gonna be like

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dA/dt = 50cos(theta) * d/dt

south oracle May 16, 2023, 12:15 PM

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Yes

crimson orbit May 16, 2023, 12:16 PM

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crimson orbit dA/dt = 50cos(theta) * d/dt

this d/dt here is confusing tho

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like yk

south oracle May 16, 2023, 12:16 PM

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Chain rule:

crimson orbit May 16, 2023, 12:16 PM

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shouldnt it be d"something"/dt

south oracle May 16, 2023, 12:16 PM

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dA/dt = dA/d(theta) * d(theta)/dt

south oracle May 16, 2023, 12:17 PM

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crimson orbit shouldnt it be d"something"/dt

d/dt f(t) means to differentiate f with t

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Nothing really special

crimson orbit May 16, 2023, 12:18 PM

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south oracle dA/dt = dA/d(theta) * d(theta)/dt

um

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what is d(theta) here?

south oracle May 16, 2023, 12:18 PM

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Did you learn the leibnitz notation of the chain rule?

crimson orbit May 16, 2023, 12:18 PM

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crimson orbit dA/dt = 50cos(theta) * d/dt

is this correct yet, or is it not?

crimson orbit May 16, 2023, 12:18 PM

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south oracle Did you learn the leibnitz notation of the chain rule?

no

south oracle May 16, 2023, 12:19 PM

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Oh that makes sense now

crimson orbit May 16, 2023, 12:19 PM

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whatever i did was like what i do for implicit diff

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diff then times d/dt

south oracle May 16, 2023, 12:20 PM

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Okay so basically (f(g(x)))' is f'(g(x)) * g'(x)

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Is it

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If we just express a= f(b) and b=g(x)

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f'(g(x)) = f'(b)= da/db

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g'(x)= db/dx

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da/ dx= d/dx (f(b)) = d/dx {f(g(x))} = {f(g(x))}'

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So yeah basically

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da/dx = da/db * db/dx

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Please review the leibnitz notation afterwards you solve this problem

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It will be used way more than the newton's notation as you learn further

crimson orbit May 16, 2023, 12:24 PM

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oh ok

crimson orbit May 16, 2023, 12:24 PM

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south oracle da/dx = da/db * db/dx

so let say you have this

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how would we apply that to my current prob

south oracle May 16, 2023, 12:24 PM

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Substitute:
a= A
b= theta
x= t

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dA/dt= dA/d(theta) * d(theta)/dt

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Boom

crimson orbit May 16, 2023, 12:26 PM

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ok

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but we cant just write it like that right

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dA has to be smth

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and d(theta) has to be smth

south oracle May 16, 2023, 12:26 PM

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We can...??

crimson orbit May 16, 2023, 12:27 PM

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then what do you do next?

south oracle May 16, 2023, 12:28 PM

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What is A in terms of theta?

crimson orbit May 16, 2023, 12:28 PM

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50sin(theta)

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but thats A not dA

south oracle May 16, 2023, 12:28 PM

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now differentiate that with theta

crimson orbit May 16, 2023, 12:29 PM

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is it 50cos(theta)?

south oracle May 16, 2023, 12:29 PM

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crimson orbit but thats A not dA

I think you're kind of getting confused here

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dA/d(theta) is just A'(theta) when A is basically A(theta)

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dA/d(theta) is NOT a fraction

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We will later learn that it kinda is but

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Not now

crimson orbit May 16, 2023, 12:30 PM

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oh alright

south oracle May 16, 2023, 12:30 PM

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Oh have you learnt about differentials?

crimson orbit May 16, 2023, 12:30 PM

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yeah

south oracle May 16, 2023, 12:30 PM

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I see

crimson orbit May 16, 2023, 12:31 PM

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but we just learn like

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A and then make it A' and then A''

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we dont use fraction much(dA/d(theta))

south oracle May 16, 2023, 12:31 PM

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We define dA to be A'(theta)d(theta)

crimson orbit May 16, 2023, 12:31 PM

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so its hard to understand

south oracle May 16, 2023, 12:32 PM

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south oracle We define dA to be A'(theta)d(theta)

If we see the definition part of a differential

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You can see delta x is just dx when delta x goes to 0

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If y= f(x), we can define dy =f'(x)dx

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The important part is

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the f' is in terms of x

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And y is here, a function of x

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That's why we state dy/dx

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To clarify what we differentiate with

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Now, if we apply that to our problem

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Since A= f(theta)= 50sin(theta),
dA= f'(theta)d(theta), is it?

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The Liebnitz notation of dA/d(theta) is just what you get when you divide dA with d(theta)

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Same goes with d(theta)

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You know here that theta is a function of t, right?

crimson orbit May 16, 2023, 12:37 PM

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yeah

south oracle May 16, 2023, 12:38 PM

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so if we say theta= g(t)

#

d(theta) = g'(t)dt

#

Therefore dA= f'(theta)d(theta)=f'(theta)g'(t)dt

#

dA/dt=f'(theta) *g(t)= dA/d(theta) * d(theta)/dt

#

There

#

This is what chain rule is, at least what I understood

crimson orbit May 16, 2023, 12:41 PM

#

then..

#

i think

#

50cos(theta) * d/dt is correct

south oracle May 16, 2023, 12:43 PM

#

Actaully, d/dt (50cos(theta))

crimson orbit May 16, 2023, 12:43 PM

#

thats the same thing no?

#

just rearrange

south oracle May 16, 2023, 12:43 PM

#

Kinda but

#

It's generally preferred to be at the left

#

Since dA is different from A

#

d is kind of an operator, not a "number"

crimson orbit May 16, 2023, 12:44 PM

#

alright

#

then what do we do next

south oracle May 16, 2023, 12:44 PM

#

find dA/d(theta)

#

We know what d(theta)/dt is

#

A= 50sin(theta)

crimson orbit May 16, 2023, 12:48 PM

#

ok

south oracle May 16, 2023, 12:49 PM

#

So what is dA?

obtuse pebbleBOT May 16, 2023, 1:18 PM

#

@crimson orbit Has your question been resolved?

obtuse pebbleBOT May 16, 2023, 1:48 PM

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plain monolith May 16, 2023, 1:55 PM

#

Anyone can help me with this?

obtuse pebbleBOT May 16, 2023, 1:55 PM

#

plain monolith Anyone can help me with this?

plain monolith May 16, 2023, 1:56 PM

#

Wait wait

#

rn_image_picker_lib_temp_a10f4d0d-7f7a-4f40-a8ee-fcf04dcfa0b3.jpg

#

Number 23

fervent nexus May 16, 2023, 1:56 PM

#

,rotate

warm shaleBOT May 16, 2023, 1:56 PM

#

plain monolith May 16, 2023, 2:05 PM

#

I figured out thank you helping @fervent nexus 🙏

#

. Close

#

,close

#

.close

fervent nexus May 16, 2023, 2:05 PM

#

.close

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steep trellis May 16, 2023, 2:41 PM

#

Which one the right way

obtuse pebbleBOT May 16, 2023, 2:41 PM

#

steep trellis Which one the right way

timid silo May 16, 2023, 2:46 PM

#

x+1= cos(-π/3)

steep trellis May 16, 2023, 2:47 PM

#

Thanks

#

Why not the other one

#

?

timid silo May 16, 2023, 2:48 PM

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How can you even do that

steep trellis May 16, 2023, 2:49 PM

#

Idk?

#

Hahaha nvm im too dumb

timid silo May 16, 2023, 2:49 PM

#

Also

#

How can cos^-1 (x+1) =-π/3 ?

#

Range of cosinverse is [0,π]

steep trellis May 16, 2023, 2:50 PM

#

I also dont know about these questions lmao

#

Teacher just wants to find x

timid silo May 16, 2023, 2:50 PM

#

No solutions is the answer of that

steep trellis May 16, 2023, 2:51 PM

#

Thats what im saying too

#

Hahaha

#

Thanks

#

.close

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tacit imp May 16, 2023, 3:03 PM

#

obtuse pebbleBOT May 16, 2023, 3:03 PM

#

tacit imp

tacit imp May 16, 2023, 3:03 PM

#

quick question, why are +- sqrt5 excluded values as well

solemn plank May 16, 2023, 3:04 PM

#

wdym by "excluded values"

tacit imp May 16, 2023, 3:04 PM

#

excluded values of x

solemn plank May 16, 2023, 3:04 PM

#

you means values of x as solutions?

#

assuming its even defined at that value

timid silo May 16, 2023, 3:05 PM

#

Isnt x not equal to +-5 , 2 , 0 ?

tacit imp May 16, 2023, 3:05 PM

#

no i mean like x cant be +- 5 because then in the first fraction we would divide by 0 which is impossible

solemn plank May 16, 2023, 3:05 PM

#

ah

tacit imp May 16, 2023, 3:06 PM

#

yes but i put it in a calculator and it said that +- sqrt5 is also an excluded value

solemn plank May 16, 2023, 3:06 PM

#

tacit imp

the +- sqrt 5 is only concerning in the second fraction

tacit imp May 16, 2023, 3:07 PM

#

yes i get it

#

but x:(a/b)= x*(b/a)

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so why should x^2-5 be a part of the excluded values

solemn plank May 16, 2023, 3:08 PM

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hm

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you could try simplifying it to make sure the polynomial at the bottom doesnt equal 0 at +-sqrt5

solemn plank May 16, 2023, 3:13 PM

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tacit imp

this is defined at x = +-sqrt5

#

tacit imp May 16, 2023, 3:13 PM

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alright thanks

solemn plank May 16, 2023, 3:13 PM

#

dont mind the ^-1

#

i wrote it wrong

tacit imp May 16, 2023, 3:13 PM

#

its all good

#

.close

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floral dagger May 16, 2023, 3:18 PM

#

Self explanatory, no clue how to solve :(

obtuse pebbleBOT May 16, 2023, 3:18 PM

#

floral dagger Self explanatory, no clue how to solve :(

willow fjord May 16, 2023, 3:23 PM

#

Hi I need help

obtuse pebbleBOT May 16, 2023, 3:33 PM

#

@floral dagger Has your question been resolved?

obtuse pebbleBOT May 16, 2023, 4:06 PM

#

@floral dagger Has your question been resolved?

obtuse pebbleBOT May 16, 2023, 4:23 PM

#

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

steep flax May 16, 2023, 5:03 PM

#

floral dagger Self explanatory, no clue how to solve :(

Have you tried anything at all?

steep flax May 16, 2023, 5:04 PM

#

willow fjord Hi I need help

Hello, jackson. This channel is occupied. Please read #❓how-to-get-help.

obtuse pebbleBOT May 16, 2023, 5:24 PM

#

@floral dagger Has your question been resolved?

obtuse pebbleBOT May 16, 2023, 6:24 PM

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worldly briar May 16, 2023, 6:26 PM

#

Can sb pls help me with Linear Transformation?

obtuse pebbleBOT May 16, 2023, 6:26 PM

#

worldly briar Can sb pls help me with Linear Transformation?

tardy epoch May 16, 2023, 6:26 PM

#

worldly briar Can sb pls help me with Linear Transformation?

JustAsk

worldly briar May 16, 2023, 6:29 PM

#

I'm not getting forward with this questions:

tardy epoch May 16, 2023, 6:31 PM

#

there are two questions

#

where first do you get stuck

worldly briar May 16, 2023, 6:32 PM

#

with the first one

tardy epoch May 16, 2023, 6:32 PM

#

do you know the definition of linear operator

worldly briar May 16, 2023, 6:33 PM

#

It is a mapping between vector spaces that respects the operations of vector addition and scalar multiplication, right?

tardy epoch May 16, 2023, 6:35 PM

#

yes

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equations are more useful though

#

a "vector" in this case is an n-by-n matrix

#

and scalar is just a real number

worldly briar May 16, 2023, 6:38 PM

#

ahh ok thank you, but how can we prove that?

#

we have to show that it is additivit and homogeneity, right?

tardy epoch May 16, 2023, 6:46 PM

#

tardy epoch equations are more useful though

.

#

just plug general "vectors" into them and see the definition is satisfied

worldly briar May 16, 2023, 6:50 PM

#

i'm sorry i don't know what you mean😅

obtuse pebbleBOT May 16, 2023, 7:05 PM

#

@worldly briar Has your question been resolved?

timid silo May 16, 2023, 7:32 PM

#

Its ok youll get there!

obtuse pebbleBOT May 16, 2023, 7:42 PM

#

@worldly briar Has your question been resolved?

stoic harbor May 16, 2023, 7:49 PM

#

what is -1-8 and how do I solve it

obtuse pebbleBOT May 16, 2023, 8:51 PM

#

@worldly briar Has your question been resolved?

tardy epoch May 16, 2023, 8:55 PM

#

worldly briar i'm sorry i don't know what you mean😅

write down the equations for a linear operator that must be satisfied

obtuse pebbleBOT May 16, 2023, 9:51 PM

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desert hull May 16, 2023, 9:56 PM

#

can someone explain to me how this was calculated i dont get it

obtuse pebbleBOT May 16, 2023, 9:56 PM

#

desert hull can someone explain to me how this was calculated i dont get it

pastel sphinx May 16, 2023, 9:59 PM

#

could you give the question for some context?

desert hull May 16, 2023, 10:01 PM

#

pastel sphinx could you give the question for some context?

ye its just that i dont how they calculated 0.35Ao mg/day, i do understand the steps to get there

pastel sphinx May 16, 2023, 10:01 PM

#

they differenciated A

#

to get A derivative

#

have you done calculus before?

obtuse pebbleBOT May 16, 2023, 10:16 PM

#

@desert hull Has your question been resolved?

desert hull May 16, 2023, 10:23 PM

#

pastel sphinx they differenciated A

no i understand that

pastel sphinx May 16, 2023, 10:23 PM

#

what did you not understand

#

once they got the derivate

desert hull May 16, 2023, 10:23 PM

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im talkin bout da calculations here

pastel sphinx May 16, 2023, 10:23 PM

#

they just dropped in the value of t

desert hull May 16, 2023, 10:24 PM

#

like when i calculate it at this step i dont get the same answer

pastel sphinx May 16, 2023, 10:24 PM

#

well A0 is a constant right

desert hull May 16, 2023, 10:24 PM

#

ye

pastel sphinx May 16, 2023, 10:25 PM

#

if there are still further discrepancies i would say either the Markscheme is wrong or there is some physics behind this that i dont know

desert hull May 16, 2023, 10:25 PM

#

nvm i get it

#

i read the 1/20 as 1/25

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thats why

pastel sphinx May 16, 2023, 10:25 PM

#

what is the A0 constant

pastel sphinx May 16, 2023, 10:25 PM

#

desert hull i read the 1/20 as 1/25

oh

desert hull May 16, 2023, 10:25 PM

#

it made me get the wrong answer

#

aight

#

.close

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rustic violet May 16, 2023, 10:37 PM

#

3x + x + 5y - y = , needs to be simplifyed where possible

obtuse pebbleBOT May 16, 2023, 10:37 PM

#

rustic violet 3x + x + 5y - y = , needs to be simplifyed where possible

pastel sphinx May 16, 2023, 10:51 PM

#

ok so whats your current approach

#

what have you tried so far

obtuse pebbleBOT May 16, 2023, 10:56 PM

#

@rustic violet Has your question been resolved?

rustic violet May 16, 2023, 10:58 PM

#

not anything yet ;-;

#

just looked at it blankley

#

would you put it into brackets?

tardy epoch May 16, 2023, 11:04 PM

#

rustic violet would you put it into brackets?

group the variables together using distributive property

#

$ab + ac = a(b+c)$

warm shaleBOT May 16, 2023, 11:04 PM

#

riemann

rustic violet May 16, 2023, 11:06 PM

#

ive got as my answer = (3x + x) + (5y + y)

#

= 4x + 6y

tardy epoch May 16, 2023, 11:07 PM

#

rustic violet ive got as my answer = (3x + x) + (5y + y)

yes

rustic violet May 16, 2023, 11:07 PM

#

is that the right way to approach it?

tardy epoch May 16, 2023, 11:08 PM

#

yes

#

ah wait

tardy epoch May 16, 2023, 11:08 PM

#

rustic violet 3x + x + 5y - y = , needs to be simplifyed where possible

you have -y here

tardy epoch May 16, 2023, 11:08 PM

#

rustic violet ive got as my answer = (3x + x) + (5y + y)

but +y here

#

which is it

rustic violet May 16, 2023, 11:17 PM

#

the minus y is in the original question

#

but when symplified made it into a plus

tardy epoch May 16, 2023, 11:19 PM

#

rustic violet but when symplified made it into a plus

that's not how simplifying works

tardy epoch May 16, 2023, 11:19 PM

#

warm shale **riemann**

c can be negative here

#

according to you, 5y - y if y =3 would become 5(3) - (3) becomes 5(3) + 3 = 18

#

but 5(3) - (3) is 12

rustic violet May 16, 2023, 11:23 PM

#

(3x + x ) + (5y-y) = 4x + 4y?

obtuse pebbleBOT May 16, 2023, 11:53 PM

#

@rustic violet Has your question been resolved?

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dim copper May 17, 2023, 12:17 AM

#

obtuse pebbleBOT May 17, 2023, 12:17 AM

#

dim copper

dim copper May 17, 2023, 12:19 AM

#

.close

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dusk ruin May 17, 2023, 12:19 AM

#

you got your answer?

dim copper May 17, 2023, 12:20 AM

#

uhm, I just figured I would read the chapter a bit more :p

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dusk pawn May 17, 2023, 12:37 AM

#

If I have a random variable with uniform distribution: X~U[0,1]. What is the pdf of Y~U[0,X]

obtuse pebbleBOT May 17, 2023, 12:37 AM

#

dusk pawn If I have a random variable with uniform distribution: X~U[0,1]. What is the pdf...

#

@dusk pawn Has your question been resolved?

obtuse pebbleBOT May 17, 2023, 1:22 AM

#

@dusk pawn Has your question been resolved?

dusk pawn May 17, 2023, 1:23 AM

#

<@&286206848099549185>

obtuse pebbleBOT May 17, 2023, 2:23 AM

#

@dusk pawn Has your question been resolved?

timid silo May 17, 2023, 4:00 AM

#

rustic violet (3x + x ) + (5y-y) = 4x + 4y?

how old r u

rustic violet May 17, 2023, 4:01 AM

#

timid silo how old r u

um

#

younh

timid silo May 17, 2023, 4:01 AM

#

15?

#

16?

#

17?

#

18?

#

19?

timid silo May 17, 2023, 4:01 AM

#

rustic violet um

?

rustic violet May 17, 2023, 4:01 AM

#

16

timid silo May 17, 2023, 4:01 AM

#

'

rustic violet May 17, 2023, 4:01 AM

#

whys that

timid silo May 17, 2023, 4:01 AM

#

your doing that question at 16?

rustic violet May 17, 2023, 4:02 AM

#

yea is that good or bad

gilded needle May 17, 2023, 4:02 AM

#

in case you guys didn't notice, this channel belongs to someone else now

#

you're creating a lot of spam

rustic violet May 17, 2023, 4:02 AM

#

sorry

rustic violet May 17, 2023, 4:04 AM

#

timid silo your doing that question at 16?

?

timid silo May 17, 2023, 4:04 AM

#

err

#

im just surprise since in my country we learn this when we r around 12-13

rustic violet May 17, 2023, 4:05 AM

#

oh right

#

im not great accademicly anyways

dusk pawn May 17, 2023, 4:24 AM

#

Get out of my channel

dusk pawn May 17, 2023, 4:25 AM

#

dusk pawn If I have a random variable with uniform distribution: X~U[0,1]. What is the pdf...

The important question is still unanswered

obtuse pebbleBOT May 17, 2023, 6:25 AM

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@dusk pawn Has your question been resolved?

obtuse pebbleBOT May 17, 2023, 8:25 AM

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whole halo May 17, 2023, 9:01 AM

#

Hi I need help with this question, I dont really know how to approach it

obtuse pebbleBOT May 17, 2023, 9:01 AM

#

whole halo Hi I need help with this question, I dont really know how to approach it

whole halo May 17, 2023, 9:13 AM

#

<@&286206848099549185>

#

.close

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junior nymph May 17, 2023, 9:43 AM

#

Can someone please explain how to calculate the change of basis matrix if you are given two basis? I will send the question now

obtuse pebbleBOT May 17, 2023, 9:43 AM

#

junior nymph Can someone please explain how to calculate the change of basis matrix if you ar...

junior nymph May 17, 2023, 9:43 AM

#

Basis 1

#

Basis 2

gleaming ridge May 17, 2023, 9:46 AM

#

junior nymph Can someone please explain how to calculate the change of basis matrix if you ar...

You want to go from which basis to which? 1 -> 2 or 2 -> 1

junior nymph May 17, 2023, 9:47 AM

#

2->1

gleaming ridge May 17, 2023, 9:48 AM

#

Then write the basis 2 in terms of basis 1

junior nymph May 17, 2023, 9:49 AM

#

How would I do that? I also have calculated a coordinate vector with respect to basis 1

gleaming ridge May 17, 2023, 9:51 AM

#

Take the first element call is c1 (from basis B`) and then write c1 as summation of elements of basis B

junior nymph May 17, 2023, 9:51 AM

#

Okay let me try

#

Awesome! I got it! Would this still work other way around as well?

gleaming ridge May 17, 2023, 9:58 AM

#

Yep

#

As long as they're a basis it would work

junior nymph May 17, 2023, 10:02 AM

#

#

How would you calculate this?

obtuse pebbleBOT May 17, 2023, 10:18 AM

#

@junior nymph Has your question been resolved?

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sharp sail May 17, 2023, 11:21 AM

#

can anyone help with this question?

obtuse pebbleBOT May 17, 2023, 11:21 AM

#

sharp sail can anyone help with this question?

sharp sail May 17, 2023, 11:21 AM

#

I’ve basically tried finding two equations for vector ON, by using two unknowns

#

.close

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weak yew May 17, 2023, 11:32 AM

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obtuse pebbleBOT May 17, 2023, 11:32 AM

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weak yew

weak yew May 17, 2023, 11:32 AM

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how do i find angle bop

obtuse pebbleBOT May 17, 2023, 11:47 AM

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@weak yew Has your question been resolved?

obtuse pebbleBOT May 17, 2023, 12:19 PM

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@weak yew Has your question been resolved?

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dawn sphinx May 17, 2023, 1:09 PM

#

obtuse pebbleBOT May 17, 2023, 1:09 PM

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dawn sphinx

dawn sphinx May 17, 2023, 1:09 PM

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Can somebody help

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I’m stuck

obtuse pebbleBOT May 17, 2023, 1:24 PM

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@dawn sphinx Has your question been resolved?

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timid silo May 17, 2023, 1:46 PM

#

Im doing differential calculus with product rule im just struggling with the algebra

obtuse pebbleBOT May 17, 2023, 1:46 PM

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timid silo Im doing differential calculus with product rule im just struggling with the alg...

supple quest May 17, 2023, 1:46 PM

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timid silo Im doing differential calculus with product rule im just struggling with the alg...

What seems to be the problem?

timid silo May 17, 2023, 1:47 PM

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Im not sure where to go from here the fraction is messing me up

supple quest May 17, 2023, 1:47 PM

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I see

timid silo May 17, 2023, 1:48 PM

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sorry for not being specific its kinda the whole thing thats a bit confusing

supple quest May 17, 2023, 1:48 PM

#

$x \frac{1}{2 \sqrt{x}}=\frac{\sqrt{x}}{2}$

warm shaleBOT May 17, 2023, 1:49 PM

#

SirLance013

timid silo May 17, 2023, 1:49 PM

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whats with the x at the start?

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i dont have that

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ohh

supple quest May 17, 2023, 1:49 PM

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Im talking about one term

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in the numerator

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so numerator becomes $\frac{\sqrt{x}}{2}+1$

warm shaleBOT May 17, 2023, 1:50 PM

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SirLance013

timid silo May 17, 2023, 1:50 PM

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ahh ok ima go ahead and attempt the question now so do i have to close the channel or should i wait until i finished the question?

supple quest May 17, 2023, 1:51 PM

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If you're clear about da question you can close it.

timid silo May 17, 2023, 1:52 PM

#

#

would this then be right?

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oh sorry its flipped

twin sapphire May 17, 2023, 1:53 PM

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,rccw

warm shaleBOT May 17, 2023, 1:53 PM

#

timid silo May 17, 2023, 1:53 PM

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would that be right so far?

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<@&286206848099549185>

grave trout May 17, 2023, 2:05 PM

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maybe

timid silo May 17, 2023, 2:07 PM

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im going to try the question again thanks for the help

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.close

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bold siren May 17, 2023, 2:11 PM

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basic math question

obtuse pebbleBOT May 17, 2023, 2:11 PM

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bold siren basic math question

bold siren May 17, 2023, 2:12 PM

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im doing revision on differeantiation

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and i encountered

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is the 2 part of the function and what happens to it when i differentiate it

fervent nexus May 17, 2023, 2:23 PM

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Chain rule

obtuse pebbleBOT May 17, 2023, 2:28 PM

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@bold siren Has your question been resolved?

bold siren May 17, 2023, 2:28 PM

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fervent nexus Chain rule

yes i know its chain rule my question is the 2 part of the function of seperat from it

fluid snow May 17, 2023, 2:57 PM

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bold siren is the 2 part of the function and what happens to it when i differentiate it

The 2 is a constant factor

bold siren May 17, 2023, 2:58 PM

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so if you were to differentiate it

fluid snow May 17, 2023, 2:58 PM

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[\frac{d}{dx}\Bigl[k \cdot f(x)\Bigr] = k \frac{d}{dx} \Bigl[f(x)\Bigr]]

bold siren May 17, 2023, 2:58 PM

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2cos(x^3)*(3x^2)

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?

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so what im reading here

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k just dosnt really matter when differentiating

fluid snow May 17, 2023, 2:59 PM

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bold siren May 17, 2023, 2:59 PM

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bold siren 2cos(x^3)*(3x^2)

and thus is correct

fluid snow May 17, 2023, 3:00 PM

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Yes, you can simplify it though

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It's just cos(x^3) * 6x^2

bold siren May 17, 2023, 3:01 PM

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wouldnt the (x^3) become (2x^3?)

fluid snow May 17, 2023, 3:02 PM

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bold siren wouldnt the (x^3) become (2x^3?)

No

bold siren May 17, 2023, 3:02 PM

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lol

fluid snow May 17, 2023, 3:02 PM

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bold siren wouldnt the (x^3) become (2x^3?)

(x^3)' = 3x^2

bold siren May 17, 2023, 3:03 PM

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hang on what

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wait

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yea

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you leave (x) that is attached to its function alone

fluid snow May 17, 2023, 3:06 PM

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bold siren so if you were to differentiate it

Also note that if the derivative of the function after the constant factor was a sum of multiple terms, you would have to multiply each of them by 2.

bold siren May 17, 2023, 3:06 PM

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sorry?

fluid snow May 17, 2023, 3:07 PM

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If we had $f(x) = 2(x^2 + x)$ for example, then [\frac{d}{dx}(2(x^2 + x)) = 2\frac{d}{dx}(x^2 + x) = 2(2x+ 1) = 4x + 2]

#

bold siren May 17, 2023, 3:08 PM

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AH

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ok that makes sense

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ty

#

.close

obtuse pebbleBOT May 17, 2023, 3:09 PM

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Channel closed

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stone stone May 17, 2023, 3:16 PM

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I have to convert this from polar-coordinate form to rectangular-coordinate but our notes didn’t cover anything like this so I’m not sure how to approach it

obtuse pebbleBOT May 17, 2023, 3:16 PM

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stone stone I have to convert this from polar-coordinate form to rectangular-coordinate but ...

stone stone May 17, 2023, 3:19 PM

#

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I’m stuck at this point but I’m not totally sure that my work is correct even here since ((1-y)/2)^2 gets kind of messy

thin pawn May 17, 2023, 3:21 PM

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I googled quickly and apparently you should use $x = r\cdot cos\theta$ and $y = r\cdot sin\theta$

warm shaleBOT May 17, 2023, 3:21 PM

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imTyp0

thin pawn May 17, 2023, 3:21 PM

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To build some kind of system of equation I believe

stone stone May 17, 2023, 3:22 PM

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Is there any way you could elaborate??

thin pawn May 17, 2023, 3:23 PM

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Thing is I haven‘t learned that yet. I know what polar and rectangular coprdinates are, i just don‘t know how to work with what you‘ve been given. I‘m trying to work it out at the same time as you :)

warm canopy May 17, 2023, 3:24 PM

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what you've done is fine, just keep going

cold rampart May 17, 2023, 3:25 PM

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stone stone Is there any way you could elaborate??

substitute what you have for r into the x = and y =

cold rampart May 17, 2023, 3:26 PM

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warm shale **imTyp0**

.

warm canopy May 17, 2023, 3:26 PM

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althought you have a typo, r^2 is x^2 + y^2

stone stone May 17, 2023, 3:26 PM

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Oh oops

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Okay, thank you guys!

#

.close

obtuse pebbleBOT May 17, 2023, 3:27 PM

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cold gulch May 17, 2023, 3:36 PM

#

A marathon swimmer starts at Island A, swims 9.2 km to Island B, then 8.6 km to Island C. The angle formed by a line from Island B to Island A and a line from Island C to Island A is 52°. How far does the swimmer have to swim to return directly to Island A?

obtuse pebbleBOT May 17, 2023, 3:36 PM

#

cold gulch A marathon swimmer starts at Island A, swims 9.2 km to Island B, then 8.6 km to ...

cold gulch May 17, 2023, 3:36 PM

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How do I solve

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Can u show me

#

??

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<@&286206848099549185>

#

.close

obtuse pebbleBOT May 17, 2023, 3:50 PM

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golden hamlet May 17, 2023, 3:55 PM

#

determine the number of zeros of the polynomial function.

f(x) = x^3 + 2x^2 + 1

obtuse pebbleBOT May 17, 2023, 3:55 PM

#

golden hamlet determine the number of zeros of the polynomial function. f(x) = x^3 + 2x^2 + 1

spice citrus May 17, 2023, 3:57 PM

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Try taking the derivative and looking at it's sign

golden hamlet May 17, 2023, 3:57 PM

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sorry, let me add smth more. i should solve this via Rational zero test, but at the moment i dont see a solution with it.

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it should be 1 or -1, but both doesn't fit

spice citrus May 17, 2023, 3:57 PM

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Does the question ask for the number of rational zeros?

golden hamlet May 17, 2023, 3:58 PM

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yes it does

spice citrus May 17, 2023, 3:58 PM

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golden hamlet it should be 1 or -1, but both doesn't fit

Well, then there are none

trim portal May 17, 2023, 3:58 PM

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it has just one real, irrational root

golden hamlet May 17, 2023, 3:58 PM

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ow.

dark stirrup May 17, 2023, 3:59 PM

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Ow indeed

trim portal May 17, 2023, 3:59 PM

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golden hamlet it should be 1 or -1, but both doesn't fit

If both dont fit, you can conclude that it has no rational zeros

golden hamlet May 17, 2023, 3:59 PM

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Ok, Thanks! atm i only learnt Rational zero test so got confused.

#

.close

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hearty pendant May 17, 2023, 4:11 PM

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imean are these values hand calculated by some formula cuz i havnt started inverse yet?

obtuse pebbleBOT May 17, 2023, 4:11 PM

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hearty pendant imean are these values hand calculated by some formula cuz i havnt started inver...

trim portal May 17, 2023, 4:12 PM

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usually inverse cos and sin are calculated using calculators

hearty pendant May 17, 2023, 4:12 PM

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ohh ohk

grim mortar May 17, 2023, 4:12 PM

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doritos

hearty pendant May 17, 2023, 4:12 PM

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ty thats all

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.close

obtuse pebbleBOT May 17, 2023, 4:13 PM

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elfin blaze May 17, 2023, 4:30 PM

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anyone need math help? i help class 8,9,10 students

obtuse pebbleBOT May 17, 2023, 4:30 PM

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elfin blaze anyone need math help? i help class 8,9,10 students

dapper thicket May 17, 2023, 4:31 PM

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<@&268886789983436800>

ruby path May 17, 2023, 4:32 PM

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elfin blaze anyone need math help? i help class 8,9,10 students

These channels are opened when people request for help, not the other way round, you can look at the other channels and help with problems that you wish to

elfin blaze May 17, 2023, 4:32 PM

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ok ok

ruby path May 17, 2023, 4:32 PM

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.close

obtuse pebbleBOT May 17, 2023, 4:32 PM

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Channel closed

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ruby path May 17, 2023, 4:33 PM

#

dapper thicket <@&268886789983436800>

Pretty sure that was the wrong ping btw

obtuse musk May 17, 2023, 4:39 PM

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ruby path These channels are opened when people request for help, not the other way round,...

yeah, this is correct; also see #❓how-to-get-help for how this server works if you want to help others @elfin blaze

obtuse pebbleBOT May 17, 2023, 4:40 PM

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subtle whale May 17, 2023, 4:47 PM

#

Can someone show me how to find the uncertainty on B using partial derivatives?

obtuse pebbleBOT May 17, 2023, 4:47 PM

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subtle whale Can someone show me how to find the uncertainty on B using partial derivatives?

subtle whale May 17, 2023, 4:49 PM

#

You can assume random values like

u0 = constant = 4.0 * PI * 10^-7
2PI = constant

B = 5.0, error 0.001
I = 10.0 error 0.002
R = 15.0 error 0.003

autumn adder May 17, 2023, 4:49 PM

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Oh man what did you say mu_0 was

subtle whale May 17, 2023, 4:50 PM

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Real value is 4PI*10-7 but I just pick random values for the sake of simplicity

subtle whale May 17, 2023, 4:51 PM

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subtle whale Can someone show me how to find the uncertainty on B using partial derivatives?

Using this method

obtuse pebbleBOT May 17, 2023, 5:06 PM

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@subtle whale Has your question been resolved?

fading quest May 17, 2023, 5:24 PM

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subtle whale Using this method

You are finding $\sigma_B$. $I$ and $R$ are the variables containing uncertainty hence you replace $\pdv{V}{d}$ and $\pdv{V}{t}$ with $\pdv{B}{I}$ and $\pdv{B}{R}$ respectively. Analogous for $\sigma_d$ and $\sigma_t$

warm shaleBOT May 17, 2023, 5:25 PM

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Duh Hello

obtuse pebbleBOT May 17, 2023, 5:41 PM

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@subtle whale Has your question been resolved?

obtuse pebbleBOT May 17, 2023, 6:11 PM

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clever plaza May 17, 2023, 6:20 PM

#

Just started as an undergraduate and haven't studied math in a very long time - I understand how to evaluate the other f(x) problems but I am having an issue understanding how to input f(x+1)=6x-4

obtuse pebbleBOT May 17, 2023, 6:20 PM

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clever plaza Just started as an undergraduate and haven't studied math in a very long time - ...

fierce vale May 17, 2023, 6:21 PM

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clever plaza Just started as an undergraduate and haven't studied math in a very long time - ...

just replace x with x+1

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then simplify

warm shaleBOT May 17, 2023, 6:22 PM

#

adamchebil33

clever plaza May 17, 2023, 6:26 PM

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That's where I am getting stuck sorry - where would I start the simplification?

tardy epoch May 17, 2023, 6:27 PM

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clever plaza That's where I am getting stuck sorry - where would I start the simplification?

use distributive property

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a(b+c) = ab + bc

clever plaza May 17, 2023, 6:27 PM

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so 6(x+1) = 6(1x)?

warm shaleBOT May 17, 2023, 6:32 PM

#

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

clever plaza May 17, 2023, 6:35 PM

#

.close

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haughty scroll May 17, 2023, 6:48 PM

#

obtuse pebbleBOT May 17, 2023, 6:48 PM

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haughty scroll

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@haughty scroll Has your question been resolved?

obtuse pebbleBOT May 17, 2023, 7:35 PM

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@haughty scroll Has your question been resolved?

haughty scroll May 17, 2023, 7:50 PM

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haughty scroll May 17, 2023, 8:17 PM

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.close

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obtuse pebbleBOT May 17, 2023, 9:13 PM

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spark shore May 17, 2023, 9:15 PM

#

obtuse pebbleBOT May 17, 2023, 9:15 PM

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spark shore

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Please don't occupy multiple help channels.

spark shore May 17, 2023, 9:15 PM

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Can somebody please shed some light on how we went from the first line to the second?

tardy epoch May 17, 2023, 9:19 PM

#

.close

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obtuse pebbleBOT May 17, 2023, 10:28 PM

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sage dagger May 17, 2023, 10:37 PM

#

Is there some sort of property I should start with

obtuse pebbleBOT May 17, 2023, 10:37 PM

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sage dagger Is there some sort of property I should start with

sage dagger May 17, 2023, 10:37 PM

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I mean identity

nocturne minnow May 17, 2023, 10:38 PM

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Probably a pythagorean related one

sage dagger May 17, 2023, 10:39 PM

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tan^2(x)+1=sec^2(x)

clear condor May 17, 2023, 10:41 PM

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ok

static beacon May 17, 2023, 10:42 PM

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you could prove both left and right is 1?

thin pawn May 17, 2023, 10:42 PM

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Usually you don‘t touch RHS

sage dagger May 17, 2023, 10:43 PM

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Hm

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What can I do to the lhs

nocturne minnow May 17, 2023, 10:43 PM

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Turn those into terms of sin and cos

sage dagger May 17, 2023, 10:44 PM

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sec^2(x) is just 1/cos^2(x) right

lean dew May 17, 2023, 10:46 PM

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Ye

sage dagger May 17, 2023, 10:46 PM

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I have (1-sin^2(x))/cos^2(x) now

sage dagger May 17, 2023, 10:46 PM

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sage dagger I have (1-sin^2(x))/cos^2(x) now

I don’t know if that’s right

lean dew May 17, 2023, 10:46 PM

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Correct

sage dagger May 17, 2023, 10:47 PM

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Ah okay

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I’m not sure what to do now, change the numerator?

lean dew May 17, 2023, 10:47 PM

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Haha uhh give me a sec i dont have access to paper at the moment

sage dagger May 17, 2023, 10:47 PM

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Sure

clear condor May 17, 2023, 10:48 PM

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i mean idk just a thing i found

sage dagger May 17, 2023, 10:48 PM

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Huh

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Did I do something wrong

lean dew May 17, 2023, 10:50 PM

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What can you turn 1-sin^2(x) into?

sage dagger May 17, 2023, 10:51 PM

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cos^2(x)

lean dew May 17, 2023, 10:51 PM

#

mhmm

sage dagger May 17, 2023, 10:51 PM

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So that just makes the fraction 1 but

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That doesn’t get me anywhere

lean dew May 17, 2023, 10:52 PM

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Well I'm not sure if there's a simpler way

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there probably is

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but try doing the RHS

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and get them equal and then you can like

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go backwards

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im currently trying to find another way but know you're heading in the right direction

sage dagger May 17, 2023, 10:53 PM

#

Ah okay

#

Yeah I’m not too sure

lean dew May 17, 2023, 10:53 PM

#

oh shit theres an easy way

#

LMFAO

#

do you have this sheet?

#

well now u do

#

what can you write sec^2(x) as?

sage dagger May 17, 2023, 10:55 PM

#

1+tan^2(x)

lean dew May 17, 2023, 10:55 PM

#

mhm

#

lhs becomesss

sage dagger May 17, 2023, 10:56 PM

#

1+tan^2(x) - sin^2(x)/cos^2(x)

sage dagger May 17, 2023, 10:56 PM

#

lean dew do you have this sheet?

Well this helps a lot

lean dew May 17, 2023, 10:56 PM

#

and what is sin^2(x)/cos^2(x)

lean dew May 17, 2023, 10:56 PM

#

sage dagger Well this helps a lot

right

sage dagger May 17, 2023, 10:57 PM

#

lean dew and what is sin^2(x)/cos^2(x)

Well it’s tan^2(x) but I thought I should write in terms of cos and sine

lean dew May 17, 2023, 10:57 PM

#

right right but now lhs just becomes 1 again

sage dagger May 17, 2023, 10:57 PM

#

Oh yeah

lean dew May 17, 2023, 10:57 PM

#

i just wanted to lyk theres another way cuz i didnt realize lol

#

well if u look at the sheet again

#

what is 1 equal to

#

hint hint

sage dagger May 17, 2023, 10:58 PM

#

sec^2(x)-tan^2(x)

#

Equals to 1

lean dew May 17, 2023, 10:59 PM

#

hint hint

#

do u notice something

#

lmao its right there

#

altho im not sure

sage dagger May 17, 2023, 10:59 PM

#

what that

lean dew May 17, 2023, 10:59 PM

#

would your teacher take that as an answer?

#

just directly converting it to 1

#

considering u aint never seen this sheet before

#

if so u might have to do some more steps

sage dagger May 17, 2023, 11:00 PM

#

Wait

lean dew May 17, 2023, 11:00 PM

#

hm

sage dagger May 17, 2023, 11:01 PM

#

So from this

#

1+tan^2(x) - sin^2(x)/cos^2(x)

#

What am I supposed to concert

#

Convert

lean dew May 17, 2023, 11:01 PM

#

remember sin^2(x)/cos^2(x) is tan^2(x)

#

so tan^2(x) - tan^2(x) is 0

#

you are left with 1

#

then you have to prove 1 = RHS

#

so you convert 1 to something that is equal to RHS

sage dagger May 17, 2023, 11:02 PM

#

Ah alright

#

I gotta head to class rn

#

I’ll read everything later

#

Ty for the help

lean dew May 17, 2023, 11:03 PM

#

take this too

#

this was the other way you were doing

lean dew May 17, 2023, 11:03 PM

#

sage dagger Ty for the help

np

obtuse pebbleBOT May 17, 2023, 11:17 PM

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civic magnet May 17, 2023, 11:37 PM

#

Are there any cheat sheets or tips to determine what test I should use on a series quickly? Like -1^n means i should use alternating series test, or a sin/cos in a series means to use the comparison test?

obtuse pebbleBOT May 17, 2023, 11:37 PM

#

civic magnet Are there any cheat sheets or tips to determine what test I should use on a seri...

civic magnet May 17, 2023, 11:37 PM

#

also how would I determine if 1/n diverges or conditionally converges?

lean dew May 17, 2023, 11:39 PM

#

Courtesy of my math teacher

lean dew May 17, 2023, 11:40 PM

#

civic magnet also how would I determine if 1/n diverges or conditionally converges?

That series is called the harmonic series

#

You can google proofs that it diverges

civic magnet May 17, 2023, 11:46 PM

#

lean dew Courtesy of my math teacher

thanks for the chart, didn't have that one yet!

lean dew May 17, 2023, 11:49 PM

#

my teacher also uses the acronym "NO PARKING" which stands for nth term, o, p series, arithmetic/alternating, ratio, komparison, integral, nth term (again i think?), geometric

#

if thats what u were looking for

civic magnet May 17, 2023, 11:51 PM

#

looking up harmonic rn, but can you explain rq why -1^(n+1) just turns into 1? I get the - sign but why the n+1?

civic magnet May 17, 2023, 11:51 PM

#

lean dew my teacher also uses the acronym "NO PARKING" which stands for nth term, o, p se...

would that be what tests to try out first?

lean dew May 17, 2023, 11:52 PM

#

civic magnet looking up harmonic rn, but can you explain rq why -1^(n+1) just turns into 1? I...

forgive me, ive never actually looked at the proofs myself and my brain is too fried rn to look at that 😅 i just know that it diverges

lean dew May 17, 2023, 11:53 PM

#

civic magnet would that be what tests to try out first?

not really, except that she REALLY emphasizes using nth term test first, hence the "NO"

#

since it's the only test for divergence

civic magnet May 17, 2023, 11:53 PM

#

lean dew forgive me, ive never actually looked at the proofs myself and my brain is too f...

all good haha, I haven't taken a math class in a couple years, then found out I needed the next one of calc all of a sudden

#

been struggling to remember

#

if you had any tips regarding what to review

lean dew May 17, 2023, 11:54 PM

#

like

civic magnet May 17, 2023, 11:54 PM

#

lean dew not really, except that she REALLY emphasizes using nth term test first, hence t...

makes sense, Ill keep that in mind ty!

lean dew May 17, 2023, 11:54 PM

#

practice wksheets or?

civic magnet May 17, 2023, 11:54 PM

#

well notes or something to keep a look at for the most part

lean dew May 17, 2023, 11:55 PM

#

hm

#

i can look thru my folder

civic magnet May 17, 2023, 11:55 PM

#

thank you!

obtuse pebbleBOT May 18, 2023, 12:10 AM

#

@civic magnet Has your question been resolved?

civic magnet May 18, 2023, 12:39 AM

#

.close

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glossy grove May 18, 2023, 12:44 AM

#

(a) f(x) = 2x^3 + 3x^2 + 2x + 8
= (x+2)(2x^2 -x + 4)
From this, one real solution is x = -2
(b) Using answer to part (a) ,hence solve x^3 + 3x^2 +4x + 32 = 0

obtuse pebbleBOT May 18, 2023, 12:44 AM

#

glossy grove (a) f(x) = 2x^3 + 3x^2 + 2x + 8 = (x+2)(2x^2 -x + 4) From this, one real...

real hound May 18, 2023, 12:45 AM

#

glossy grove (a) f(x) = 2x^3 + 3x^2 + 2x + 8 = (x+2)(2x^2 -x + 4) From this, one real...

Remainder Theorem

#

or like

#

Notice that the part after (x+2) is "quadratic form"?

obtuse pebbleBOT May 18, 2023, 12:59 AM

#

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inner stratus May 18, 2023, 1:17 AM

#

I'm confused as to if my solution to this problem is correct.
So, in this problem, would the A vector be 18cos(42) i + 18sin(42) j and B vector be 10cos(180+31) i + 10sin(180+31) j?
https://cdn.discordapp.com/attachments/1108563563720753152/1108563563867537458/image.png

obtuse pebbleBOT May 18, 2023, 1:17 AM

#

inner stratus I'm confused as to if my solution to this problem is correct. So, in this proble...

inner stratus May 18, 2023, 1:17 AM

#

Is my reasoning correct?

obtuse pebbleBOT May 18, 2023, 1:32 AM

#

@inner stratus Has your question been resolved?

inner stratus May 18, 2023, 1:47 AM

#

.close

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rich silo May 18, 2023, 1:48 AM

#

lol, the moment I took a look, you closed it xD

obtuse pebbleBOT May 18, 2023, 2:26 AM

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grand schooner May 18, 2023, 2:31 AM

#

obtuse pebbleBOT May 18, 2023, 2:31 AM

#

grand schooner

grand schooner May 18, 2023, 2:32 AM

#

Hi I need the intersection of C

#

But i dont have much info

opaque lily May 18, 2023, 2:39 AM

#

im pretty sure it is impossible to find C without knowing B

grand schooner May 18, 2023, 2:39 AM

#

F

#

thanks anyways

rich silo May 18, 2023, 2:39 AM

#

B is 2A

opaque lily May 18, 2023, 2:39 AM

#

ohhh

#

it is possible in that case

rich silo May 18, 2023, 2:39 AM

#

Yes

grand schooner May 18, 2023, 2:40 AM

#

you take like cos

opaque lily May 18, 2023, 2:41 AM

#

there might be some way of using cos, but you could also find the equation for both lines then find their point of intersection with y1 = y2

jolly ginkgo May 18, 2023, 2:41 AM

#

rich silo B is 2A

how come?

#

doesn't A look bigger than B?

rich silo May 18, 2023, 2:43 AM

#

Well, without knowing B, it is impossible to find the intersection and thus solve the problem

#

They must have forgotten to put it

jolly ginkgo May 18, 2023, 2:43 AM

#

grand schooner But i dont have much info

what about slopes

rich silo May 18, 2023, 2:43 AM

#

But, the drawing looks accurate, not roughly

#

We can say B=2A

jolly ginkgo May 18, 2023, 2:43 AM

#

rich silo We can say B=2A

but but

rich silo May 18, 2023, 2:44 AM

#

whaaaat 😛

jolly ginkgo May 18, 2023, 2:44 AM

#

A looks greater than B

#

maybe it is A=2B

rich silo May 18, 2023, 2:44 AM

#

Are you kidding me?

#

B is after A

grand schooner May 18, 2023, 2:44 AM

#

distance calculo works?

rich silo May 18, 2023, 2:45 AM

#

B is after A, B is to the right of A

jolly ginkgo May 18, 2023, 2:45 AM

#

rich silo B is after A, B is to the right of A

yes

rich silo May 18, 2023, 2:45 AM

#

of course its x-coordinate is greater than A's

jolly ginkgo May 18, 2023, 2:45 AM

#

oh you mean angle with X axis?

rich silo May 18, 2023, 2:45 AM

#

B's x-coordinate is twice A's x-coordinate

jolly ginkgo May 18, 2023, 2:45 AM

#

rich silo B's x-coordinate is twice A's x-coordinate

ah I thought you were talking about angles

rich silo May 18, 2023, 2:46 AM

#

Ohhhh, there was a misunderstanding then!

jolly ginkgo May 18, 2023, 2:46 AM

#

grand schooner distance calculo works?

show the whole question?

#

a proper photo

jolly ginkgo May 18, 2023, 2:46 AM

#

rich silo Ohhhh, there was a misunderstanding then!

yes mb

rich silo May 18, 2023, 2:46 AM

#

I meant since they most likely forgot to put the x-coordinate of B

#

And the drawing is accurate

grand schooner May 18, 2023, 2:47 AM

#

it's in spanish

#

#

I'll translate for you

elfin burrow May 18, 2023, 2:47 AM

#

oh they are perpendicular

nocturne minnow May 18, 2023, 2:47 AM

#

grand schooner

This would have been helpful because L1 is perpedicular to L2

#

That's useful info

jolly ginkgo May 18, 2023, 2:48 AM

#

elfin burrow oh they are perpendicular

as i expected

nocturne minnow May 18, 2023, 2:49 AM

#

rich silo B's x-coordinate is twice A's x-coordinate

Just looks like this was a coincidence because the lines were perpendicular

grand schooner May 18, 2023, 2:50 AM

#

a) find the coordinates of point C, knowing that L1 is perpendicular to L2
c) calculate de area of the triangule rectangule ABC

nocturne minnow May 18, 2023, 2:50 AM

#

Find the equation of L1

#

Use that to find the equation of L2 because you know L1 and L2 are perpendicular

jolly ginkgo May 18, 2023, 2:50 AM

#

nocturne minnow Just looks like this was a coincidence because the lines were perpendicular

there are no coincidence

grand schooner May 18, 2023, 2:52 AM

#

nocturne minnow Find the equation of L1

sorry to ask, but how would you do it?

nocturne minnow May 18, 2023, 2:52 AM

#

You have two points

#

You should know how to find the equation of a line given two points

grand schooner May 18, 2023, 2:53 AM

#

oh...

#

thanks

obtuse pebbleBOT May 18, 2023, 3:08 AM

#

@grand schooner Has your question been resolved?

obtuse pebbleBOT May 18, 2023, 3:23 AM

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shut field May 18, 2023, 5:40 AM

#

hi for this parametric equation i get x = 1-3k and 3+2k but the solution says this

obtuse pebbleBOT May 18, 2023, 5:40 AM

#

shut field hi for this parametric equation i get x = 1-3k and 3+2k but the solution says t...

shut field May 18, 2023, 5:41 AM

#

it goes through the points (1,3) and (-2,5)

obtuse pebbleBOT May 18, 2023, 5:56 AM

#

@shut field Has your question been resolved?

knotty gulch May 18, 2023, 5:56 AM

#

does ur solution work

shut field May 18, 2023, 5:59 AM

#

knotty gulch does ur solution work

wdym?

wispy wadi May 18, 2023, 6:00 AM

#

your solution works too anno, take -k instead of your k

#

you get the solution you took a screenshot of

shut field May 18, 2023, 6:04 AM

#

!close

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.close

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#

knotty gulch May 18, 2023, 6:12 AM

#

cos² theta - sin² theta = 1-2sin² theta

obtuse pebbleBOT May 18, 2023, 6:22 AM

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whole cipher May 18, 2023, 6:34 AM

#

obtuse pebbleBOT May 18, 2023, 6:34 AM

#

whole cipher

whole cipher May 18, 2023, 6:35 AM

#

I plug in the number in my calc but something is wrong 😭

#

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!close

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.close

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obtuse pebbleBOT May 18, 2023, 8:29 AM

#

ruby path May 18, 2023, 8:29 AM

#

When is tan x undefined

#

Yes

#

hmmCat

#

I think

#

You should stop thinking about trig in terms of triangles when you reach graphs

unique nebula May 18, 2023, 8:31 AM

#

Strictly speaking

#

The function is continuous

ruby path May 18, 2023, 8:31 AM

#

Do you understand the concept of radians?

ruby path May 18, 2023, 8:31 AM

#

unique nebula The function is continuous

There should be a hole at pi/2 and so on

#

,w plot y = tanx cosx

unique nebula May 18, 2023, 8:31 AM

#

ruby path There should be a hole at pi/2 and so on

Functions do not care where the are not defined

warm shaleBOT May 18, 2023, 8:31 AM

#

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unique nebula May 18, 2023, 8:31 AM

#

Don't plot it anywhere

ruby path May 18, 2023, 8:31 AM

#

Generally speaking you do not modify a function even if it can be simplified

unique nebula May 18, 2023, 8:31 AM

#

Functions ignore undefined parts

ruby path May 18, 2023, 8:32 AM

#

You get a hollow circle there

unique nebula May 18, 2023, 8:32 AM

#

The function tan(x) cos(x) has portions of the real line which are not in its domain at all

ruby path May 18, 2023, 8:32 AM

#

tanxcosx and sinx are not the same function

unique nebula May 18, 2023, 8:32 AM

#

Both tan(x)cos(x) and sin(x) are continuous functions

ruby path May 18, 2023, 8:34 AM

#

,w tanxcosx at x = pi/2

warm shaleBOT May 18, 2023, 8:34 AM

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ruby path May 18, 2023, 8:34 AM

#

pandaHmm

unique nebula May 18, 2023, 8:34 AM

#

@ruby path
The function tan(x) cos(x) has portions of the real line which are not in its domain at all

#

Not in its domain at all

#

Read carefully

#

Do not mislead

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obtuse pebbleBOT May 18, 2023, 9:01 AM

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@marsh lily Has your question been resolved?

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@marsh lily Has your question been resolved?

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@marsh lily Has your question been resolved?

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exotic creek May 18, 2023, 2:49 PM

#

obtuse pebbleBOT May 18, 2023, 2:49 PM

#

exotic creek

exotic creek May 18, 2023, 2:50 PM

#

#

what did i do wrong here?

#

this is the answer

#

obtuse pebbleBOT May 18, 2023, 3:06 PM

#

@exotic creek Has your question been resolved?

exotic creek May 18, 2023, 3:06 PM

#

<@&286206848099549185>

tame narwhal May 18, 2023, 3:07 PM

#

it shows you how to properly calculate the quartiles

#

so that 3/12 values are below Q1 and 3/12 are above Q3

#

same principle you used when calculating the median

#

so that 6/12 values are below and above the median

exotic creek May 18, 2023, 3:08 PM

#

shouldn't it be the same for n/4 and 3n/4 tho?

#

why doesn't it work?

tame narwhal May 18, 2023, 3:10 PM

#

because Q1 is the same as the median of the lower half

#

if you were given just the first 6 numbers, how would you get the median?

exotic creek May 18, 2023, 3:11 PM

#

(n+1)/2?

tame narwhal May 18, 2023, 3:11 PM

#

yes, which is exactly what was done in the solutions picture you show

exotic creek May 18, 2023, 3:12 PM

#

but ur finding the median of 6 numbers not including the other 6

#

so you're saying 3n/4 is wrong for finding the lower quartile of a set of numbers?

#

i should be using the median of half of the set of numbers?

#

isn't that the same as n/4?

tame narwhal May 18, 2023, 3:14 PM

#

it is not, you have the visualization of that in the answer

#

n/4 is the 3rd value, which is 172. but the median of the first 6 values is (172 + 175) / 2 = 173.5

exotic creek May 18, 2023, 3:15 PM

#

isn't n/4 is how you find the lower quartile?

tame narwhal May 18, 2023, 3:18 PM

#

no. according to wikipedia there is no universal agreement for selecting quartile values

#

but see Method 1, which is what your answer shows: https://en.wikipedia.org/wiki/Quartile#Method_1

Quartile

In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three main quartiles are as follows:

The first quartile (Q1) is defined as...

#

you have an even number of values, so you split the data into lower and upper halves. then the quartiles will be the medians of those halves

exotic creek May 18, 2023, 3:20 PM

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so n/4 is only for odd number of values?

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and 3n/4

tame narwhal May 18, 2023, 3:21 PM

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if n is odd then n/4 and 3n/4 will not be integers

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on the wikipedia page, there are 2 examples. you can see that the different methods for getting quartiles give different answers

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so you can ask your teacher if they have a preference

exotic creek May 18, 2023, 3:42 PM

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alr

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.close

obtuse pebbleBOT May 18, 2023, 3:42 PM

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Channel closed

Closed by @exotic creek

Use .reopen if this was a mistake.

obtuse pebbleBOT May 18, 2023, 4:14 PM

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dim nacelle May 18, 2023, 4:15 PM

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Stuck in this. I think I’m struggling with the distributive law and am confused how to get this down to Xsmall1 = Xsmall2

obtuse pebbleBOT May 18, 2023, 4:15 PM

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dim nacelle Stuck in this. I think I’m struggling with the distributive law and am confused ...