#help-10

1 messages · Page 508 of 1

obtuse pebbleBOT
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@lone shore Has your question been resolved?

obtuse pebbleBOT
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@lone shore Has your question been resolved?

halcyon tulip
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You have to express length in terms of breadth or vice versa.
$your length is 6m less then your breadth,
So if l=length
b=breadth
=>l=b-6
Now form equation with perimeter and solve it by substituting value of l or b$

obtuse pebbleBOT
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@lone shore Has your question been resolved?

timid silo
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with ur brain

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`So let the width be x
//They said the length of the rectangle is 6 less than 2x the width
//so we can say
2 * width - 6 = 2x - 6 = length

//We know how to calculate the perimeter right?

2(length + breadth) = 2(2x-6 + x) = 2(3x-6) = 6x - 12
//They said the perimenter is equal to 150m

//So now we know

6x - 12 = 150
x = 27

//Now we know -> breadth = x = 27
//So length is -> 2x - 6 = 2(27) - 6 = 48`

obtuse pebbleBOT
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@lone shore Has your question been resolved?

pure iron
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Only for c

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Can anyone help

slate zephyr
pure iron
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Huh

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Wdym

tardy epoch
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.close

obtuse pebbleBOT
#
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meager dagger
obtuse pebbleBOT
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@meager dagger Has your question been resolved?

obtuse pebbleBOT
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@meager dagger Has your question been resolved?

obtuse pebbleBOT
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@meager dagger Has your question been resolved?

obtuse pebbleBOT
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dull lichen
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how do i draw this, what are the steps

obtuse pebbleBOT
forest sinew
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pick a couple points on the line

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then connect them

dull lichen
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like random ?

forest sinew
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usually you make choices that give you nice numbers

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a line works like

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you pick an x, then you have no choice in y

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theres only one y that makes the equation true, once you pick an x

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it works the other way too, you pick a y, theres only one x

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a common choice is 0

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if y is 0, whats x?

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if x is 0, what does y have to be?

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then u have 2 points

dull lichen
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honestly idk

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there's a line
(1, 0) (1, 5)

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what do i do next

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gradient is 5-0/1-1= 5

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wait what do you do if there is no y intercept

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okay ill just avoid using a parallel line

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(1, 0) (0, 3)

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3-0/0-1= -3

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y=mx + c
y=-3x + 3

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what now

forest sinew
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oh lmc

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y=12-4x

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so if x = 0, what is y

dull lichen
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yeah thats what im tryna draw

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12

forest sinew
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youre gonna have to use your own scale

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if y is 0, what is x

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0 = 12 - 4x

dull lichen
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3

forest sinew
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nice

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id just write 12 somewhere

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on the y scale

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then connect those

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done and done

dull lichen
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huuh

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3 on the x and 12 on the y ?

forest sinew
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yea

dull lichen
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like that ?

forest sinew
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so uneven scales

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but why not!

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yea

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looks good to me

dull lichen
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does that work in all cases of y= ()- ()x

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?

forest sinew
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what just connect a couple point?

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2 points define a line so yea in general

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sometimes one of the variables is never 0

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but this is an easy problem

dull lichen
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okay

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but

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doesnt it usually look like y=mx+c

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why is it y=12-4x

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is it just a different way of writing it to create problems ?

forest sinew
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its the same

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y = -4x + 12

dull lichen
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🤦

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gotchu

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thanks

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.close

obtuse pebbleBOT
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obtuse pebbleBOT
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dull lichen
#

.close

obtuse pebbleBOT
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dull lichen
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how

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ping please

obtuse pebbleBOT
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Please don't occupy multiple help channels.

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timid silo
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I must say i dont know where to start any clue to how i might start would be helpfull thanks

nocturne minnow
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Apply log properties

oblique light
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This is simple

timid silo
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I know

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I know its simple but i dont know how

oblique light
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Lets try this

timid silo
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...

oblique light
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Take the base 10 exponent of both sides

timid silo
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whats that?

oblique light
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Like you have a=b rn. Make it 10^a = 10^b

timid silo
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I am aware of that thank you

oblique light
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Wtf

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How do you get that in your discord tray

timid silo
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Ill tell you after ive solved the problem ;)

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😄

oblique light
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Ok

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Do what I just said

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Now

timid silo
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10^a
a meaning?

oblique light
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The expression on the lhs

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Just raise 10 to the power of both sides of the equation

timid silo
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okay and a = log10(x^3) - log10(x)?

oblique light
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Yep

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So on the right you have 10^4. And on the left you have 10^(log10(x^3)-log10(x))

timid silo
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okay yep

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Ive got that

oblique light
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Now you can express the lhs as a quotient

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Because you have subtraction in the exponent

timid silo
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im unsure of what to do i dont fully understand

oblique light
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10^(5-3) = 10^5/10^3

timid silo
oblique light
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Thats something different

timid silo
oblique light
oblique light
timid silo
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oh alright but it still becomes 10^(5-3) = 10^5/10^3?

oblique light
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Just as an example

timid silo
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ohh

oblique light
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So we have 10^(log(x^3)-log(x))

timid silo
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yep

oblique light
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What can you do with that

timid silo
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I suppose i can express it as a quotient

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hehe

oblique light
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Yes

timid silo
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Yeah, problem is i dont truely know what that means

oblique light
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A quotient is something divided by something else

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4/5 is a quotient

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Fractions are quotients

timid silo
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ohh okay

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now i know that but... idunno

oblique light
timid silo
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Looking

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ohh holdon

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so
10^(log10(x^3)) / 10^(log10(x)) = 10^4

oblique light
timid silo
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is it
10^(log10(x^2)) = 10^4?

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bruh this was confusing asf my head no likey

oblique light
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Almost

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What is 10 to the log10 of something

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They cancel out

timid silo
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wait

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no

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whhat

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huh

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is it just something?

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meaning x^2 = 10^4

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?

timid silo
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?

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yeah

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so x^2=10^4

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10^4 = 10000 meaning x = 100

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?

oblique light
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Yes

timid silo
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Oh i thank you dearly wow. That felt harder than it was... hahaha

timid silo
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I belive you can thank people

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how?

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thank you

#

thanks

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.thank

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.close

obtuse pebbleBOT
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rocky sierra
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hi need help on this question

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oh nevermind

nocturne minnow
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Do you know what irrational means?

oblique light
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Money

nocturne minnow
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Not exactly

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So then you answered the question

worthy drum
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"20 points"?! is this a test? froggy

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For assurances, your 2nd attempt answer sounds best

obtuse pebbleBOT
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@timid silo Has your question been resolved?

slate zephyr
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@timid silo Do you know what irrational means like dldh06 said?

obtuse pebbleBOT
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obtuse pebbleBOT
tardy epoch
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Lram means what

unique solstice
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Whats a midpoint sum then

tardy epoch
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Write out the formulas for all three and compare them

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You can probably deduce the right Riemann sum from the left and trapezoidal terms +- some endpoint values

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My guess is you don't need to

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Just leave it as a variable

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What formula does your textbook give

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Mram

obtuse pebbleBOT
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@civic trellis Has your question been resolved?

tardy epoch
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Where does 1.5 come from

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It has to come from an equation

obtuse pebbleBOT
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dusk ruin
#

hello, I'm trying to set up my dfq for this, figured out 2lbs = k(0.75ft), so k=8/3 lb/ft

dusk ruin
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but idk how to get the mass, since pounds are force.

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any help?

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it looks like slugs, the imperial units for mass, can be found here as pounds/accel gravity

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so 2/32 = 1/16th of a slug

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,close

#

.close

obtuse pebbleBOT
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final urchin
obtuse pebbleBOT
final urchin
#

Have no idea how to solve

spiral maple
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what does mean and sd mean?

obtuse pebbleBOT
#

@final urchin Has your question been resolved?

final urchin
#

.close

obtuse pebbleBOT
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wanton dagger
#

Question 9)I don’t even understand the wording of this question, what are they asking?

crimson berry
#

how many hours are there during the weekend that this sign does not address

wanton dagger
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Saturday and Sunday combined?

crimson berry
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yeah they say the weekend ends at 12 midnight on sunday

wanton dagger
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Ok

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I found that Sunday is 12hrs

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How would I find for Saturday

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@crimson berry

crimson berry
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?

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show work

wanton dagger
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For Sunday the parking ends at 12 midnight and there are 24hrs in a day so I did 24-12 to get 12hrs

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Ok I got it thanks

#

.close

obtuse pebbleBOT
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radiant cobalt
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hi guys for ii, do i use integration by parts

radiant cobalt
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is it like this

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how did the x^3 dissapear??

nocturne minnow
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It didn't

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It made u = x^3

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You made u = x^2

radiant cobalt
radiant cobalt
nocturne minnow
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Still same thing, u sub

radiant cobalt
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ohh

radiant cobalt
nocturne minnow
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Yes

radiant cobalt
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ok

nocturne minnow
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Wait

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You can just u sub

radiant cobalt
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ok

radiant cobalt
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im confuse why does this question deosnt need by parts

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cuz theres algebra and trigo

nocturne minnow
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Not everything needs integration by parts

obtuse pebbleBOT
#

@radiant cobalt Has your question been resolved?

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obtuse pebbleBOT
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wintry stream
#

can someone please explain how to solve this using partial decomposition

nocturne minnow
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How well do you know PFD?

wintry stream
#

whats that?

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partial decomp?

nocturne minnow
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Partial fraction decomposition

wintry stream
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i dont think i know it that well

short spruce
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pershmaps learn it

nocturne minnow
#

This precalculus video tutorial provides a basic introduction into partial fraction decomposition. The full version of this video contains plenty of examples and practice problems with repeated linear factors and repeated quadratic factors. Partial fraction decomposition is the process of taking a complex fraction and breaking it into multiple...

▶ Play video
tardy epoch
#

@wintry stream feel free to ask questions about the video. I'm sure @short spruce has watched and understood it 10 times by now

obtuse pebbleBOT
#

@wintry stream Has your question been resolved?

obtuse pebbleBOT
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obtuse pebbleBOT
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tardy glen
obtuse pebbleBOT
tardy glen
#

How would it be possible to simplify/solve this

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Ive tried using geometric but the "a" changes

tardy glen
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So in a/(1-r) formula is almost relivent because of the 1/2^n but the numerator changes with n

thorn rose
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you can just factor it out

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thonk

tardy glen
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Wowi

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I feel stupid

thorn rose
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welp

tardy glen
#

Ive spent way to long om this

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Thank you

#

.close

obtuse pebbleBOT
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wide pelican
#

.o[en

#

.open

obtuse pebbleBOT
wide pelican
#

.close

obtuse pebbleBOT
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left canopy
#

Is it possible to compute the upper limit $b$ in an expression $$\int_{a}^{b}f(x)dx=t$$ where $b>a$and t is given?

quaint glen
#

wrong \ on your \int

warm shaleBOT
quaint glen
#

If you can compute an antiderivative of f, or at the very least compute its value at 0 and b it should be pretty easy. just solve F(b)-F(0)=t for b

brittle swan
#

if you know the antiderivative of f yes

left canopy
#

One sec, ill get on my computer to type this out faster

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Okay, so I know that $\int_{-3}^{b}2^{-x}dx=24$ and that the indefinite antiderivative is $-\frac{2^{-x}}{\log2}+c$

warm shaleBOT
left canopy
#

I would just compute the antiderivative at $x=0$, then?

warm shaleBOT
left canopy
#

Or would it be $x=-3$ in this case?

warm shaleBOT
quaint glen
left canopy
#

Right, and that would return the value of b. Makes sense, thanks and sorry for the sloppy tex

quaint glen
#

Uh there's more to do after computing -2^(-x)/log(2) when x=-3 if that's what you mean

left canopy
#

Oh, okay, what would be the next step? My bad

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Ah, just saw your message again

quaint glen
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just solve F(b)-F(-3)=24 for b

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where F is that antiderivative of 2^(-x)

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i gtg now sorry if you have anymore questions

left canopy
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np, ty

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When I compute this, I keep getting $b$ such that $a>b$. Any thoughts on why this would happen?

warm shaleBOT
left canopy
#

I'll close this as this is more of a computation problem ig.

#

.close

obtuse pebbleBOT
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wanton dagger
obtuse pebbleBOT
wet verge
sage geode
#

Have you tried anything so far?

wanton dagger
#

I know what a discriminant is but how would I use that here?

sage geode
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When does a quadratic equation have at least 1 solution?

wet verge
#

do u know the quadratic formula

wanton dagger
#

Ye

wet verge
#

from the quadratic formula what does the discriminant tell u

wanton dagger
sage geode
#

I said at least 1

wet verge
sage geode
#

Not just 1

wanton dagger
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When the discriminant is greater than zero, it has 2 solutions

sage geode
#

Yeah, so it has at least 1 (1 or 2) solutions when the discriminant is great than 0 or equal to it

wanton dagger
#

Ok

sage geode
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So you'd need the discriminant satisfy that inequality

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In this question

wanton dagger
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So I use the b^2 -4ac

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What would I place in place of b?

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(?K+1)

sage geode
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Yes in this case b, the coefficient of x, is k + 1

wanton dagger
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Ok

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What about in this case?

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I did this, is this correct?

sage geode
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Well first of all here you'd need k to be positive, because if it was negative then the parabola would go downwards

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Meaning it'll be negative somewhere

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And secondly, if a quadratic is always positive, it means that it has no real roots

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Do you'd need its discriminant to be negative

wanton dagger
#

Ok

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So what should I do first then?

sage geode
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What'd the discriminant of the quadratic be in this case?

wanton dagger
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(3k)^2 - 4(k)(9)

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?

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@sage geode

sage geode
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Yeah, now you need 9k^2 - 36k < 0

wanton dagger
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Ok

sage geode
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So k^2 - 4k < 0

wanton dagger
#

Yep

sage geode
#

Oh yeah btw you'd also need to consider the case when k = 0, because the discriminant and quadratic formulas don't work in that case

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As you can see k = 0 works

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Because 9 > 0

sage geode
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The signs won't flip because k is positive

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As I said earlier

wanton dagger
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But this is the answer

sage geode
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Yes it is

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You get k - 4 < 0 after dividing

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So k < 4

wanton dagger
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I’m a little confused

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Can you check my working out

sage geode
#

In the photo you sent you made the discriminant positive

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Meaning the quadratic does have roots

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Which is opposite of what we needed

wanton dagger
#

So you mean to say the signs are “less than?”

#

So I got this

#

Thanks for your help

#

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feral swallow
#

Any videos about this topic

obtuse pebbleBOT
feral swallow
#

Question 3

#

Or can someone explain

idle thunder
#

Use laws of indices

feral swallow
#

Thank you so much

idle thunder
#

@feral swallow whats this? 👀

#

is this a Examination

feral swallow
#

No?

#

Book lmao

#

Examination practice questions💀

idle thunder
#

👌 catGiggle

feral swallow
#

Is the answer for the first one p × q?

#

Ohh yesss

obtuse pebbleBOT
#

@feral swallow Has your question been resolved?

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wise pagoda
#

Can anyone explain how to solve this combination problem:
How many ways can you select 4 letters in the word "connection"

wise pagoda
wise pagoda
fervent comet
#

Oh wait this is simple

#

Wait nvm

solar axle
#

i think it's 10C4 divided by the ways you can choose each repeat, so divided by 2! * 3!

solar axle
#

unless there are any letters repeating that aren't 'n' and 'c'

wise pagoda
#

wait let me give you the video i followed

wise pagoda
solar axle
#

2! as well then

#

2 * 2 * 6 = 24

wise pagoda
#

no based on what i watched you cant just devide them i know what you mean but i think its just applicable to permutations

solar axle
#

depression

#

yea i think ur right i get a fractional number of ways

wise pagoda
#

i think its just applicable for permutations if you are to arrange the whole word

solar axle
#

yea

wise pagoda
#

my final answer there is 71 i added a couple of possibilities that are not in my solution

solar axle
#

hmm ok

#

i will figure out how many it is

#

1 sec

wise pagoda
#

but idk if what i did is right

solar axle
#

i think it's... 48?

wise pagoda
#

how?

solar axle
#

bash

#

wait no

#

i got 53 this time

#

interesting

#

literal bash

wise pagoda
#

hm

#

i got 50 on the first

#

i asked a college student and he got 55

solar axle
#

lol

#

i mean

#

my method is literally

#

"hey let's count every single way to do it"

wise pagoda
#

thats the right answer but how do i put it in equation

#

HOLY CRAP I GET IT NOW

#

so the correct answer is 53

wise pagoda
#

the possibiity of getting
2n, 2o or 2c

#

which is 3

#

so 50 + 3 = 53

#

thankyouu

#

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maiden veldt
#

could someone help me with this

obtuse pebbleBOT
lusty goblet
obtuse pebbleBOT
#

@maiden veldt Has your question been resolved?

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timid silo
#

Hello, how i can find Y ?

obtuse pebbleBOT
grave berry
#

cuz they are in same segment

timid silo
#

oh ok thx

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

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mighty echo
#

what if all the a's = 0 and all the b's = 1, then the equality holds but the equation has no solution for x? is this a mistake?

lusty goblet
#

Seems to be a mistake. The correct statement is supposed to be:
... if the sequence a and the sequence b is linearly dependent.

#

Whoops, a typo that completely changes the meaning.

mighty echo
#

what do you mean by sequence a and sequence b is linearly dependent? you mean if the set of vectors formed like <ak, bk> is linearly dependent?

worthy comet
#

no, he means that the two vectors $(a_1, \dots, a_n)$ and $(b_1, \dots, b_n)$ are linearly dependent

warm shaleBOT
#

Alexander42

mighty echo
#

ok i see

#

thanks

#

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timid silo
obtuse pebbleBOT
timid silo
#

Can anyone explain this to me in the dumbest way possible

#

Is this a transformation based on the basis

#

Is this just explaining matrix multiplication in regards to a transformation with the basis?????

#

Ping me if you can help!

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

spiral maple
#

the scalars that make up the linear combination becomes the coordinate vector

timid silo
spiral maple
#

like if I have $f=1+2t-t^2$ and write this wrt the canonical basis, then $[f]_B=[1,2,-1]^T$

warm shaleBOT
timid silo
#

Ahhhhh ok

#

Ur smart

#

Ty 👍 👍

#

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tropic lava
#

.help

obtuse pebbleBOT
#

Commands:
clopen: .close, .reopen
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

tropic lava
#

I have 2 values for a interquartile range

Q1=81 Q2=151

How do I solve?

tropic lava
#

Sorry. How do I find the outliers

#

The full question being asked is

For a set of observations, Q1 = 81 and Q3 = 151. Values greater than X and less than Y are possible outliers

#

What would the formula for solving this be?

hasty linden
#

to find outliers take Q3-Q1 = IQR *1.5 to find outliers

tropic lava
#

Thx

#

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tropic lava
#

.open

tropic lava
obtuse pebbleBOT
tropic lava
#

So 151-81=70

70*1.5= 105

But thats 1 value? I need to find 2 outliers

obtuse pebbleBOT
#

@tropic lava Has your question been resolved?

tropic lava
#

<@&286206848099549185>

daring rock
#

All you need to do now is add 105 to your Q3 and subtract 105 from your Q1

#

Any values higher than that ceiling or lower than the floor are outliers

tropic lava
#

Thanks.

daring rock
#

No problem

tropic lava
#

So it be greater than 186 and less than 46?

#

Juzt making dure

#

Cause 105+81=186
And
105-151=46

#

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vocal verge
#

How to do this?

obtuse pebbleBOT
vocal verge
#

We're learnt sine n cosine rule
We've learnt radiant:
Length of arc: S = r (theta)
Area of sector: 1/2 (r^2) (theta)
Area of segment: 1/2 (r^2) [(theta) - sin(theta)]

obtuse pebbleBOT
#

@vocal verge Has your question been resolved?

vocal verge
#

<@&286206848099549185>

obtuse pebbleBOT
#

@vocal verge Has your question been resolved?

obtuse pebbleBOT
#

@vocal verge Has your question been resolved?

obtuse pebbleBOT
#

@vocal verge Has your question been resolved?

pine sail
#

Well use trigonometry to calculate OAP

#

$SinA =OP/OA$ correct?

#

There you have it then.

warm shaleBOT
#

Sakata Yaksha

pine sail
#

same For ODQ

obtuse pebbleBOT
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wispy heath
#

blue area must be calculated. I know I have to do primitive functions subtracted from eachother, but im a bit stuck.

tardy epoch
#

show what you've got so far

wispy heath
#

I made both functions primitve:

#

However I quickly realised that doing ln0 gives math error.

#

The area under the y1 line from 0 to 2 is 8/3.

#

And the area under the y2 line from 0 to 2 is, well, undefined?

tardy epoch
#

might be better to separate your problem into two steps

#
  1. integral setup
#
  1. solving the integral
#

what'd you get for 1?

wispy heath
#

8/3

#

which seems reasonable.

#

Dividing the problem might be the best solution

#

Just making sure that I have all functions ready

#

Oh my

#

I just found out how to solve it

#

I'll try a method

#

Taking the area from y2(0 to 2) and subtracting it from y1, will give me that large empty space to the left.

#

Then I just subtract that area from y2's total area.

obtuse pebbleBOT
#

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sudden finch
obtuse pebbleBOT
tardy epoch
#

Use double angle formula twice

sudden finch
#

Can you ellaborate on how to so?

#

If you don't mind

slate zephyr
#

Don't we need triple angle formula?

tardy epoch
#

If they've learned it sure

slate zephyr
#

If we apply double angle formula twice

#

we just get sin(4x) though, right?

sudden finch
#

Heres my log tables

tardy epoch
#

sin(3t) = sin(t+ 2t)

#

That's once

#

Then again on sin(2t)

slate zephyr
#

That's angle sum formula

tardy epoch
#

Ah shit

#

Yea angle sum formula twice

sudden finch
slate zephyr
#

😄

sudden finch
#

Which one do I use?

tardy epoch
tardy epoch
sudden finch
#

Can you go into more detail

slate zephyr
#

A = 2x, B = x, apply "compound angle" formula for sin from your sheet .

sudden finch
#

Where are you getting 't' from?

slate zephyr
#

Riemann named it t in his text, it's called x for you.

sudden finch
#

Wait what happens to the cos's tho?

#

Man can someone do it on a page I think i'm just dumb

slate zephyr
#

We are starting with the sin.

sudden finch
#

Ok I wrote that

slate zephyr
#

sin(3x) = ...

#

What did you get so far?

sudden finch
#

I'm only at sin(x+2x)

slate zephyr
#

x+2x = 3x

sudden finch
#

Man I'm so confused

slate zephyr
#

You can take your time. 🙂

sudden finch
#

I need help please hahaha

#

So

#

What do I do next?

slate zephyr
#

We are trying to find another expression for sin(3x)

#

similarly for cos(3x) later

sudden finch
#

Ok ok

slate zephyr
#

afterwards we can solve the equation system.

sudden finch
#

So just sin 3x turns into wht

slate zephyr
#

"When asking for help, do not insist with getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer." from the rules 😮

sudden finch
#

Oh sorry

#

I'm just ina hurry to understand

slate zephyr
#

Hurry is bad in mathematics

sudden finch
#

Ok my bad I'm sorry

slate zephyr
#

sometimes we just take time to unconfuse ourselves

#

this is true at all levels of matheatics.

sudden finch
#

I'm just really confused and really stressing thats all

#

Ok so lets start again

#

What do we do with the sin3x at first

#

We apply the compound formulae to it?

slate zephyr
#

3x = 2x + x and "compound angle", yes

sudden finch
#

Correct?

slate zephyr
#

I would suggest starting a separate calculation for that

sudden finch
#

Ok

slate zephyr
#

sin(3x) = sin(2x + x) = ...

sudden finch
#

Sin2x + sinx?

slate zephyr
#

no

slate zephyr
sudden finch
#

The sin (a+b)?

slate zephyr
#

ye

#

A = 2x, B = x

sudden finch
#

So

#

= sin2x cos x + cos2x sin x?

slate zephyr
#

yeah

sudden finch
#

Oh ok thats the first line right?

#

Thts only for sin 3x?

slate zephyr
#

yeah

sudden finch
#

Ok how do we do the next part

slate zephyr
#

and we are not done yet because now there is sin(2x) and cos(2x)

#

we need to replace those too, we only want sin(x) and cos(x).

#

We want to reduce the number of unknowns

#

and sin(x) and sin(2x) are like very different unknown numbers.

sudden finch
#

So what do we get rid of?

slate zephyr
#

sin(2x)

#

Check your sheets if you find something.

sudden finch
#

I don't rly know what I'm looking for

slate zephyr
#

something with sin(2x)

sudden finch
#

Ok lemme see

#

Wait

#

I found sin2a =

severe dune
#

What’s the question

sudden finch
#

In double angle fomulae

slate zephyr
sudden finch
#

=2*

#

Could this come in any use?

slate zephyr
#

Hm I think there is something better

severe dune
#

Have u tried using de moirés theorem to expand it

slate zephyr
#

You are right that we can use this

sudden finch
#

Sin 2a = 2sin A cos A?

severe dune
#

In terms of powers and then divide

slate zephyr
#

but tan is something new yet again.

slate zephyr
sudden finch
#

Nope

#

We havn't done that yet

#

Its on our course but we havn't done it yet

slate zephyr
#

But Omar is right in that complex numbers are really good for these kind of tasks.

#

They also make it superflous to keep such tables in mind but that's not today's lesson. 🙂

sudden finch
#

So

#

Here i'll send a pic

slate zephyr
#

ok

sudden finch
#

Right?

slate zephyr
#

let's ask Wolfy

#

,wolf simplify sin(3x)

sudden finch
#

Oh thats very complicated

slate zephyr
#

hm looks different, did something go wrong?

#

Wolfy is making 3 suggestions

#

it's just 3 sin(x) cos²(x) - sin³(x)

#

le me see, maybe it's actually the same

sudden finch
#

Oh ok I just needed to join them together

slate zephyr
#

I think it's different 😦

#

Okay let me try work it out per hand

sudden finch
#

Its awkward

slate zephyr
#

sin(3x) = sin(x) cos(2x) + cos(x) sin(2x)

sudden finch
#

Is that it final or....

slate zephyr
#

= sin(x) (cos²(x) - sin²(x)) + cos(x) 2 sin(x) cos(x)

severe dune
#

Wait what year are you in

sudden finch
#

I'm from ireland which is my last year of highschool for america

slate zephyr
#

I am a master student.

severe dune
#

I’m form the uk not sure how it works there

sudden finch
#

I'm impressed

severe dune
#

Have a look at complex numbers it’s isn’t that difficult

#

Actually much easier way

sudden finch
#

Is there a way without using complex numbers?

severe dune
#

Yes

slate zephyr
#

I agree with Omar00 but I think the teacher will not be happy.

#

Yes

sudden finch
#

Thats what I'm thinking

slate zephyr
#

We are doing it atm

#

Also to fully explain complex numbers to you will take us some time.

sudden finch
#

Ye I'l lleave it up to the teCher

#

Teacher

#

Ok so back to where we were

slate zephyr
sudden finch
#

Lemme see

#

Why is there a bracket

slate zephyr
#

because we had

#

sin(x) cos(2x)

sudden finch
#

Oh I get it

slate zephyr
#

which is the same as

#

sin(x) ((((cos(2x)))))

#

then use cos(2x) = cos²(x) - sin²(x)

severe dune
#

You’ve done this right

slate zephyr
#

which is what Wolfy told us I think

sudden finch
slate zephyr
#

ye

sudden finch
#

Ok lemme register this 2 seconds

severe dune
#

This uses no complex numbers only what you’ve been taught

sudden finch
#

Ok that makes it more understandable

slate zephyr
#

,rotate

warm shaleBOT
slate zephyr
#

@severe dune Please slow down a bit. See rules, please no giving away the answer.

sudden finch
#

Ok lets move onto cos3x

severe dune
#

My b

sudden finch
#

Sin x just stayes by itself?

severe dune
#

Same rule for cos 3x

slate zephyr
#

yeah

#

it's basically the best oppertunity to see if you learnt the principles

severe dune
#

What do u right for your final proof sentence or words like out of curiousity

#

Do u write lhs proven

sudden finch
#

You asking me?

severe dune
#

Yeh

sudden finch
#

Therefore that equation = 2?

slate zephyr
#

lhs proven? I think in this case you would give a set of possible answers.

sudden finch
#

Its not asked in the question i don't think

slate zephyr
#

like x = { pi n + pi/4 | n integer } (This is an example, not the solution lol)

sudden finch
#

Is the final proof sentence needed?

severe dune
#

In exams I’m pretty sure

slate zephyr
#

From school's perspective it's not a proof though but a "calculation".

#

In Germany we never wrote answer sentences in the final years.

severe dune
slate zephyr
#

Wow okay that's rude 😄

sudden finch
#

We I don't think thats needed here

slate zephyr
#

I know that I got into trouble in earlier years because they wanted us to write "Question sentences" and "Answer sentences".

sudden finch
#

Ye*

#

Can I ask out of curiousity i'm still not there yet but

severe dune
sudden finch
#

Does the last like 2(cos^2x+sin^x) the bracket just cancel itself out?

#

Line^

#

Just leaving 2?

severe dune
#

Yes

slate zephyr
severe dune
#

Sin^2 x

sudden finch
#

Oh yes

slate zephyr
#

yeah sin² + cos² = 1

sudden finch
#

This rule

severe dune
#

They will never get enough of that identity

slate zephyr
#

yeah it's the most basic rule and very good.

sudden finch
#

Ahh then its 2(1) = 2

severe dune
#

Yup

slate zephyr
#

@sudden finch, did you finish?

sudden finch
#

Yes thanks a lot guys

#

I appreciate it a lot

slate zephyr
#

,wolf simplify cos(3x)

unique solstice
#

,w unsimplify cos(3x)

warm shaleBOT
unique solstice
sudden finch
#

.close

obtuse pebbleBOT
#
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slate zephyr
obtuse pebbleBOT
#
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weary nest
#

Yo how do I form a radical extraneous equation

obtuse pebbleBOT
weary nest
#

I just can't get my head around it

obtuse pebbleBOT
#

@weary nest Has your question been resolved?

obtuse pebbleBOT
#
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#
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timid silo
obtuse pebbleBOT
timid silo
#

Q: use a graph to solve the equation on the given interval.

#

help i don't understand the question

severe dune
#

Draw the graph of 6cos(x+pi/6)

timid silo
#

what does viewing window mean

severe dune
#

Not exactly sure perhaps it’s stating the domain

timid silo
obtuse pebbleBOT
#

@timid silo Has your question been resolved?

timid silo
#

aight

#

.close

obtuse pebbleBOT
#
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obtuse pebbleBOT
#
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obtuse pebbleBOT
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full ledge
#

Hello, im just confused on this problem. How can you get the measurement when theres nothing given? And does the pentagon make a difference?

idle thunder
#

We know one of the interior angles of a pentagon 👀

full ledge
idle thunder
#

The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where n is the number of sides

#

That means one of the interior angles should be

idle thunder
#

Yeah

full ledge
#

Ohhhhhh

idle thunder
#

What's that simplified

full ledge
#

Man my teacher didnt give a single solution for this, all she said was to research it on the web

#

Thanks man

idle thunder
#

Did you get the interior angle?

full ledge
#

Wait imma write it down first

full ledge
idle thunder
#

That's the sum of the interior angles

#

Since its a regular polygon, what would be one of the interior angles of the pentagon?

idle thunder
#

Awesome

#

So now we know 5 angles of whats given

full ledge
idle thunder
#

Those are all sides

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Not angles

full ledge
#

Oh my bad

idle thunder
#

These are all 108 since its a regular pentagon

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So use them geometry rules

full ledge
#

Man im still confused even with the given measurements

#

Is m∠PTR, m∠RTS, and m∠QTS all 162°?

obtuse pebbleBOT
#

@full ledge Has your question been resolved?

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light karma
#

is the singularity of a function at a point just whether or not it divides by zero?

light karma
balmy mortar
#

A singularity is where the function is undefined I guess?

#

Due to dividing by 0

obtuse pebbleBOT
#

@light karma Has your question been resolved?

light karma
#

.close

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fathom harbor
#

why cant u divide by 0

obtuse pebbleBOT
fathom harbor
#

why

nocturne minnow
#

It breaks math

slate zephyr
fathom harbor
fathom harbor
slate zephyr
#

but 10/0 = a

fathom harbor
#

but whats a

slate zephyr
#

some number

#

let's say

#

10/0 = 0

fathom harbor
#

yes

slate zephyr
#

then this means 10 = 0*0

#

see if we have 100 apples

nocturne minnow
fathom harbor
slate zephyr
#

and divide them for 10 persons

slate zephyr
#

then 100 / 10 = 10

fathom harbor
#

best channel

slate zephyr
#

because 10 * 10 = 100

fathom harbor
#

ill go watch video

#

brb

#

also

balmy mortar
#

It's just the way math is defined.

fathom harbor
#

0 / 5 = 0

balmy mortar
#

You can define x/0 = 0 for all x if you want, but some rules would break

#

and you would have to write exceptions for a lot of things

fathom harbor
#

so why isnt 5 / 0 = 0

slate zephyr
#

Yeah an advanced note is also that in certain parts of complex analysis one can divide by 0.

balmy mortar
#

just to accommodate this one rule

slate zephyr
#

Also you can make limits with 0.

fathom harbor
#

wut is limit

slate zephyr
#

you look at where things go

balmy mortar
#

what logic is this

fathom harbor
unique solstice
#

Five goes into zero 0 times

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Zero goes into five ????? times

timid silo
#

you cant divide a number by nothing lmao

fathom harbor
#

also why does 0 / 5 = 0

slate zephyr
#

I think @fathom harbor managed to hit some topic that triggered every mathematician checking the channel lol.

unique solstice
#

Because 5 * 0 = 0

fathom harbor
#

but why is 0 /5 = 0

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i mena

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0

unique solstice
#

Because 5 goes into 0 no times

slate zephyr
#

see my example above with the apples

nocturne minnow
#

How many times does 5 go into 0?

fathom harbor
balmy mortar
#

How many times does 5 go into 1?

fathom harbor
balmy mortar
#

1/5 = 0 remainder 1

nocturne minnow
#

Do you know division?

fathom harbor
slate zephyr
#

if we say 77 / 11 = 7 we mean by that, that if someone has 77 and divides them equally among 11, everyone gets 7. Because 11 * 7 = 77. You cannot play this game if 11 would have been 0.

balmy mortar
#

1 = 5x0 + 1

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Have you seen remainder division?

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6 = 5x1 + 1

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so 6/5 is 1 remainder 1

fathom harbor
balmy mortar
#

3 = 5x0 + 3

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3/5 = 0 remainder 3

slate zephyr
fathom harbor
#

0 / 0 =

#

also that

nocturne minnow
balmy mortar
#

Doesnt exist, cannot divide by 0

fathom harbor
#

ok i forgor

balmy mortar
fathom harbor
#

ok

balmy mortar
#

0/5 = 0 r 0

fathom harbor
#

ok

balmy mortar
#

Hence 0/5 = 0

fathom harbor
#

ok

slate zephyr
#

Keep in mind also that you can define anything in mathematics, one can say 0/0 = 0 for example. But this makes trouble everywhere we divide something so we generally don't like that.

fathom harbor
#

wait what about

#

if i cant divide by 0

#

can i divide by negative numbers

#

like

#

-1

#

-2

nocturne minnow
#

You mean like 5/-1?

balmy mortar
#

u can divide by anything except 0

fathom harbor
#

ye

fathom harbor
#

-1 is less than 0

nocturne minnow
#

Zero breaks math

timid silo
balmy mortar
#

-1 goes into 5, -5 times

fathom harbor
slate zephyr
#

Okay I am out, nobody seems to read my expanations here. 😄

balmy mortar
#

-5 x -1 = 5

fathom harbor
#

i do read them

fathom harbor
#

why

timid silo
#

this is hurting my brain

fathom harbor
nocturne minnow
balmy mortar
#

...

fathom harbor
nocturne minnow
#

It seems like you are underage, like under 13

fathom harbor
#

i am 13

nocturne minnow
#

To be asking those questions

fathom harbor
slate zephyr
unique solstice
nocturne minnow
#

You should have learned some sort of concept on negative numbers

nocturne minnow
fathom harbor
nocturne minnow
#

Then videos, khan academy is good

#

For teaching

fathom harbor
#

ok

balmy mortar
#

Alright negative multiplication right?

fathom harbor
balmy mortar
#

Imagine i borrow money from you

fathom harbor
#

yes

balmy mortar
#

You give me $1

#

So you can write -$1

fathom harbor
#

ye

balmy mortar
#

man this is not easy to explain

timid silo
#

positive * negative = negative
negative * positive = negative
negative * negative = positive
positive * positive = positive

#

this might help a bit - same applies to division

balmy mortar
#

no im gonna have to scrap that example for now

fathom harbor
#

ok

timid silo
#

two same = positive
two different = negative

fathom harbor
timid silo
#

you have to memorize that

fathom harbor
#

why

nocturne minnow
timid silo
#

you use it in math until you die

balmy mortar
#

Ok ok how about this

fathom harbor
balmy mortar
#

say you have some assets

#

That is worth some positive amount ok?