#help-19

1 messages · Page 158 of 1

lost crane
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To find the decimal value of a percentage you divide by 100

pale trench
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okay ty

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i got 0.2

lost crane
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yes

pale trench
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i guess that makes sense

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so for example 30% would equal 0.3?

lost crane
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yes

pale trench
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interesting

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okay so 68,400.93 x 0.2

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=

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13680.186

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?

lost crane
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yes

pale trench
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and then i round that right

lost crane
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Yes money is usually rounded to the nearest cent (2dp)

pale trench
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so uhhhh

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13,680.19?

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and it says "Assuming Lorna finances the remaining cost at an annual interest rate of 7.15% for 10 years, find the monthly payment."

odd edgeBOT
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@pale trench Has your question been resolved?

pale trench
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is it 4,638.53

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hm, the answer (it gave me the answer after too many tries) says 576.42

languid ravine
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don't use chatgpt, you just found 20% of 64835 in the second question

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chatgpt can't do math

pale trench
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yep

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i meant the assignment itself gave me the answer

languid ravine
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oh i read the question wrong i'm sorry

pale trench
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it's okay!

languid ravine
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so lorna already paid 13,680.19

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so how much does she still owe?

pale trench
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do i just subtract that

languid ravine
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yes

pale trench
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uhhh looks like

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51,154.81 ?

languid ravine
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yes

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so she needs to pay 7.15% of that

pale trench
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51,154.81 x 0.715?

languid ravine
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0.0715

pale trench
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okay

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looks like

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3657.568915 ?

languid ravine
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yup

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and rounded to 2 decimal places is?

pale trench
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3657.57?

languid ravine
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yes

pale trench
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how did the answer key get 576.42

languid ravine
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i don't know, from what i can see 576.42 was your answer which is wrong

pale trench
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that's so strange, the thing said that was the answer

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wait let me retry, it might be buggy

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i have 2 tries to get the answer right, and i put in the wrong answer one time, so the website gave me an answer which was 576.42 so i pressed enter and that was ALSO wrong, then Player helped me work out the problem and we got 3,657.57, which it says is ALSO wrong so i'm very confused

odd edgeBOT
#

@pale trench Has your question been resolved?

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hearty kelp
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am i right with A here?

odd edgeBOT
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@hearty kelp Has your question been resolved?

hearty kelp
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wait @brittle beacon does that mean yes 😭

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sorry to ping

vale vortex
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just use a calculator

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and keep doubling it

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till u get

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that number

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and count how many times u doubled it?

brittle beacon
hearty kelp
hearty kelp
vale vortex
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ah gotcha

hearty kelp
#

.close

odd edgeBOT
#
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vale vortex
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what are the bounds

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do u have to find them ur self

steep mantle
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i mean you can see the bounds are the intersections

vale vortex
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so

orchid garden
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^ $$x^2-2x = -x^2+4x$$ is pretty simple to solve

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

vale vortex
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u set them equal to eachother

orchid garden
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I have no idea why that didn't compile

steep mantle
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$$x^2-2x = -x^2+4x$$ is pretty simple to solve

clever fjordBOT
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Skissue ping4response

vale vortex
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well 0 is given

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but

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its how u find the top bound

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than u do some weird calc 2 formula shit

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and integreate outer minus inner

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squared maybe?

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i forget the exact formula

orchid garden
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It isn't volume

vale vortex
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oh

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u just integregrate

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the outer bound

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no

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that makes no sense

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thats def right

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u have to subtract them

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f(x) - g(x)

proven cape
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$\int_{x_1}^{x_2} \int_{y_1(x)}^{y_2(x)}} dydx$

vale vortex
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but its (-x^2 +4x) - (x^2 -2x)

lethal wharf
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Hi

vale vortex
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u gotta be careful with the negatives

clever fjordBOT
#

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

lethal wharf
vale vortex
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actually im wrong

lethal wharf
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Bros are cooking

vale vortex
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i think

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solve for x

proven cape
vale vortex
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if ur stuck im confident i know how to find the bounds now

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if thats what ur confused about

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so

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u have

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-x^2 + 4x = x^2 - 2x

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put it all on one side and tell me what u get

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yes

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also

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just to be clear

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i was exactly right

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about the outer - inner

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idk what that volume dude is talkin about

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no

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bruh'

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like

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add x^2

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to both sides

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till one side is 0

orchid garden
vale vortex
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and all terms are on one side

vale vortex
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u left ur message open to interpretation

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combine like terms

steep mantle
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dint you just take the bounded integral of the 2 equations subtracted

vale vortex
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ngl i have no idea what that means

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if u mean outer minus inner thats what I said

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correct

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now factor

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those are the bounds

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u got it from there?

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or u need more help

steep mantle
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like
$$\int^{x_2}_{x_1}-x^2+4x-x^2+2x , dx$$

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or am i stupid

vale vortex
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try it your self

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and tell us what we get

vale vortex
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and there is a minus sign

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in the middle

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u need to be very careful with negatives

clever fjordBOT
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Skissue ping4response

vale vortex
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thats right

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try integrating

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and show me what u get

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its really straight forward

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dont plug the bounds in

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show me the anti derivitive

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u got

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i cant help you than

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if you dont send a ss of ur work

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u can literally type out

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what the anti derivitive is

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if u want

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u dont gotta take a pic

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just show me what u got

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and ill tell u where u went wrong if u did

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you need

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to integrate

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do you know how

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this is

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a calc 2 problem

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you learn integration in calc 1

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if u dont know how to integrate u cant solve it

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and theres too much too teach

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u should just go watch a video or smth

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on the different rules of integration

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do you know how to take a derivitive?

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whats the power rule

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ok

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good

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so

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the power rule for integration is

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you add 1

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to the exponent

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and than divide by it (it being the exponent)

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knowing that informaton you should be able to solve this problem

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ill give u an example

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the -x^2 would turn into -x^3 over 3

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gl

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.close

odd edgeBOT
#
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mystic shard
#

given 0 ≤ θ ≤ 2π, solve 2sinθ-√2=0

How do i solve this problem?

pastel orbit
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get it into the form sin(theta) = number, and then use the unit circle catthimc

mystic shard
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sin(θ)= √2/2

what do i do with the unit circle?

dapper canyon
mystic shard
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i don't know

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i assume its 0, but i wouldn't know why

dapper canyon
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do you anything about sin and cos?

mystic shard
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yeah

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its the soh cah toa thing

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to calculate the sides of a triangle

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ohhh i think i get it now

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sin(θ)= √2/2

=π/4

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and that would be one solution

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then π-(π/4) = 3/4π

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and that would be the second solution

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so θ = π/4, 3/4π

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am i correct?

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<@&286206848099549185> can you please check my work?

hardy mica
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it seems right to me

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just plug it back into the equation and check if it gives the correct answer

mystic shard
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oh yeah it does

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so what about something like this:

sin2θ=√3/2

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where the 2 is inside of sin

hardy mica
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consider the range for 2θ

mystic shard
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oh so y=√3/2

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meaning 0 ≤ 2θ ≤ 4π

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then what?

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oh then you go back to the chart

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so it would be

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2θ = π/3, 2/3π

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right?

hardy mica
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0 ≤ 2θ ≤ 4π

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what about 2π ≤ 2θ ≤ 4π

mystic shard
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oh i forgot to clarify... the problem was

given 0 ≤ θ ≤ 2π, solve sin2θ=√3/2

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you can't do anything to that 0 right?

hardy mica
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yeah, we need to look at solutions for 2θ between 2π and 4π just as much as looking at solutions between 0 and 2π

mystic shard
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yeah, if we are looking between 2π and 4π, and 0 and 2π, wouldn't the minimum be 0 and max be 4π?

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making the inequality 0 ≤ 2θ ≤ 4π

hardy mica
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how many solutions will there be between 0 and 4π?

mystic shard
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idk

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how do you know that?

hardy mica
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refer back to the graph

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do you have a graph of sinx that stretches from -2π to 4π

mystic shard
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i don't

hardy mica
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just copied from google:

mystic shard
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just made this from desmos

mystic shard
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we would need something bigger

hardy mica
mystic shard
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oh right

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so there would be 4 solutoins

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wait no 6

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no theres 7

hardy mica
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list them out

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and see if they are in the range required

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0 ≤ 2θ ≤ 4π

mystic shard
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oh nvm there is 4

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so we already have two solutoins

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how do i find the other two

hardy mica
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how long is a period of sinx

mystic shard
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you said infinite?

hardy mica
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(after how much x does sinx repeat itself)

mystic shard
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oh after π

hardy mica
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no

mystic shard
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2π final answer

hardy mica
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just list out the possible values of 2θ then solve for θ

mystic shard
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what i am so confused

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we don't know theta

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how would we list for 2θ

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if we don't know what it is

hardy mica
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no, we try to solve for 2θ first then move on to find θ from that

mystic shard
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ok we solve for 2θ and got π/3 and 2/3π

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so it would be θ= π/6 and π/3

hardy mica
mystic shard
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idk

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isn't that what we are trying to solve?

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we r trying to find all 4 sollutions

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so far we have 2

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how would we find the other 2?

hardy mica
mystic shard
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nope 😀

hardy mica
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like, how much is the part of the graph shifted to the right to have it be exactly the same as itself?

mystic shard
hardy mica
# mystic shard 2pi

yup, a point of the graph will have the same y value after shifting to the right by 2π

mystic shard
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it takes 2pi for the graph to repeat itself

mystic shard
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so 9/3pi - pi/3?

hardy mica
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so what are the 2 other values for 2θ

mystic shard
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THEN

theta = pi/6, pi/3, 7/6pi, 4/3pi

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BOOOM

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correct?

hardy mica
mystic shard
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wiat so suppose you didn't have the graph

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how would you solve it then

hardy mica
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sinθ = sin(θ+2π) is always true

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as well as sinθ = sin(π-θ)

mystic shard
#

thanks so much

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thank you

#

.close

odd edgeBOT
#
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signal perch
#

how do i figure this out?

odd edgeBOT
charred spindle
#

Do you have notes about consumer surplus? Is it just S - D?

odd edgeBOT
#

@signal perch Has your question been resolved?

signal perch
odd edgeBOT
#

@signal perch Has your question been resolved?

odd edgeBOT
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dim dew
odd edgeBOT
dim dew
#

for a)
When we count levels, we start with 0 not 1 correct?
So level of g would be level 2?
a = level 0
b,c,d = level 1
e,f,g,h,i,j = level 2

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so g = level 2

hazy temple
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right

dim dew
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so for b) we look for the longest level

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to determine the height?

hazy temple
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yes

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the longest path but yes the logic is the same

dim dew
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so its 4?

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b = 4

olive ledge
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It should be 3

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It's the number of edges from the root node to the deepest node

dim dew
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what about vertex k?

hazy temple
dim dew
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there are 4 verticies all together going up

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ohhh we just count highest level?

olive ledge
#

Edges

dim dew
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okok

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so height = longest level

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or longest path

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from root to any vertex

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c) internal verticies = parents so they have children.
so we include a?
a,b,c,d,g,j Since they all reproduce?

olive ledge
#

Vertices are the nodes itself, edges are the lines that connect the nodes.

dim dew
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for d) leaves are all the children.
so they can't have any kids.
e,f,k,h,i,l,m

dim dew
#

nicee

dim dew
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e) parent of h
its d?

olive ledge
#

Right

dim dew
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f) child of c = g

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what if the question asked me child of e.
Would it be DNE? or 0? or nothing?

olive ledge
#

DNE

dim dew
#

okok

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can i ask more questions

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regarding this stuff

olive ledge
#

Yeah sure

dim dew
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so verticies are the points.
Edges are always 1 less.
So E = V -1

olive ledge
#

Number of edges is n-1

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Right

dim dew
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so 26 edges

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20 internal verticies that means they are parents. IF i wanna find out leaves. its the children

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but whats 5-ary? or 8-ary what is that

olive ledge
#

Every internal node will have exactly 5 children and similiary for 8-ary

dim dew
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ohh ok

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so m-ary the m only applies to internal node (excluding root)

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so for 20 internal verticies.
Each will have. 5 children.
so 5*20 = 100 children.

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but what about the root, that also has verticies

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100+1 = 101??

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wait no root is included in interrnal verticies

olive ledge
#

That's right

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So it should be just 100

dim dew
#

hm

olive ledge
#

Wait

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That would actually be wrong

dim dew
#

okok

olive ledge
#

$L = I(N-1) + 1$

clever fjordBOT
#

ColdTe²

olive ledge
#

I is the number of internal nodes, N the number of children each node can have

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L is the leaf nodes

dim dew
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okayokay

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L = leaf
I = internal vverticies
N = m in the m-ary?

olive ledge
#

Yes

dim dew
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so L = 100(4)+1
L = 401?

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wait no

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i forgot question

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L = 20(5-1) + 1

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= 20(4) +1

olive ledge
#

81

dim dew
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81?

olive ledge
#

Right

dim dew
#

okay so thats a formula I need to remember

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L = I(M-1) +1

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E = V -1

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  1. E = V - 1
    so E = 100-1
    E = 99
olive ledge
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10000

dim dew
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oh wait yee

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E = 10,000 -1
9,999

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  1. I = 100
    m = 5
    V = ?
    V = I + L
    L = 100(5-1) + 1
    L = 400 + 1
    L = 401
    V = 401 + 100 = 501?
olive ledge
#

Right

dim dew
#

or i was thinking

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another. formula would be
V = I*m + 1

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so V = 100*5 + 1
V = 500 + 1 = 501

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for 18

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i mean 19

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hmm

olive ledge
dim dew
#

I = 1000
E = ?
Full binary so each vertex has 2 kids?
so 1000^2?

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wait no

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full binary = m-ary m = 2
2-ary?

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so L = 1000(2-1) +1
L = 1001
V = L + I
so V = 1001 + 1000 = 2001
E = V - 1
so E = 2001 -1 = 2000

olive ledge
#

It's 2-ary I'm not sure about the edges let me check

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That's right

dim dew
#

I was thinking another way to do it would be

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V = I * M +1
So V = 1000(2) + 1
SO V = 2001
E = 2001-1 = 2000

olive ledge
#

That's prolly the easier way

dim dew
#

I like the formula you gave, L = I(m-1) + 1
I can use it to double check work

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thats the one that starts with 1

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so 1
1.1, 1.2, 1.3
1.1.1, 1.1.2, 1.1.3 (under vertex 1.1)
1.2.1, 1.22. (under vertex 1.2)
1.3.1 (under vertex 1.3)
1.1.3.1 (under vertex 1.1.3)

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or do we start from 0?

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wait it would be 0 (root vertex)
1, 2, 3 (child of 0 or root vertex)
1.1, 1.2, 1.3 (child of vertex 1)
1.3.1 (child of vertex 1.3)
2.1, 2.2 (child of vertex 2)
3.1 (child of vertex 3)

olive ledge
#

The root should be numbered 0 other than that children are labelled 1,2,..N from left to right

dim dew
#

rightt

olive ledge
#

Right

dim dew
#

okok

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there are three orders

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Pre-Order, In-order, Post-order

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Inorder = Left -> Root -> Right

olive ledge
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Postorder = Left -> Right -> Root

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Preorder = Root -> Left -> Right

dim dew
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okok

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im a bit confused on this

olive ledge
#

What did you get as the postorder

dim dew
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im still working through it

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trying to look through examples

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so for post order its Left right root. SO root comes very end.
So would it be e, f,k,g,b,h,i,c,j,d,a?

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so parents come last?

olive ledge
#

That's right

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Traverse through each sub-tree with that order

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And that's basically it

dim dew
#

but thats basicallhy traversing it right?

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that would be the answer e, f,k,g,b,h,i,c,j,d,a?

dim dew
#

so what if we did this

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but inorder, pre-order

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so inorder = Left root right
e,b,f,k,g,a,h,c,i,j,d

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Preorder = Root -> Left -> Right
a,b,e,f,g,k,c,h,i,d,j

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Prorder = parents come first

odd edgeBOT
#

@dim dew Has your question been resolved?

olive ledge
#

@dim dew it's correct

dim gale
#

true

odd edgeBOT
#
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mighty locust
#

how do i do this

odd edgeBOT
mighty locust
#

this what i did

olive ledge
#

If you sub u = x^2 + 4 then du = 2xdx not dx

mighty locust
#

i was trying to get dx alone so i can repalce it in the equation

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so the du=2xdx turned into du/2x=dx

olive ledge
#

I can see that

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I meant step 3

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Where you made a change in the variables again

mighty locust
#

so i dont get it

olive ledge
#

du != dx there

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du = 2xdx so you can't merely have

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dx there

mighty locust
#

ohh

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so how do i solve it

olive ledge
#

$\f32 \int \frac{du}{u}$

clever fjordBOT
#

ColdTe²

olive ledge
#

$\f32 \ln(u) + C$

clever fjordBOT
#

ColdTe²

mighty locust
#

oh thats it

olive ledge
#

Pretty much just sub for u again

mighty locust
#

so i dont need to use the arc tan formula

olive ledge
#

Right

mighty locust
#

so will there be a situation where i wil have to use that formula instead of this

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or will this always work

olive ledge
#

If in this case it was just dx instead then that would have been absolutely fine

mighty locust
#

okay thanks

#

.close

odd edgeBOT
#
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distant umbra
#

if i were to parametrise a plane

odd edgeBOT
distant umbra
#

something lke

#

0,0,0--->1,3,7

#

then is this right

#

x=t
y=3t
z=7t

desert tinsel
distant umbra
forest sky
#

a plane requires two parameters. do you mean a line segment?

distant umbra
#

yeaa sorry

desert tinsel
#

x=t, y=… z=…

distant umbra
#

cool thanks

#

.close

odd edgeBOT
#
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odd edgeBOT
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distant umbra
#

here why are they multiplying with the magnitude?

distant umbra
#

or is it that to convert DA to DS?

forest sky
#

that's the jacobian which converts from dS to dA, yes

distant umbra
#

cool thanks

#

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odd edgeBOT
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quasi roost
#

hey guys i did my exam and i skipped this question bc i dont know how to do it, help please 🥺❤️

question 7 on the page

inner horizon
inner horizon
#

@quasi roost

#

where r u

#

i can help u

#

...

#

bro posted the question and disappeared

odd edgeBOT
#

@quasi roost Has your question been resolved?

odd edgeBOT
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true lodge
#

hi

odd edgeBOT
true lodge
#

I had a question about paramterization

quartz trellis
#

send

true lodge
#

so something like lets say x^2 + z^2 = 4

#

thats a cylinder

#

If i wanted to paramterize

#

I know since there are no ys, its basically infinity on the y

#

so how would i paramterize it

#

im thinking <rcostheta, y, rsintheta>

#

so its going across y axis

#

so y = y

#

x = rcostheta

#

z=rsintheta

#

r(u,v) = r(r,theta)

odd edgeBOT
#

@true lodge Has your question been resolved?

lament stream
#

help

true lodge
#

huh

frozen stream
lament stream
#

how to solve indefinite integrals

next loom
true lodge
#

huh

true lodge
#

Can someone tell me the steps needed to solve these?

#

Im thinking

  1. draw a rough sketch
  2. paramterize it (find its intervals)
  3. Plug in parametization to F
    Then get r'(paramterization)

Idk

lament stream
#

pls help

quartz trellis
odd edgeBOT
#

@true lodge Has your question been resolved?

#
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wraith pelican
#

I need some help solving this integral. I already simplified a little using the given assumption, but I struggle on how to proceed with the two smaller integrals.

Any ideas?

wraith pelican
#

<@&286206848099549185>

odd edgeBOT
#

@wraith pelican Has your question been resolved?

odd edgeBOT
#

@wraith pelican Has your question been resolved?

strange glacier
#

is that capital A

odd edgeBOT
#

@wraith pelican Has your question been resolved?

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frigid scroll
#

how would you calculate this limit knowing you have 0*infinite indetermination (idk if its a good word).

frigid scroll
#

i know that i have to use the criterion of the pincers

#

but i do not know how to apply it to an exercise

tepid pelican
#

I'd try to squeeze it between 2 simpler sequences

#

the denominators are really ugly

#

it would be good to make them all of the same denominator

frigid scroll
tepid pelican
#

but maybe you will be able to find their limits more easily

tepid pelican
#

so you cant nicely add those fractions up

frigid scroll
#

i could just use n^2+n

#

as it wont change anything

tepid pelican
tepid pelican
frigid scroll
#

well

#

limit of n^2+k/n^2+n ,when n goes to infinite is still 1 no matter how big is k

tepid pelican
#

well, thats true, but it doesnt guarantee much

#

in this case it works out but not in general

frigid scroll
#

thats all i need

#

if it works in this case

tepid pelican
#

to do it more formally, notice that
$\frac{k}{n^{2}+n}\le\frac{k}{n^{2}+k}\le \frac{k}{n^{2}}$

#

then you can analyze both the bounding sequences

clever fjordBOT
#

MæthIsAlwaysRight

tepid pelican
#

anyway, try simplifying it with denominator n^2 + n now

#

what does a_n become? And what will the limit be?

frigid scroll
#

oh no

#

nvm

tepid pelican
frigid scroll
tepid pelican
#

Define a new sequence $b_{n}=\frac{1}{n^{2}+n}+\frac{2}{n^{2}+n}+ \dots +\frac{n}{n^{2}+n}$ and analyze it

clever fjordBOT
#

MæthIsAlwaysRight

tepid pelican
#

try simplifying that sum though

#

you can add up the fractions now

frigid scroll
#

i will write it now

tepid pelican
#

once you simplify it, you will be able to find the limit

frigid scroll
#

i dont know how to use the bot

#

n(n+1)/2/n^2+n

tepid pelican
frigid scroll
#

so thats n^2+n/2/n^2+n

#

ohhhhh

#

1/2

tepid pelican
#

$b_{n}=\frac{1}{n^{2}+n}+\frac{2}{n^{2}+n}+...+\frac{n}{n^{2}+n}=\frac{\frac{n\left(n+1\right)}{2}}{n^{2}+n}$

clever fjordBOT
#

MæthIsAlwaysRight

tepid pelican
#

now you could do the same thing for $c_{n}=\frac{1}{n^{2}}+\frac{2}{n^{2}}+...+\frac{n}{n^{2}}$

clever fjordBOT
#

MæthIsAlwaysRight

tepid pelican
#

and again find that the limit is 1/2

frigid scroll
#

n^2+n/2/n^2*

tepid pelican
#

and since
bn <= an <= cn, limit of an must be 1/2 as well

frigid scroll
#

wait but how is the limit of c_n 1/2

tepid pelican
#

$\frac{\frac{n\left(n+1\right)}{2}}{n^{2}}$

frigid scroll
#

n^2/2/n^2 + n/2/n^2

clever fjordBOT
#

MæthIsAlwaysRight

frigid scroll
#

still i dont see it

tepid pelican
#

$\frac{\frac{n\left(n+1\right)}{2}}{n^{2}}=\frac{\frac{n^{2}}{2}+\frac{n}{2}}{n^{2}}=\frac{1}{2}+\frac{1}{2n}$

clever fjordBOT
#

MæthIsAlwaysRight

tepid pelican
#

its just algebra

frigid scroll
#

wait right

#

ok

tepid pelican
#

in general, whenever you have polynomial / polynomial with same degrees, the limit is gonna be just the ratio of leading terms

frigid scroll
#

now i understand

#

thank you so much

#

.close

odd edgeBOT
#
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fair olive
#

Help

odd edgeBOT
#

Please don't occupy multiple help channels.

fair olive
#

I need help

#

which one is correct i am confidently sure mine is correct

ionic spoke
#

that one

fair olive
#

Yes

fair olive
viscid flint
#

wait how could it be negativ

#

you're multiplying two positif numbers

hexed patrol
#

btw u have two chats open with the same stuff

#

close one of them

fair olive
#

which one bro

#

🤥

hexed patrol
fair olive
#

It is closed thanx bro i was looking everywhere for that channel

viscid flint
#

his bounds are wrong

fair olive
viscid flint
#

y varies from 0 to 2, not 0 to 4

fair olive
#

yes i know

viscid flint
#

try it with the correct bounds and you'll probably get the same answer

fair olive
#

bc the f graph changes behaviour at x=2 that's why

#

i split the regions

viscid flint
#

yes, your approach is fine as well

#

,w int[0,2] integral[y²,y+2] xy dx dy

clever fjordBOT
viscid flint
#

there we go

fair olive
odd edgeBOT
#

@fair olive Has your question been resolved?

odd edgeBOT
#

@fair olive Has your question been resolved?

odd edgeBOT
#
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hexed wadi
odd edgeBOT
hexed wadi
#

i used quotient rule and got 1/9

#

why does the answer key have -1/9

#

where did i go wrong 😭

odd edgeBOT
#

@hexed wadi Has your question been resolved?

odd edgeBOT
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spiral roost
#

Does anyone have any hints on how to approach this?

spiral roost
#

@pastel dew C_5 minor would be constructing a minor (collapsing edges, deleting vertices or edges) from the graph and obtaining a cycle with 5 vertices (C_5).

#

Complete bipartite graph is just 2 vertices in the first set, n-2 in the second and every vertex in the first has an edge to every vertex in the second partition

pastel dew
#

interesting

odd edgeBOT
#

@spiral roost Has your question been resolved?

spiral roost
#

<@&286206848099549185> ?

odd edgeBOT
#

@spiral roost Has your question been resolved?

odd edgeBOT
#

@spiral roost Has your question been resolved?

odd edgeBOT
#
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opal path
#

is this -1/81

odd edgeBOT
fair olive
#

.reopen

opal path
#

bit too late for that lmao

pastel orbit
opal path
#

(f^-1)'(2) = 9

#

wait

pastel orbit
opal path
#

hold on

#

G'(x) = -(f^-1)'x/((f^-1)x)^2 = -9/9 = -1?

pastel orbit
#

indeed

#

well, that's too many parentheses for me to keep track of kekehands

#

,, G'(2) = -\frac{1}{(f^{-1}(2))^2} \cdot \frac{1}{f'(f^{-1}(2))}

clever fjordBOT
#

higher!

pastel orbit
#

that's just by the chain rule and inverse function thm

#

and when you evaluate this, you do indeed get -1

#

so congratulations!

opal path
#

wait a minute

#

actually wait yeah

#

cool thx lmao

pastel orbit
opal path
#

.close

odd edgeBOT
#
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pastel orbit
odd edgeBOT
#
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fallow flame
#

help pls

odd edgeBOT
royal herald
#

@fallow flame what have you tried

fallow flame
#

dividing 900 by 2

royal herald
#

for what reason

fallow flame
#

this is why I’m asking for help

royal herald
#

calculate how many grams of flour it takes to bake 1 bun

odd edgeBOT
#

@fallow flame Has your question been resolved?

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feral beacon
#

Jimmy has the letters for the state of MISSISSIPPI written on cards, one letter per card. He turns the cards over and mixes up the order. If he selects one card at a time without replacing the cards, what is the probability that he will spell the word MISS in order?

vale vortex
#

Low

#

Actually probably not

#

1/11 is chance for m

feral beacon
#

so here's my thing. I get 7920 as the total permutation, but this problem is messing with me so much because I'm not sure if the S's are considered different for the sake of the order

vale vortex
#

4/11 for i

#

4/11 for s

#

3/11 for s

feral beacon
#

but I know I'm supposed to calculate another permutation and then take the probability of that

#

1/495

3/365

1/165

48/495

#

those are the choices

vale vortex
#

Yea what i got was wrong

#

Who knows

#

Gl

feral beacon
#

I've already made the educated guess on it but I just want to understand the framework of these types of problems of finding the probability of the order through the permutation, if I was really going to take the actual real world probability I'd do weights of it but it definitely wont apply to this problem

#

@vale vortex bad response. don't answer if you can't provide insight

vale vortex
#

I’ll do what i want

#

It’s a open chat

#

Monopoly man

amber schooner
weary pelican
vale vortex
#

Never said it wasn’t

#

I didn’t plan on helping after i got it wrong anyway

weary pelican
#

So comply with their demand to leave if they do not want your help

vale vortex
#

Though this is a help channel

#

So probably stop arguing here

weary pelican
#

Oh we can ask moderators

#

do you want to?

vale vortex
#

Feel free I don’t give a shit I did nothing wrong

#

Bro is the kind of guy to tell on you to the teacher

weary pelican
#

I am a teacher in training

vale vortex
#

Adds up than

weary pelican
#

so...

amber schooner
#

then

elfin zodiac
#

Enough of this, the channel is not for discussion off topic

#

@feral beacon show your working

feral beacon
#

11 P 4 = 11 times 10 times 9 times 8 = 7920

#

after that I lose direction

weary pelican
#

ok

feral beacon
#

either 11^4 or any other idea doesn't add up to those choices, and I'm not sure if any of the repeating letters count as seperate values or the same

#

its so semantic and frustrating but I'm just going to assume that they are completely different for the sake of this instance

#

the following questions follow a format as " given a set of cards 1-10 randomly flipped around what is the probability you draw the 1,2 and 3 cards in order"

sand horizon
weary pelican
#

don't forget to do the same assumption when computing how many "MISS" you can make

feral beacon
#

its basically probability = numbered of desired permutations divided by overall permutations right?

weary pelican
#

well prob = number of desired cases/total number of cases yes

feral beacon
#

that comes to 7920/39 million roughly and that answer choice isnt there

weary pelican
#

when each case has the same likelyhood

#

wait

#

7920/3900000?

#

uhm

feral beacon
#

39916800 is 11!

weary pelican
#

but

#

11P4 is the total number of cases

#

you're choosing an arrangement of 4 letters out of those 11

#

and the "desired" cases is 'MISS'

feral beacon
#

yep yep

weary pelican
#

so

#

11! has nothing to do in this computation

feral beacon
#

oh RIGHT

#

but then at that point how am I discerning the order

#

because im my mind im thinking that permutation selects order from the 11

weary pelican
#

aren't you already discerning the order?

#

you did 11P4

#

so you chose the letters in order

#

11C4 would have been the incorrect choice since it doesn't care about order

feral beacon
#

11p4 is the total permutations for the entire set then

#

so within that amount how would i go about getting the order

weary pelican
#

11P4 is the number of ways to choose and order 4 things from a pack of 11 things

weary pelican
feral beacon
#

yeah

weary pelican
#

well

#

what should the first letter be

#

and how many choices for that

feral beacon
#

1/11

weary pelican
#

you mean 1

feral beacon
#

yeah

weary pelican
#

ok

#

how many choices for the next letter

feral beacon
#

i dont know i guess

weary pelican
#

I should be the next letter right?

feral beacon
#

i dont know if each 'I' is counted individually

weary pelican
#

if you counted them individually in the total count

feral beacon
#

which i'm assuming it is, so it would be the same probability of each letter for each yeah

weary pelican
#

you're gonna have to be consistent

feral beacon
#

i am

weary pelican
#

alr

feral beacon
#

for the sake of this there are no repeating letters

#

so the chance of getting the M is the same as getting the S

weary pelican
#

wait

#

what?

feral beacon
#

yes

weary pelican
#

If you're counting each letter as a separate letter

#

meaning MISSISSIPPI and MISSISSIPPI are different

feral beacon
#

yes

weary pelican
#

I think you lost me there

#

because either you're talking about "the same as getting an S"

feral beacon
#

my bad. i meant the probability is the same for each letter regardless of obvious appearance

weary pelican
#

okok

feral beacon
weary pelican
#

alr

#

so

#

how many choices do we have for the second letter

feral beacon
#

same amount of choices we would have for the first letter minus 1

weary pelican
#

bear in mind we're trying to make the word "MISS"

#

we said there was only one choice for the first letter, since there's only one M

#

now we're moving on to the second letter

#

how many choices do we have

#

(still trying to make "MISS")

feral beacon
#

honestly it might be better to explain it as 1234567891011

#

if i were trying to make 1-2-3-4 appear

weary pelican
#

sure but "MISS" isn't given by a single digit sequence

#

it could be 1234

#

it could be 1534

#

it could be 1362

#

all of those sequences lead to the same 4 letter word

feral beacon
#

in the class I'm in it is asking for a single digit sequence

#

a single digit sequence in order

#

given the amount of permutations what is the probability this order appears as exact in a random shuffle

weary pelican
#

so now the question is

#

how many sequences lead to MISS

#

that's what we were trying to find

#

notice that any sequence that spells "MISS" starts with "1"

#

because there's only one M to choose from

feral beacon
#

yeah yeah

weary pelican
#

so now when we have to choose the other "digits"

#

for example the second letter

#

how many possible digits can represent the second letter

feral beacon
#

my friend

weary pelican
#

it has to be an I

#

how many choices do you have

feral beacon
weary pelican
#

yes

feral beacon
weary pelican
#

wdym

feral beacon
#

all the i's and s's and p's are considered different

weary pelican
#

yes

#

so if you're trying to spell MISS

#

how many choices for the second letter

feral beacon
#

so I don't have choices between the i's or s's so the probability is the same

weary pelican
#

notice that it's an I

feral beacon
#

youre trying to solve the problem. I'm trying to understand the process of what to do after the first permutation

weary pelican
#

can the second letter be represented by the digit "3" for example

feral beacon
#

no

weary pelican
#

correct

#

because digit 3 is an S

#

how many digits can I choose from

#

to make the second letter

feral beacon
#

10

weary pelican
#

I doubt all of those 10 digits would make the second letter "I"...

feral beacon
#

1/10 is the probability of choosing that letter among what we have without replacement of this set

#

11 letters we start with

#

we hit on the M

weary pelican
#

ok, first of all

feral beacon
#

10 left, 1/10 to get the correct next letter

weary pelican
feral beacon
#

yes

weary pelican
#

so

#

say I already chose the M

#

there is "ISSISSIPPI" left

#

are you sure that I only have 1/10 chance

#

to get an I?

#

for my second letter

feral beacon
#

2345678910 is left

weary pelican
#

23456789-10-11 but yes

feral beacon
#

yeah

weary pelican
#

you're saying only one of those is the correct digit?

#

which one would it be?

feral beacon
#

yes

#

2

weary pelican
#

huh

feral beacon
#

bro

weary pelican
#

so 1534 isn't possible?

#

even though it spells MISS as well?

feral beacon
#

I'm obviously aware there are multiple letters that fit. I am asking you personally to treat this as a unique sequence with no repeating values. this problem uses two permutations

feral beacon
weary pelican
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so, to be clear

feral beacon
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and you said it yourself

weary pelican
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right now you're asking

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how many ways to get 1234?

feral beacon
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yes

weary pelican
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well, 1

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if you had to use in that order, MISS from MISSISSIPPI

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there is only one way to get it

feral beacon
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yes

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now what is the permutation after the total amount, what is the logic I am supposed to follow in constructing that

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11P4 is total permutations for an 11 element set, inside that what is the permutation of getting the first 4

weary pelican
#

again, if you have 11 different elements lined up

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there are 11P4 ways to pick and order 4 of them

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and there is only one way out of 11P4 to pick and keep the order of the first 4

feral beacon
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1/1980 is not a choice

weary pelican
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yep

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because the I in "MISS" can be reached by another I than the 2nd one

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and the Ss can be different Ss

feral beacon
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so this problem is explicity counting multiple instances of other letters

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right

weary pelican
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if you decide to treat the letters as different

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you have to change the meaning of "getting MISS"

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or at least understand that 1234 is not the only way

feral beacon
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but that still doesnt really get me to it

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Annie writes the numbers 1 through 10 on note cards. She flips the cards over so she cannot see the number and selects three cards from the stack. What is the probability that she has randomly selected the cards numbered 1, 2, and 3?

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this is basically the same question, although explicitly doesnt want replacement

weary pelican
#

not really the same question

feral beacon
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i do the first permutation to get 720

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its basically the same yeah

weary pelican
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because initially the cards are already distinguishable from each other

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here's a better one

feral beacon
#

process wise it is largely the same within the scope

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and I'm simply having trouble with identifying the second permutation to fill out the probability, that's really my issue

weary pelican
#

I can start with a simpler example:

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Annie wrote the word "MOM" with each letter on a separate card, turned the cards over and shuffles them. If she selects one card, what is the probability that it is "M"?

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here we wouldn't have to do the same "letters are distinguishable and become numbers" trick

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because there's much less of them

feral beacon
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please my friend. I really shouldn't have used that example to start. I want to know how to approach getting the second permutation among a set of unique elements

weary pelican
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and the problem is simpler

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are you talking about the original question?

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because there aren't just two permutations that work for MISS

feral beacon
#

okay i give in

weary pelican
#

if you want to compute the number of permutations that give MISS

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considering every letter is "different"

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you have 1 choice for the first letter since you only have one "M" to choose from

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you have 4 Is in total

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so you have 4 choices for the second letter

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then you also have 4 Ss

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so 4 choices for the third

feral beacon
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if every letter is different how can you have multiple of the same letter

weary pelican
#

I1 I2 I3 I4

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pick one of those for the second letter

feral beacon
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then they arent really different then are they

weary pelican
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you decided to treat them differently

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when you did 11P4

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but they are all "I" in the end

feral beacon
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oh

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so i did half the problem

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so I have to consolidate occurrences within the 7920 for the multiple letters

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4 total letters

weary pelican
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there are four total "different" letters that are Is

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so when you have to choose an I as the second letter

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you have four different "letters" to choose from

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or digits when you viewed it as 1234567891011

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choose between 2, 5, 8 and 11

feral beacon
#

right

weary pelican
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alright

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so just to recap

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there are 11P4 ways to make a 4-lengthed sequence of numbers from 1 - 11 without repeat

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and we're looking for the number of those 4-lengthed sequences

feral beacon
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yeah

weary pelican
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that will spell "MISS" in the end

feral beacon
#

yeah

weary pelican
#

so 1234 is one of those sequences but as we found out there are potentially more

feral beacon
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yeah

weary pelican
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so the sequences that spell MISS will always start with "1"

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so one choice for the first digit

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four choices for the second digit, right?

feral beacon
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yes and yes

weary pelican
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and then how many choices for third and fourth?

feral beacon
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4 and 3

weary pelican
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yes!

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I think we should now be close to the answer

feral beacon
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what so its 4 times 4 times 3 divided by 7920

weary pelican
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yep

feral beacon
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wow

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yeah that makes sense, thank you so much that helps a lot

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mentally i was thinking i had to do some other xPy calculation again so I was tunneling on that

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.close

odd edgeBOT
#
Channel closed

Closed by @feral beacon

Use .reopen if this was a mistake.

odd edgeBOT
#
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junior iron
#

hey

odd edgeBOT
junior iron
#

i have a few questions

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in algebra 2

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im struggling on

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can somone help me

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it is abbt square root functions

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