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wide oriole
wide oriole
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<@&286206848099549185>

obtuse pebbleBOT
#

@wide oriole Has your question been resolved?

warm canopy
#

You are not asking any questions

obtuse pebbleBOT
#
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obtuse pebbleBOT
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slender osprey
#

I need to find the distance between Q and P. Not sure how to find it with only one number.

nocturne sun
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I'm not sure about the proof, we aren't given that at school, but

$$\frac{OP}{ON} = \frac{OQ}{OM} = \frac{OP}{MN}$$

warm shaleBOT
nocturne sun
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assuming QP and MN are parallel

slender osprey
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And you did use the correct lettering? I just want to make sure since this is the first time I've seen this equation.

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@nocturne sun

nocturne sun
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I'm gonna check my book just to make sure

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can't find the page atm

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oh nvm found it

versed turret
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Notice they are similar triangles

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And the scale factor is 2

slender osprey
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I have done a small bit of scale factoring and I have absolutely no clue what im doing

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(ignore my unusual name. I'm pranking a friend)

slender osprey
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Please do ping me when you respond. Still doing work.

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if ABD is the triangle, wouldn't it be 180* or 360*? since they end up connecting on all sides. (D is 46 degrees while B is 38)

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@nocturne sun you still active?

versed turret
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So ON/OP = OM/OQ = MN/QP

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Notice that ON is twice the length of OP, so ON/OP = 2

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Thus, MN/QP = 2 ⟹ QP = MN/2 = 14.4/2 = 7.2

obtuse pebbleBOT
#

@slender osprey Has your question been resolved?

slender osprey
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ty for the original question answered.

slender osprey
#

.close

obtuse pebbleBOT
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obtuse pebbleBOT
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real pebble
#

Hey, im struggling with a part of a springs question that is linked to dynamics

real pebble
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this is the whole question shown

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i dont have a clue where to start

solar trellis
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But ignore the weight... they should have said that in the question

real pebble
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yeah, it isnt stated anywhere, just need to derive it all out

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the forces would be the F=ma and F=-kx correct?

real pebble
solar trellis
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a as in acceleration?

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Or in S(k,a)

real pebble
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yeah newtons second law

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so acceleration

solar trellis
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@real pebble

real pebble
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im not entirely sure if i need it

solar trellis
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Let's call acceleration x'' (2nd derivative of x) for consistent naming

real pebble
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this is the info for the first part

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might be useful

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ive managerd to workout this part, but its the 2) i havent and in the first i didnt use th S(k,a) stuff

real pebble
solar trellis
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mx'' isn't a force acting on the ball

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Its the result of forces acting on the ball

real pebble
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yeah, so far ive gotten that ma''=-kx

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rearranging would give x''+k/m*x=0 as the final part right?

solar trellis
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Yes

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Usually k refers to the spring constant

real pebble
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so from this, would i need to do a homogeneous 2nd order ODE to figure out the rest?

solar trellis
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Yes..

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is there an expression for the spring constant in terms of k and a?

real pebble
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for this module, we use fuck all numbers lol

solar trellis
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Because I think a should be relevant somewhere

real pebble
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we've literally only needed to derive the expressions for each unless we are provided with numbers to use

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that is the whole question

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been given no numbers and only been told to derive the expressions

solar trellis
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I actually gtg now, hopefully someone else will continue this and help you

real pebble
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ah okay, np

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thanks anyways, think i know what ive got to do now that i can use the second order ODE for it

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just stuff i needed to revise for an exam, so no rush really,

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.close

obtuse pebbleBOT
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stiff bear
#

Quick question am I allowed to cross multiple this “1” out it’s the only way I found to get rid of it and don’t know if I am allowed to do so

silver python
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not quite

twin sapphire
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well you added a multiplication out of nowhere so no

silver python
obtuse pebbleBOT
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@stiff bear Has your question been resolved?

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shell pine
obtuse pebbleBOT
shell pine
#

the apothem is 13.8 correct?

timid silo
warm shaleBOT
timid silo
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Approximately yes

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But that approximation is not needed

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Area = $\frac{2a}{\sqrt{3}}3a$

warm shaleBOT
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Pi Creature

timid silo
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this is the general formula where a is the apothem

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For a hexagon

obtuse pebbleBOT
#

@shell pine Has your question been resolved?

obtuse pebbleBOT
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shell pine
obtuse pebbleBOT
shell pine
#

@timid silo

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its wrong

rancid dust
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do you need help with this

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hints below

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||you want to split this into 6 equilateral triangles||

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||each equilateral triangle is congruent to the next||

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||the area of an equilateral triangle is s^2 * sqrt(3) / 4||

shell pine
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i did it

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but

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its wrong

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and i dont know why

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i did this

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and got 665.895643283

timid silo
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U gave 665.5 rather than 665.8

timid silo
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,w (16*sqrt(3)) / sqrt(3) * 3 * 8 * sqrt(3)

warm shaleBOT
timid silo
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It's 665.10....monkey

shell pine
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yes ik

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if ik the sides for a hexagon can i just do x times 6

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to get my aswer

timid silo
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That's a part

shell pine
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so x times 6 then what

timid silo
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then use the formul area = 0.5a s

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Where s is the perimeter or 6x

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And 6*0.5 turns into a 3

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Which I simplified in the formula

shell pine
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sides?

timid silo
shell pine
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what if i only know the side

timid silo
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Then ig u can calculate the apothem as well

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Btw is the last problem solved?

shell pine
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yes

timid silo
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Use the formula
$\frac{2a}{\sqrt{3}}=$side length

warm shaleBOT
#

Pi Creature

timid silo
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And isolate a this time

shell pine
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so is 6/2 the apothem

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?

timid silo
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,w (2*a) / sqrt(3) = 6

warm shaleBOT
timid silo
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No ig

obtuse pebbleBOT
#

@shell pine Has your question been resolved?

obtuse pebbleBOT
#

@shell pine Has your question been resolved?

#
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minor light
#

I am so confused on this please help me

obtuse pebbleBOT
kindred spoke
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what exactly is your confusion?

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Is it on how to solve the question, what the question means, etc.?

minor light
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Ik it has something to do with exponents but I always have trouble with it

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How to solve

kindred spoke
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I see

minor light
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Sorry should've been more clear

kindred spoke
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$a^m \cdot a^n = a^{m+n}$

warm shaleBOT
#

Science Done Right

kindred spoke
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This is the most important one in all of them

minor light
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I def don't remeber that

kindred spoke
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next, $(a^m)^n = a^{mn}$

warm shaleBOT
#

Science Done Right

kindred spoke
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This is the second most important one

kindred spoke
minor light
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Ok

kindred spoke
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$(10w^3)^2 = 10^2 \cdot (w^3)^2$

warm shaleBOT
#

Science Done Right

kindred spoke
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Try to evaluate this

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using the above two rules

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If you need help you can ask me

minor light
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Oo

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Ok

kindred spoke
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$10^2 = 100$, and as per our second property $(w^3)^2 = w^6$

warm shaleBOT
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Science Done Right

kindred spoke
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Did you understand?

minor light
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Not really

kindred spoke
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So the numerator looks like $100 \cdot w^6$

warm shaleBOT
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Science Done Right

kindred spoke
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@minor light Do you know like basic exponent properties?

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If no, I can teach it briefly and I can help

minor light
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I did, but I can't find my notes on them so I vaugley remeber them

kindred spoke
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these are very important

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Please read through this

minor light
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Alr

kindred spoke
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$1. a^m \cdot a^n = a^{m+n}$

$2. \frac{a^m}{a^n} = a^{m-n}$

$3. a^0 = 1$, For all a $\neq$ 0.

$4. a^{-m} = \frac{1}{a^m}$

$5. (a^m)^n = a^{mn}$

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The second, third, and fourth property are true when a is NOT 0

minor light
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Ok

kindred spoke
warm shaleBOT
#

Science Done Right

kindred spoke
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These are all of them, sorry

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Try solving the problem now, and if you have any questions you can ping

minor light
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Oo

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K

kindred spoke
#

Btw, the answer is $20 \cdot w^5$

warm shaleBOT
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Science Done Right

kindred spoke
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But please try solving it

minor light
#

Ok thanks man

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Ok got it

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Thank you

#

.close

obtuse pebbleBOT
#
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nocturne schooner
#

Equilateral triangle ABC has sides of length 4. The midpoint of BC is D, and the midpoint of AD is E. The value of EC^2 is

nocturne schooner
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ping me pls

kindred oasis
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Have you tried drawing the triangle?

nocturne schooner
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yea

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bottom left conrer is a, top middle is b, right corner is c

kindred oasis
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It's an equilateral triangle, so the median is also the height

nocturne schooner
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ye

kindred oasis
nocturne schooner
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90

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wait im tripping

kindred oasis
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So you can apply Pythagoras theorem

nocturne schooner
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ye

kindred oasis
nocturne schooner
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wait lemme see

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oh yea

kindred oasis
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Should be something like that

nocturne schooner
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Oh bruh

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i got the edges abc order wrong

kindred oasis
nocturne schooner
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huh

kindred oasis
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You can find CD and DE right?

nocturne schooner
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cd is 2

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de is squaretoo of 12 divided by 2

kindred oasis
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Yep

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Yeah sorry it's right

kindred oasis
nocturne schooner
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MANE I KNOW WHY

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IT IS CUS I DREW MY DIAGRAM WRONG

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nvm

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its not

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fuck me

kindred oasis
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CD = 2, ED = √3, apply Pythagoras theorem and find CE²

nocturne schooner
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ye i got it

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thanks

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.close

obtuse pebbleBOT
#
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acoustic granite
obtuse pebbleBOT
acoustic granite
#

im having trouble with this q

gilded needle
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well maybe start by taking the inverse of both sides

acoustic granite
#

i did that

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ill send pic

kindred spoke
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and invert again

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What's wrong?

acoustic granite
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i did that one moment

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maybe i jus messed up somewhere im sending a pic

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pic didnt send so had to write on laptop, my b for messy writing

kindred spoke
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Why did you invert 1/8? I don't think you should

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wait

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they asked for an expression for a-1 btw

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No I think he distributed that inverse to both terms

gilded needle
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if you invert the left hand side of the original equation then you just get A + 9BC^(-1)

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and you also need to invert the right hand side

acoustic granite
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why not 1/9?

gilded needle
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inverse of (stuff)^(-1) is just (stuff)

acoustic granite
#

i see

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why isnt it A^-1?

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ur takling that inverse right

gilded needle
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yes when you invert the LHS, you get another -1 exponent, and the two -1's cancel out

acoustic granite
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theres only 1 tho

gilded needle
#

$((A+9BC^{-1})^{-1})^{-1} = A + 9BC^{-1}$

warm shaleBOT
#

OurBelovedBungo

gilded needle
#

yes, i'm telling you to take inverses of both sides

acoustic granite
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OH

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my bad

gilded needle
#

that gives you a new -1 on each side

acoustic granite
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ok I see so u get A+9BC-1 on the LS

gilded needle
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right

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the purpose of doing this is that now we can isolate the A on one side of the equation

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by subtracting 9BC^(-1) from both sides

acoustic granite
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i need A^-1 though

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so I take inverse again both sides

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right

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this is the answer btw

gilded needle
#

yes

acoustic granite
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im getting this

gilded needle
#

in your first equation you didn't invert the RHS

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you have to invert (1/8)C

acoustic granite
#

ah f sorry i forgot

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is this right now

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if so how would I be able to simplify it more to get to that final form

gilded needle
#

the first and second lines are right

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the third is not

acoustic granite
#

oh b^-1

gilded needle
#

you can simplify the second line as follows:

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$A = (8I - 9B)C^{-1}$

warm shaleBOT
#

OurBelovedBungo

gilded needle
#

and therefore $A^{-1} = C(8I - 9B)^{-1}$

warm shaleBOT
#

OurBelovedBungo

acoustic granite
#

how u get I ?

gilded needle
#

$8C ^{-1}= 8IC^{-1}$

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we need the $I$ because we're gonna pull out the common factor $C^{-1}$ and to do that, both terms of the other factor need to be matrices

warm shaleBOT
#

OurBelovedBungo

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OurBelovedBungo

acoustic granite
#

I see

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how did u split the C from the ^-1

gilded needle
#

in other words, $8 - 9B$ doesn't make sense because $8$ is a scalar and $9B$ is a matrix

warm shaleBOT
#

OurBelovedBungo

gilded needle
acoustic granite
gilded needle
#

ah, I used $(XY)^{-1} = Y^{-1}X^{-1}$

warm shaleBOT
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OurBelovedBungo

gilded needle
#

where $X = 8I - 9B$ and $Y = C^{-1}$

warm shaleBOT
#

OurBelovedBungo

acoustic granite
#

ion get it

gilded needle
#

right

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because $Y^{-1} = (C^{-1})^{-1} = C$

warm shaleBOT
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OurBelovedBungo

gilded needle
#

and $X^{-1} = (8I - 9B)^{-1}$

warm shaleBOT
#

OurBelovedBungo

acoustic granite
#

oh so u take the inverse of both sides

gilded needle
#

yes

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since we want $A^{-1}$ on the LHS

acoustic granite
#

ah that makes a lot more sense

warm shaleBOT
#

OurBelovedBungo

gilded needle
#

we need to take inverses of both sides

acoustic granite
#

gotcha

#

alright thanks a lot

obtuse pebbleBOT
#

@acoustic granite Has your question been resolved?

#
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timid silo
#

I don’t understand sinusodial functions

obtuse pebbleBOT
timid silo
#

How do sinusoidal functions work?

#

.close

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prisma raft
obtuse pebbleBOT
prisma raft
#

help pls

#

number 6

prisma raft
# prisma raft

help in number 6 about elimination of elimination of arbitrary constants

obtuse pebbleBOT
#

@prisma raft Has your question been resolved?

prisma raft
#

<@&286206848099549185>

twin sapphire
#

i dont understand what you are asked to do with this equation

prisma raft
#

Help me to solve number 6

twin sapphire
#

i get that

prisma raft
#

Ok

twin sapphire
#

but what do you need to do

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in 6

prisma raft
#

Eliminate

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the arbitrary constants

twin sapphire
#

so you want to get a differential equation only involving y?

prisma raft
#

yes

#

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This video is all about elimination of arbitrary constants in order to find the differential equation.

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twin sapphire
#

first i think you need to compute the first and second derivative of y

prisma raft
#

like this examples

twin sapphire
#

even the third maybe aswell

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do that first

prisma raft
#

I need help only in number 6

twin sapphire
#

i got that but i told you the first step to solve it

obtuse pebbleBOT
#

@prisma raft Has your question been resolved?

obtuse pebbleBOT
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obtuse pebbleBOT
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copper marten
#

let G be a group. Is it true that if $x \in G$ and $ord(x) = ord(G)$, then $G = \langle x \rangle$ (and thus $G \cong \mathbb{Z}/(ord(x))\mathbb{Z}$?

warm shaleBOT
#

Rœmer

copper marten
#

i don't see how the assumptions imply $G = \langle x \rangle$ in particular

warm canopy
#

well you know that $\left<x\right>$ is a subgroup of G right?

warm shaleBOT
#

Rœmer

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iCaird

copper marten
#

yes

warm canopy
#

and whats the order of $\left<x\right>$

warm shaleBOT
#

iCaird

copper marten
#

$ord(x)$

warm shaleBOT
#

Rœmer

warm canopy
#

which is?

copper marten
#

$ord(G)$

warm shaleBOT
#

Rœmer

warm canopy
#

so you have a subgroup sitting inside G, which is the same size as G

copper marten
#

so they must be equal

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makes a lot of sense now

warm canopy
#

bingo

copper marten
#

thanks lol

kind hawk
#

(assuming that the order is finite)

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depending on definition infinite might be allowed

warm canopy
#

idd good catch

obtuse pebbleBOT
#

@copper marten Has your question been resolved?

obtuse pebbleBOT
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wanton kraken
obtuse pebbleBOT
wanton kraken
#

"In triangle ABC, CM is median, and straight line AQ crosses the median at its middle, and BC at point Q"

#

"If BC=a find CQ"

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I struggle with this

#

how do I find CQ

#

<@&286206848099549185>

obtuse pebbleBOT
#

@wanton kraken Has your question been resolved?

obtuse pebbleBOT
#

@wanton kraken Has your question been resolved?

wanton kraken
#

I've concluded that this problem is too evil and in my best of hopes I won't meet it in exams

#

.close

obtuse pebbleBOT
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subtle kite
obtuse pebbleBOT
subtle kite
#

Help please

#

Better view

#

<@&286206848099549185>

obtuse pebbleBOT
#

@subtle kite Has your question been resolved?

obtuse pebbleBOT
#

@subtle kite Has your question been resolved?

twilit ivy
# subtle kite

why is v=5?
it’s coming to rest so it should be v=0 no

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steady summit
#

Can any one help me please my math teacher gave this question to me and he told me that it has some physics problem in it so if i am allowed to share this question that would be great but if it is not then i will delete it

tardy epoch
#

,rotate

warm shaleBOT
tardy epoch
#

Can you take a screenshot. That's hard to read

obtuse pebbleBOT
#

@steady summit Has your question been resolved?

steady summit
#

Ok one min

steady summit
#

I cannot understand any thing from this question and i tried for about one week to solve this question but i failed

#

@tardy epoch
Can you please help me ??

obtuse pebbleBOT
#

@steady summit Has your question been resolved?

steady summit
#

<@&286206848099549185>

obtuse pebbleBOT
#

@steady summit Has your question been resolved?

polar topaz
#

a is constant

#

M is constant

#

So Centripetal force is constant

#

F= mv^2/r

#

@steady summit

#

Only change in r

#

you have the radius of both A and B

#

and you know the angular velocity for A

steady summit
#

Ok then , what

polar topaz
#

F = m r w^2

#

use the formula and sub the values

#

r (a) w(a) ^2 = r (b) w (b) ^2

#

see if that works

steady summit
#

Ok

polar topaz
#

And then you find the rate of change

#

of w to distance

#

Change in w / change in distance

steady summit
polar topaz
steady summit
#

Yes

polar topaz
#

uh show the steps

steady summit
#

I am sorry but can you tell me the steps again

#

I am bad at physics 😩

polar topaz
#

ok

#

we know that m is constant since its the same ball

#

and it said uniform acceleration so A is also constant

#

F = ma, so the centripetal force is constant

#

by formula F = rw^2

#

we know the force at A is equal to force at B

#

so F(a) = F(b)

#

radius of a times angular velocity a squared

#

r(a) * w(a)^2

#

equals to the same of b

#

r(b) * w(b)^2

#

r (a) is 18.2

#

r(b) is 5.5

#

W (a) = 0.28

#

We dont know w (b)

#

so we sub the values

#

18.2 * 0.28^2 = 5.5 * w(b)^2

steady summit
#

That is what i did

polar topaz
#

w(b) = 0.50934539094

#

New w - old w / 350

#

0.50934539094 - 0.28 /350

steady summit
#

Oooh

polar topaz
#

0.00065527254

#

did you do the root

steady summit
#

I get it

steady summit
#

I forgot

polar topaz
#

lol

steady summit
#

Thanks

#

😍

obtuse pebbleBOT
#

@steady summit Has your question been resolved?

obtuse pebbleBOT
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cursive shore
obtuse pebbleBOT
cursive shore
#

2n-3 is my equation

#

but the answer sheet thinks its +2

warm canopy
#

Does your equation work for n=1 or n=2?

obtuse pebbleBOT
#

@cursive shore Has your question been resolved?

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charred yew
#

Hey, I am stuck on this question. Can anyone help me?

orchid otter
#

i think

#

you must substitute your intensity

#

and log bot sides and get x down of the power

#

and solve for x

#

@charred yew

timid silo
#

yeah, but since its 40% it has to be in decimals

#

you could leave it as 40% sure, but that will confuse you further down the line.

charred yew
#

So do I sub 40% for I?

#

Then just solve for x by taking the log of both sides?

orchid otter
#

yes

charred yew
#

Thank you 🙂

#

.close

obtuse pebbleBOT
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stray quiver
#

Hello I have question

obtuse pebbleBOT
stray quiver
#

I will type out the question real quick

#

Consider two similar solids (3D Figures), whose similarity ratio is 2:3.

#

If the surface area of the smaller figure is 120 square meters, what is the surface area of the large figure?

sonic violet
#

2/3 = 120/x

silk geode
#

is it 3/2 * 120????

sonic violet
#

Set up the proportion and solve for x

stray quiver
#

does it have something to do with like the formula for surface area

#

like

sonic violet
#

Don’t think it would matter since they are similar, don’t take my word for it though

stray quiver
#

it says round to the nearest two decimals so

#

3/2*120 would be 180

sonic violet
#

Sheit

stray quiver
#

and 2/3=120/x would also be 180

#

so

#

im confused

sonic violet
#

180.00😝

stray quiver
#

does the fact that they are 3d solids change anything

#

im pretty sure it does

#

right

silk geode
sonic violet
#

Oh, you have to do 2^2/3^2 = 120/x

#

nah wait

stray quiver
#

yeah i was thinking of that

#

and for volume

#

it would be (2/3)^3

#

= 120/x

#

right

sonic violet
#

Ya

stray quiver
sonic violet
#

Does it give a decimal number

stray quiver
#

let me check

#

oh no

#

its 270

#

;-;

sonic violet
#

Ya that’s why I said nah🥹

stray quiver
#

or is it 2/3 = (120/x)^2

#

just learned this today

silk geode
#

why dont u try to derive it instead of guessing

stray quiver
#

wat

#

?

#

anyone here

astral ivy
#

@stray quiver what’s the “similarity ratio”

#

What does that mean exactly

stray quiver
#

like

#

the length of one edge of one side of a cube is 6

#

and the length of one edge of side of another cube is 9

#

then the similarity ratio would be 2:3

stray quiver
#

i keep getting 270

#

but they are telling me to round to 2 decimal places

#

so i am very confused

astral ivy
#

Ah i see

stray quiver
#

my formula is

#

(2/3)^2 = 120/x

astral ivy
#

Hm

#

How did you get 270

#

Oh

#

Lol

stray quiver
#

cause

astral ivy
#

Nvm nvm

stray quiver
#

(2/3)^2 = 4/9

astral ivy
#

That’s odd

stray quiver
#

4/9 = 120/x

#

cross multiple

#

4x = 9(120)

#

4x=1080

#

x=270

astral ivy
#

Yeah

stray quiver
#

le tme take a picture

#

to show you

#

could it just be there as deception

#

the round to nearest 2 decimals

#

@astral ivy you heree

obtuse pebbleBOT
#

@stray quiver Has your question been resolved?

obtuse pebbleBOT
#
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soft charm
obtuse pebbleBOT
pallid flame
#

do you remember formula for average over an interval

soft charm
#

there is an equation for that

pallid flame
#

yes what it is

soft charm
#

i have no idea

pallid flame
#

ok do you know average rate of change formula

#

from like algebra 1

soft charm
#

not really

#

if i saw it i would probably know it

pallid flame
#

ok do you know how to find slope between two points

soft charm
#

yes

pallid flame
#

ok what is that formula

soft charm
#

y1-y2

#

y2-y1

pallid flame
#

what

soft charm
#

/2

#

ok give me a sec

#

change in y/change in x

pallid flame
#

which is what

#

points (x1, y1) and (x2, y2)

soft charm
#

its obvious

pallid flame
#

?

soft charm
#

x2 and y2

pallid flame
#

what

#

that’s not a slope

soft charm
pallid flame
#

yes

#

in terms of the points i described

soft charm
#

yes

#

its y2-y1

pallid flame
#

no

soft charm
#

yes it is, thats exactly what it is

#

💀

#

change in y = y2-y1

#

change in x = x2-x1

#

to find the slope you put the delta y on top of delta x

#

because rise over run

stray quiver
#

.reopen

#

bruh

nocturne minnow
stray quiver
#

why was this close alll my question wasnt resolved

nocturne minnow
nocturne minnow
soft charm
#

from algebra I

nocturne minnow
#

I mean, you gave the formula in parts

#

jnmwn was asking for the entire formula

pallid flame
#

you said slope = y2 - y1 which is incorrect

#

slope = (y2 - y1)/(x2 - x1)

nocturne minnow
#

Like if you asked me for the formula for area of a triangle, you wouldn't say base times hieght

#

Then times one half

#

Would you? You'd say the entire formula, one half base times height

soft charm
#

whatever zzz

nocturne minnow
#

It makes a difference

astral ivy
obtuse pebbleBOT
#

@soft charm Has your question been resolved?

#
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#

Please don't occupy multiple help channels.

nocturne minnow
#

Don't open multiple channels, even if you have multiple questions

#

That means, close one of your channels

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

obtuse pebbleBOT
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tawdry vortex
#

i dont get part b

obtuse pebbleBOT
tawdry vortex
#

i was able to slove part i) but idk what to do with part ii)

#

wait nvm i got it

#

.close

obtuse pebbleBOT
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delicate sand
obtuse pebbleBOT
delicate sand
#

hello

#

<@&286206848099549185>

tardy epoch
delicate sand
#

oh sorry

#

ill wait 30 mins then

polar topaz
#

eh

#

its dependent probability

#

for first

#

total = 2+23 = 25

#

probability defective : 2/25

#

non defective 23/25

#

2/25 * 23/24

#

@delicate sand

#

why is there 3 defective toys when there is only 2 defective items in part 2 😱

#

Oh wait

#

sheesh its from 3 box

#

2/25 * 23/25 * 2 part 1

#

(23/25) ^3 part 2

obtuse pebbleBOT
#

@delicate sand Has your question been resolved?

obtuse pebbleBOT
#
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delicate sand
#

.reopen

obtuse pebbleBOT
#

delicate sand
polar topaz
#

its from seperate boxs

delicate sand
#

OKE

delicate sand
delicate sand
polar topaz
#

oh

#

i wrote it wrong

delicate sand
#

so for part 2 its (2/25)^3

polar topaz
#

ye

delicate sand
#

okay thank youuu

delicate sand
#

is it

#

(2/25 * 23/25)*2 or to the power of 2

polar topaz
#

times 2

delicate sand
#

oke

#

thank you sap

#

.close

obtuse pebbleBOT
#
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delicate sand
#

.reopen

obtuse pebbleBOT
#

delicate sand
#

oh jk i have one more

polar topaz
#

One fixed

#

find prob of one girl in 2 childs

delicate sand
#

1/2?

polar topaz
#

idk whats the prob

#

1/2 ig if its not given

delicate sand
#

2 girls in 3 children

#

and then 2nd child is a girl

polar topaz
#

yeah but one girl is child

delicate sand
#

2/3 or 1/2

polar topaz
#

i mean there is always a girl

#

so you need to find a girl a boy combination

delicate sand
#

boy girl girl

#

or girl girl boy

#

those are the two combinations

polar topaz
#

yeah

#

total 4 combs

#

b b , b g , g b, gg

#

1/2

delicate sand
#

but theres three children

#

so how is that

polar topaz
#

but one girl is always fixed

delicate sand
#

three children with 2 girls with 1 girl being the middle child

delicate sand
polar topaz
#

normally its

BBB
BGB
BBG
BGG
GBB
GGB
GBG
GGG

#

second is always G

#

so

#

BGB

BGG

GGB

GGG

delicate sand
#

yeah and then we narrow it down to two girls

#

so

#

BGG

GGB

polar topaz
#

yeah

#

2/4

#

1/2 prob

delicate sand
#

okay

#

so 1/2 is the probability

#

of this

polar topaz
#

y

delicate sand
#

none noen thank u

#

mwamwa

#

.close

obtuse pebbleBOT
#
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thorn hearth
obtuse pebbleBOT
thorn hearth
#

So I be using partial sum and like I go over 3/2

#

But apparently the answer is 1/3

#

So I'm like Umm

#

<@&286206848099549185>

obtuse pebbleBOT
#

@thorn hearth Has your question been resolved?

obtuse pebbleBOT
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icy palm
#

i understand that i have to get the exact trig value but i dont get how to get a or b

brittle blaze
#

use when cos is 0 to get b and then you will be able to solve for a

timid silo
icy palm
#

but cos 0 is 1

timid silo
#

probably

brittle blaze
#

bc cos(90) is 0 so its just y=b

#

which is 1

timid silo
#

i think

icy palm
#

im lost

timid silo
#

u meant to see at 90

#

not 0

brittle blaze
#

i thought he was saying when cos is 0

#

which is 90 yeah

#

bc the y value is 1

timid silo
#

long story short you know that

$a*cos(90)+b=1$

$\implies 0+b=1$ so $b=1$

icy palm
#

uhm

#

ye

brittle blaze
#

yeah thats whay i was getting at, so then you will be able to get a now

warm shaleBOT
#

Pi Creature

icy palm
#

alr

#

gimme a min

timid silo
#

now try to solve for a

icy palm
#

so b is 1

timid silo
#

solve for a

#

now

icy palm
#

OH

#

2

#

i subbing b back into that equation

#

and i was getting 0

#

._.

#

is that right?

timid silo
#

Sub when x=0

icy palm
#

alr

#

thx mate

obtuse pebbleBOT
#

@icy palm Has your question been resolved?

obtuse pebbleBOT
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static patio
obtuse pebbleBOT
static patio
#

converges or diverges ?

junior nymph
#

Converges

timid silo
static patio
timid silo
#

well think of some test

#

which would be appropriate

#

there is one that should strike

junior nymph
#

Split it like this and apply the sum rule, to check each if each of them converges.

warm canopy
timid silo
#

oh i was leaning towards integral test

#

nozoomi u got many options now michal

warm canopy
#

Can just do a straight up comparison I think

static patio
timid silo
#

oh

static patio
#

hmm

timid silo
#

like 3n^2<3n^3

warm canopy
#

See if you can bound it by 5n^3

static patio
#

(3n^2 + 2n^3)/(n+5n^5) <= (3n^2 + 3n^3)/(n+5n^5)

warm canopy
#

Eh you didn't do what Arkos said

static patio
#

hmm

#

idk

#

i have to bound only numerator ?

warm canopy
#

Both

obtuse pebbleBOT
#

@static patio Has your question been resolved?

static patio
#

(3n^2 + 2n^3)/(n+5n^5) <= (3n^2 + 3n^3)/(5+5n^5)

static patio
#

.close

obtuse pebbleBOT
#
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obtuse pebbleBOT
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pale apex
#

How do I get the unknown parts ( final answers rounded to two decimal places and the angle measure to the nearest minute)

timid silo
#

cos(x)=Adjacent/Hypotenuse
sin(x)=Opposite/Hypotenuse
tan(x)=Opposite/ Adjacent

carmine kelp
#

For the angle B, 180-90-28

pale apex
#

.close

obtuse pebbleBOT
#
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glossy island
#

W=3n+t
Express w in terms of n and w

obtuse pebbleBOT
glossy island
#

Do i just make t the subject?

worn ocean
#

subject?

glossy island
#

Rearranging equation

worn ocean
#

just take 3n to the other side?

#

t = w - 3n

glossy island
#

Oh

worn ocean
#

is that what u mean

glossy island
#

in terms of n and w

#

i didnt get what they meant by this

glossy island
#

.close

obtuse pebbleBOT
#
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#

@fleet horizon Has your question been resolved?

broken bridge
#

yes

obtuse pebbleBOT
#
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obtuse pebbleBOT
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high crow
obtuse pebbleBOT
high crow
#

Can anyone explain this equation to me

#

And what a cubic formula is

charred remnant
#

still need help?

high crow
#

Yep

charred remnant
#

you solve the inequalities?

high crow
#

Wait a min

kindred spoke
charred remnant
#

Hi science!

kindred spoke
#

you can take x^2 out from the first two terms

high crow
#

Oh

kindred spoke
charred remnant
kindred spoke
#

let me write in latex

high crow
#

It said to do them like these

charred remnant
#

i prefer using computer and tricks to solve cubic and higher power

warm shaleBOT
#

Science Done Right

kindred spoke
#

Take 4x -1/2 common again

warm shaleBOT
#

Science Done Right

kindred spoke
#

Now, this is quite easy to solve. the entire thing is 0, if any of the terms is 0

#

if 4x - 1/2 = 0, x = 1/8 or 0.125

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i x^2 + 1 = 0, x = +/- i

#

that's imaginary

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so we take x = 0.125

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So that's the critical point, at which the expression in the image = 0, and not < 0

#

@high crow are you following me?

high crow
#

Not quite

kindred spoke
high crow
#

Ok

kindred spoke
#

go slowly, I will wait :D

kindred spoke
high crow
charred remnant
#

science, i think there's good trick that you could you to solve the cubic

kindred spoke
charred remnant
high crow
#

Oh ok

kindred spoke
#

if we find that, we will get the values for < 0

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which was required

charred remnant
#

right @high crow

high crow
#

Mhm

#

Continue please

charred remnant
#

in order for 2 integer to multiply together and give you a number that is lower than 0

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that is lower than 0

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Then those 2 integer CANNOT have the same sign

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as you know, 2 postive number multiply together will give you a number greater than 0

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ex: 5x6=30>0

high crow
#

Yeh

charred remnant
#

2 negative number multiply together will give you a number that is greater 0

high crow
#

Yeh

charred remnant
#

alr you get it the def

charred remnant
#

@high crow

high crow
#

Yeh

kindred spoke
kindred spoke
#

if it's less than 0, the cubic has to be less than or greater than the critical point, 0.125

#

I hope this all doesn't sound too complex

high crow
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It will take a while for me to process I don’t come for an English speaking country

charred remnant
#

no worries, science it's really good at explaining in a simple way

high crow
#

<@&286206848099549185>

obtuse pebbleBOT
#

@high crow Has your question been resolved?

earnest parrot
#

What do you need help with now?

earnest parrot
#

It's the zero that corresponds to the factor (4x-1/2)

#

(4x-1/2)=0, then x=1/8 is a solution

high crow
#

K

high crow
#

Done

#

.close

obtuse pebbleBOT
#
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royal cargo
obtuse pebbleBOT
#

@royal cargo Has your question been resolved?

hybrid gull
royal cargo
#

has it been 15 minutes

#

oh

#

<@&286206848099549185>

hybrid gull
#

I mean, what have you tried?

royal cargo
#

and then ive tried (a+b)^2 identity

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that got me no where too

#

so im not sure how to approach the question really

hybrid gull
#

Find the LHS of the second equation in terms of θ using the first equation

#

Show your work

royal cargo
hybrid gull
#

Okay so take the LHS of the second equation, that expression with m

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And replace m with the sec + tan

royal cargo
hybrid gull
#

Show your work

obtuse pebbleBOT
#

@royal cargo Has your question been resolved?

royal cargo
hybrid gull
#

Now algebra - expand the parentheses

obtuse pebbleBOT
#

@royal cargo Has your question been resolved?

obtuse pebbleBOT
#
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warped flume
obtuse pebbleBOT
warped flume
#

Integration problem

#

Thats all the question gives

solar trellis
#

what have you tried?

warped flume
#

Substituting sinx

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Cosx

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Sinxcosx

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1+sinxcosx

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I tried using trig identities to simplify

robust sleet
#

an interesting one

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do u have to do it with numerical integration

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because finding the integral is very very hard

gilded needle
#

do the double angle trig identities help?

tardy epoch
#

,w integral sqrt(sin^3(x) cos(x))/(1+sin(x)cos(x)) dx

warm shaleBOT
gilded needle
#

$\sin(2x) = 2\sin(x)\cos(x)$ and $\sin^2(x) = \frac{1}{2}(1 - \cos(2x))$

robust sleet
#

the answer is very long

warm shaleBOT
#

OurBelovedBungo

solar trellis
#

also you can factor out sin^2

warped flume
solar trellis
#

u = pi/2 - x might also help

warped flume
solar trellis
#

well.. you don't have to start from scratch after every failed attempt. continue with the simplest expression you have so far