#help-10

1 messages · Page 23 of 1

wild swallow
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your job is to verify if the formula provided gives the same results

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which also verifies that it is a valid way to write the square

patent stump
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how do I do that/

wild swallow
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construct a truth table

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list all combinations of inputs and their corresponding outputs

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see if they're the same

patent stump
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ok

obtuse pebbleBOT
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glad karma
obtuse pebbleBOT
twin shard
#

Thanks!!

glad karma
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I was wondering if anyone could explain dimensional análisis like dimensions and the graphing thing I’m not sure how it’s called

robust sleet
# twin shard Thanks!!

By doing that (2x+1) in numerator and denominator scrap off and I think that's furthest simplification u can do

robust sleet
glad karma
robust sleet
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Your graph

glad karma
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ehh im not sure the teacher just said something or rise over run and left us at that

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from what I understood you find the positions in the graph or whatever and put them in rise over run format to figure out its speed

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but im mostly confused about conversions

robust sleet
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so we have km hm dam m dm cm mm

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To go from one lower to next one is x10

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1 m is 10 dm

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So we have 158.2cm

obtuse pebbleBOT
#

@glad karma Has your question been resolved?

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glad karma
#

thank you

#

!!!

obtuse pebbleBOT
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severe dune
obtuse pebbleBOT
severe dune
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I don't understand why the answer is the last one

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Can anyone please explain it to me

plain stag
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In the last one, after you separate, you have 1 - (integral)

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Since your approximation overestimates the integral, when you subtract the estimate, you're subtracting a slightly larger number

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And when you subtract a larger number, the difference becomes smaller

severe dune
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but isnt -fx just a reflection

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in the x axis

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so wouldnt the overestimation,be the same

plain stag
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You're overestimating the integral, but that estimate is being subtracted

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Like let's say the integral is numerically 1.9, but your estimate gives 2

severe dune
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ohhhhh

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because its negative#

plain stag
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The actual value of d is -0.9, but your approx. gives -1

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Which is smaller

severe dune
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oh ok ok got it

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thanks man

plain stag
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Np

severe dune
#

.close

obtuse pebbleBOT
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versed gyro
obtuse pebbleBOT
versed gyro
#

i need help factoring this please

pallid flame
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first what is x^2 - 22x + 121 factored @versed gyro

versed gyro
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(x-11)(x-11)?

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what about y^2

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what do i do with that

pallid flame
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so (x - 11)^2

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now how do you factor a^2 - b^2 @versed gyro

versed gyro
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uhh

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i duuno

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im stuck 😦

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<@&286206848099549185>

astral ivy
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@versed gyro are you familiar with “difference of squares”

versed gyro
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yes

obtuse pebbleBOT
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@versed gyro Has your question been resolved?

versed gyro
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i give up on life

obtuse pebbleBOT
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@versed gyro Has your question been resolved?

obtuse pebbleBOT
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thin pine
#

Is matrix A invertible if $L_a$ is invertible

obtuse pebbleBOT
thin pine
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also what is L_a mean

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$\text{L_a}$

weary delta
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L_A usually denotes the linear transformation defined by the matrix A

thin pine
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can you explain that

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all matrix transformations are linear correct?

warm canopy
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it might also be the linear map that is left multiplication by A

weary delta
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All matrices with constant entries define some linear transform

warm canopy
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no way to know without context

weary delta
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Yeah, I just took a look at my old lecture notes and the only L_a was the linear transformation, but who knows what yours means

obtuse pebbleBOT
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@thin pine Has your question been resolved?

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bitter slate
obtuse pebbleBOT
bitter slate
south inlet
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(-1)^2

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is -1 * -1

bitter slate
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oh I see

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so -3-10+13

south inlet
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yeah

bitter slate
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hmm the answer isnt 20

south inlet
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-3 - 10 + 13 isnt 20

bitter slate
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whoops

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thanks

#

.close

obtuse pebbleBOT
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obtuse pebbleBOT
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ornate orbit
obtuse pebbleBOT
ornate orbit
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I got up to here but idk where to go now

hardy widget
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for f+g you're right

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for f-g it's the same logic, just subtract

ornate orbit
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Yea but how would I get domain

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For either one

hardy widget
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They're polynomial functions, meaning that there's no value that when raised to a positive integer power that will result in something non-permissible
this is why the domain of all polynomials is the set of reals

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and that applies to this

ornate orbit
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So domain is just all reals

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For both of these

hardy widget
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ornate orbit
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Ty

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.close

obtuse pebbleBOT
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obtuse pebbleBOT
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shadow estuary
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solve for x

obtuse pebbleBOT
shadow estuary
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can someone pls help me

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i need to solve for x

worthy cargo
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maybe I'm dumb but I think it needs to equal to something to find a value for x

shadow estuary
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the whole thing is automatically equal to 0

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i think

worthy cargo
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oh ok

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well what have you tried so far, anything?

shadow estuary
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i tried multiplying the denominators from all equations with each other

worthy cargo
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also again I may be wrong but if the fraction is equal to zero then you only care about the numerator since the only thing that divides into zero is zero

shadow estuary
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wdym

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wait could u try solving it and tell me what u get pls

worthy cargo
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ok well you could plug it into wolfram alpha

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but think about it logically

shadow estuary
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my guy what is a wolfram alpha??

worthy cargo
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it is online calculator

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but only thing that divides into zero is zero

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so you only have to set your numerator to zero and solve that

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is that easier to solve for you?

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0/y = 0 for all values of y except for 0 in which case it is undefined

shadow estuary
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so there is no zero?

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its just undefined?

worthy cargo
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no

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you are telling me the equation is equal to zero right

shadow estuary
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bro im not looking for imaginary solutions btw

shadow estuary
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well nvm

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the paper never says its = to 0

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it just says to solve this

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CHRISSY WAKE UP

timid silo
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bro is right

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if its equal to 0 only numerator counts

worthy cargo
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,w 2+2

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oh ok

worthy cargo
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just checking if that's the cmd

shadow estuary
worthy cargo
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,w (((2x)/(x-1) - (3/x))/((-2)/(x-1) - 4)) = 0

worthy cargo
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what divides into 0 that is not 0

timid silo
worthy cargo
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oh that too

timid silo
worthy cargo
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yeah there are only imaginary solutions

timid silo
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to simply it tho

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,w (((2x)/(x-1) - (3/x))/((-2)/(x-1) - 4))

timid silo
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oh damn

shadow estuary
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i think my teacher is a son of a bitch

timid silo
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idk how this works

worthy cargo
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you forgot =0

worthy cargo
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I think yours works

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I just put too many parenthesis cuz I hate inputting stuff like this with keyboard

shadow estuary
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i dont understand

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when do u cancel the denominators?

timid silo
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when it equals 0

shadow estuary
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i know

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but how did u cancel the denominator

worthy cargo
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0 * anything = 0 so if you multiply that messy denominator on both sides it cancels

shadow estuary
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i think i did something wrong when i did it

timid silo
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if you have $\frac{a}{b}=0$ you multiply both sides by $b$ you get $a=0$

warm shaleBOT
#

jswatj

worthy cargo
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yeah latex is helpful I am on phone and lazy as well

shadow estuary
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ok

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so what are the solutions again?

worthy cargo
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,w (((2x)/(x-1) - (3/x))/((-2)/(x-1) - 4)) = 0

worthy cargo
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those

shadow estuary
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did u use the pythagorean theorem to get that??

worthy cargo
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bro what is your teacher teaching you

shadow estuary
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its in pythagorean theorem format

worthy cargo
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is it??

shadow estuary
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looks like it

timid silo
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if you want to simplify it, its just $\frac{\frac{2x}{:x-1}-\frac{3}{x}}{-\frac{2}{x-1}-4:}=\frac{2x^2-3x+3}{-4x^2+2x}$

worthy cargo
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that's just how you write complex numbers

warm shaleBOT
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jswatj

shadow estuary
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and then what do u do??

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after its simplified to that

timid silo
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then thats it

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if all you're doing it simplifying it

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thats as far as you can go

shadow estuary
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how do u solve for x

worthy cargo
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oh yeah maybe they want you to simplify

shadow estuary
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when its simplified like that

timid silo
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if there's no equation then you can't solve it

worthy cargo
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yeah you need it to be equal to a value

shadow estuary
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its = to 0

timid silo
worthy cargo
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lmao

timid silo
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i'd suggest reading this before starting this exercise

shadow estuary
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bro

worthy cargo
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is that a good book

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unironically

shadow estuary
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how did u get the complex solutions?

timid silo
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jk of course

worthy cargo
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oh ok

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I was boutta say

shadow estuary
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how do u get it when its simplified like this

timid silo
warm shaleBOT
#

jswatj

worthy cargo
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right

shadow estuary
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why cant i solve the bottom

timid silo
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cause bottom vanishes remember

shadow estuary
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its still there

timid silo
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alright ready?

shadow estuary
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yes

timid silo
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$\frac{2x^2-3x+3}{-4x^2+2x}=0 \implies 2x^2-3x+3=0$

warm shaleBOT
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jswatj

timid silo
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there i removed it

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gone now

shadow estuary
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ohhhhhhhh

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u just multiplied by the bottom part

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and because thats = to 0 it disappeared

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mf bottom part

worthy cargo
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yep

shadow estuary
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we should petition or something

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to make it so that bottom parts are abolished

worthy cargo
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right I agree completely

shadow estuary
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this is wrong

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its discrimination against the top part

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always confusing them kids

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and making them think the bottom part matters

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and when they think the bottom part matters, they totally ignore the top part

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and then the top part feels discriminated against

worthy cargo
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yep

shadow estuary
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im so glad we're in agreement on this issue

obtuse pebbleBOT
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@shadow estuary Has your question been resolved?

timid silo
#

eddie wake up, i dont like this

shadow estuary
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you know, this isn't the first time we've met

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hey, helloooo?

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time to wake up! time to wake up! time to wake up swatty

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swatty wake up

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i don't like this...

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swatty wake upppp!!

timid silo
#

actually?

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who r u

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you got me curious

shadow estuary
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i dont like this

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swatty WAKE UPP

obtuse pebbleBOT
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timid silo
obtuse pebbleBOT
timid silo
#

help pls

#

thought i was right

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the (f*g) (3) problem

sage geode
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It says composition of f and g at 3, not their product

timid silo
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Can you workout the problem pls

tardy epoch
timid silo
#

kk

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is this it

tardy epoch
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i don't recommend guessing and checking

timid silo
#

Ok I read a bit of it

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I can simplify my problem to f(g(3))

#

.close

obtuse pebbleBOT
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timid silo
#

Is the answer 16,777,168

obtuse pebbleBOT
tardy epoch
#

lots of context missing. how many original dna molecules are there

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

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timid silo
#

do i need to use u-sub + ibp here?

obtuse pebbleBOT
timid silo
#

nvm

#

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random ocean
timid silo
#

yep

obtuse pebbleBOT
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cedar cedar
#

how do I approximate the zeros of $f(x) = xe^{-x} -\frac{1}{4}$?

warm shaleBOT
#

suspect

timid silo
#

also the function is concave between 0 and 1, so the newton method will work, and if you approximate it for 2 and 3 you will see that there is another zero, and its convex on that interval

obtuse pebbleBOT
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drifting swan
#

Hello, can you please help me to solve the following question: when can I model an object of study as a particle and when as a rigid body?

obtuse pebbleBOT
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kind talon
#

h

obtuse pebbleBOT
kind talon
#

What is the formula of the sequence please ?

obtuse pebbleBOT
#

@kind talon Has your question been resolved?

versed cave
mint tendon
#

i think they may want the explicit formula

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in that case you're going to need to solve the linear nonhomogeneous recurrence relation

warm shaleBOT
kind talon
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what is a() please @versed cave @mint tendon

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I don't understand the formula

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for example if I want to get the first number in this sequence what should I do?

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the second number

mint tendon
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its a function defined by the terms that come before it

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you have to set some sort of "seed" for it

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and for this equation you need 3 seeds, since its a third order linear recurrence relation

warm shaleBOT
mint tendon
#

from here you can find any positive integer value

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but you need to know the terms that come before

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if you want an explicit formula that doesnt depend on that, you'll need to solve the recurrence relation

kind talon
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Yes I want a fomula doesn't depnend

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is there one xd ?

mint tendon
#

yep

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its not fun but it does exist

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do you want to know how to arrive at the formula or just the formula itself

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this doesnt seem like hw so im willing to go with the latter if you are

obtuse pebbleBOT
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mint tendon
#

@kind talon

obtuse pebbleBOT
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undone finch
#

A hyperbola passing through (8,6) consists of all points whose distance from the origin is a constant more than its distance from the point (5,2). Find the slope of the tangent line to the hyperbola at (8, 6).

undone finch
#

I'm not really familiar with hyperbolas, this is an implicit differentiation exercise

kind talon
mint tendon
#

ignore that

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first find the constant

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you can do that by finding the dist from (8,6) to origin and from (8,6) to (5,2)

obtuse pebbleBOT
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@undone finch Has your question been resolved?

undone finch
obtuse pebbleBOT
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@undone finch Has your question been resolved?

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timid silo
#

I know the problem isn’t done yet. Still need to take the derivative but is up to here looking fine? I’m not used to all the addition/subtraction signs on the bottom

obtuse pebbleBOT
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@timid silo Has your question been resolved?

tribal yew
#

you're supposed to get 1/y (dy/dx)

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on the lhs

timid silo
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yeah ik

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but before I do that is the right side correct

tribal yew
#

no it doesn't work that way

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you can't split the logarithm into two parts like that

timid silo
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one moment

tribal yew
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ln(x+tanx) is not equal to ln(x) + ln(tanx)

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or is it ln(xtanx)?

timid silo
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it’s ln (xtanx)

tribal yew
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oh

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my bad

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yeah

timid silo
#

all good here

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is this what you mean?

tribal yew
#

yeah

#

it's looking good

timid silo
#

thank you! i appreciate it

tribal yew
#

np

timid silo
#

.close

obtuse pebbleBOT
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gray creek
#

Any help?

obtuse pebbleBOT
velvet spade
gray creek
#

For 1. I got lim Cos(x) = 1 = Sec (x) lim

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Under the lim is x -> 0

#
  1. Lim x/sin (x) = 1
    x->0
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  1. I'm kinda confused
velvet spade
obtuse pebbleBOT
#

@gray creek Has your question been resolved?

gray creek
#

For Part 2 I saw that all the function approached 1

obtuse pebbleBOT
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obtuse pebbleBOT
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@fluid snow Has your question been resolved?

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grave sand
#

When buying something in bulk i. e. 10x it gets a discount. This means buying 9 is more expensive than 10 and idk how to get that into my function?

grave sand
#

The problem is as follows: somebody buys tread and makes gloves with it.

#

every roll has 50g in them, and 120g is needed for a pair of gloves

#

1 roll cost 12.95$, and 10 cost 89$

#

p = sellling price and x = gloves. y = profit

#

what i have written will only buy the thread neccessary but how would i make it buy more when cheaper?

obtuse pebbleBOT
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red pulsar
#

Good afternoon, I understand the problem up until Part 6. I am unsure where they are getting 41/25 from and could use some help

obtuse pebbleBOT
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@red pulsar Has your question been resolved?

red pulsar
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<@&286206848099549185>

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small rock
obtuse pebbleBOT
small rock
#

Just wondering if I did this right, it says to write your final answer in terms of f(x)

austere folio
#

i can help

stable rain
#

seems right

small rock
#

Cool I figured it was but just checking

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primal idol
obtuse pebbleBOT
primal idol
#

Hello, I'm not sure if my integral set-up is correct.

small rock
#

You need a dx at the end

#

Also it looks like you wrote as subscript instead of in the middle of the integral sign which looks a bit confusing

primal idol
#

Says my answer is incorrect

#

Not sure where I got it wrong

#

I guess i should change (x+4) to just x?

obtuse pebbleBOT
#

@primal idol Has your question been resolved?

hardy widget
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@primal idol Has your question been resolved?

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bitter heath
obtuse pebbleBOT
bitter heath
#

so im quite confused on what this last question is asking me

#

i know that constant speed = 0 acceleration

#

there are threee parts to this question, this is the last

#

first asked for acceleration of the car which A= 2.6 m/(s^2)

#

second question is what t is, t = 9.2s

#

then the last, finding L

#

which am not sure what to do

nocturne minnow
bitter heath
#

would the 24m/s be the change of velocity or the final? for specifically this part

bitter heath
nocturne minnow
#

No, I don't think you need that

#

Recall that $v = \frac{d}{t}$ where t is the time it takes for the car to travel the length of the ramp

warm shaleBOT
#

dldh06

nocturne minnow
#

If you have that time, and you have v, you can find d

bitter heath
#

ohhh

#

that is the equation for speed correct?

nocturne minnow
#

Yes

bitter heath
#

ok i got it now, thanks alot for your help

#

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timid silo
obtuse pebbleBOT
obtuse zenith
timid silo
#

Sorry, I don’t

obtuse zenith
#

Triangle inequality theorem states that the sum of the lengths of two sides of a triangle must be greater than the length of the third side

timid silo
#

Ohh

#

So would it be x < 9.7 < 18.7

#

?

obtuse zenith
#

You always want x in the middle in the case of a compound inequality

timid silo
#

Oh ok

#

9.7 < x < 18.7

#

?

obtuse zenith
#

What is 9.7 + 18.7?

timid silo
obtuse zenith
#

Yes, so the side length must be less than 28.4

#

That is ONE condition

#

We have another condition to satisfy

timid silo
#

oh ok

timid silo
obtuse zenith
#

28.4 would be your maximum

#

The next condition you have to satisfy is the minimum side length

timid silo
#

9.7 < x < 28.4

obtuse zenith
timid silo
#

Is it 9.3

obtuse zenith
#

The sum of the new side and the 9.7 must be greater than the largest side we're given, which is 18.7

#

9.7 + x > 18.7

#

Solve for x (minimum side length)

#

Then you plug that into the inequality and you get your answer

#

The format for an inequality in the context of this question would be

minimum side length < x < maximum side length

obtuse pebbleBOT
#

@timid silo Has your question been resolved?

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keen bronze
#

The perimeter of a rectangle is 76 meters. Find the length and width if the length is an even integer and the width is 3 times the next consecutive even integer.
Length = ? meters Width = ? meters

keen bronze
#

I just have no clue on how to do this

prime pebble
#

length being an even integer means that length L is equal to 2k for some integer k

#

then what is the next even integer?

keen bronze
#

uh

#

I have no clue

#

what does k represent in your equation?

prime pebble
#

is 2k+1 even?

#

it's an integer number

#

think about what it means for a number to be even

keen bronze
#

devisable by 2?

prime pebble
#

yes

#

now think what would be the next even number if you already know that 2k is even

keen bronze
#

4k?

#

im confused

#

I dont know what the k represents

prime pebble
#

it's just an integer number, nothing else

#

well what's special about even numbers here: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... ?

keen bronze
#

they are smaller even numbers

prime pebble
#

"smaller"?

keen bronze
#

like um

#

not on as large as the numbers after it?

#

but I guess thats obvious

prime pebble
#

don't you see how there's always an odd number between two even numbers?

keen bronze
#

oh yes of course

prime pebble
#

then what is the next number if 2k is even?

#

or say "m" is any even integer number

keen bronze
#

ok

#

and then

#

there is an odd number

#

and then another even

#

no matter what even number we begin with

prime pebble
#

so what's that number in terms of k?

#

if you go from 2k to 2k+1 then is 2k+1 odd or even?

keen bronze
#

odd

prime pebble
#

well then what's the next even number for 2k?

keen bronze
#

2k+2

prime pebble
#

now go back to your problem given that you now know that length is 2k and next even number for 2k is 2k+2

keen bronze
#

okay

#

.close

obtuse pebbleBOT
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native flicker
#

If a computer program generates all the permutations of a set containing 10 elements and writes the output to a file at a rate of 1000 permutations per second, how long will it take to generate all permutations?

tardy epoch
native flicker
#

I think it is 10! ?

#

So it is 10!/1000?

#

3628.8 seconds?

tardy epoch
#

If it's producing a random permutation, then it's a coupon collector's problem

native flicker
#

I think it is new permutations

#

There are no repeats

tardy epoch
native flicker
#

Okay thank you for your help 🙂

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brazen kite
#

I need help finding a equivalent proposition and proving it as asked in part b

warm canopy
#

Hints: De Morgan, writing implications as or statements, distributing

brazen kite
#

I have this so far idk how much of it is right

obtuse pebbleBOT
#

@brazen kite Has your question been resolved?

brazen kite
#

<@&286206848099549185>

urban frost
#

would u like to try again

urban frost
brazen kite
wild swallow
#

when it says "construct a truth table" that might be part of the requirements of the question

brazen kite
#

I did construct one

wild swallow
#

ah alright

#

just thought you might be skipping it and doing the algebra directly

urban frost
#

idk but i feel the second step isnt necessary

urban frost
#

i also think u should express it in a more clearer manner

#

state that ur using implication equivalence

obtuse pebbleBOT
#

@brazen kite Has your question been resolved?

brazen kite
#

.close

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timid silo
#

Can someone please help me, I have no idea how to do it and I’m so confused : , )

rain mountain
timid silo
#

Can you explain pls🥹 @rain mountain

uneven palm
#

@timid silo

uneven palm
timid silo
#

Ohhh, I get it now. So it’s just the operations that make up the thing

uneven palm
#

yeahh.. I guess

#

here’s a nicer definition:
Terms are single numbers, variables, or the product of a number and variables.

rain mountain
timid silo
#

Wait so then which are the factors

uneven palm
timid silo
#

OHHH

#

It’s the ones on the right side

uneven palm
#

indeed

rain mountain
timid silo
#

I see

#

I feel so dumb, this whole time I’ve been over complicating it 😭

rain mountain
timid silo
#

It’s fine, it actually let me out 2 and 2 together and sort of figure out myself almost

uneven palm
rain mountain
#

it happens smtimes

timid silo
#

Thank you guys catlove

uneven palm
#

np

rain mountain
obtuse pebbleBOT
#

@timid silo Has your question been resolved?

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obtuse pebbleBOT
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swift root
#

My professor tried to show this example 5 in class and it just didn’t click could someone please help.

tardy epoch
swift root
#

The second page is just the solution

#

I can’t even follow it

#

I had to watch a recording of the lecture and his voice keeps cutting out so it’s hard to follow

tardy epoch
swift root
#

Wrong pic

#

I really couldn’t follow it at all

#

I’m terrible at applications

tardy epoch
#

where first do you get lost?

#

the picture?

swift root
#

Yeah and how where he gets the -30 degrees

#

I also forgot the radio for a 30 60 90 triangle because I took geometry in 2015 so that confused me as well

#

But I really just don’t know how to go about solving an application like this at all

tardy epoch
#

it's given

#

you just have to draw the triangles after setting up the coordinate axes to be on the block

swift root
#

I guess the only thing I can do is try to watch the example again

#

I’m sorry I’m just more visual than anything so trying to explain it in words doesn’t help much

swift root
#

Man U people in this discord or so snobby nvm lol

#

.close

obtuse pebbleBOT
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winged mirage
#

The number of cents in $x

obtuse pebbleBOT
proven zephyr
#

do you know how many cents is in a dollar?

winged mirage
#

divide by 100??

sage iron
#

use dimensional analysis if you want to be cool

winged mirage
#

so x/100?

proven zephyr
#

no...

#

first of all

#

how many cents is in a dollar

winged mirage
#

100

proven zephyr
#

yes

#

if there is x amount of dollars

#

what do you do with the amount of cents

winged mirage
#

100x

proven zephyr
#

yes

#

that should be your answer

winged mirage
#

ohh thank you

#

.close

obtuse pebbleBOT
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winged mirage
#

.reopen

obtuse pebbleBOT
#

winged mirage
#

The cost in dollars of x books at y cents each.

#

@proven zephyr

proven zephyr
#

ok so

#

lets convert the price to dollars first

#

to convert dollars to cents, you multiply by 100

#

to convert cents to dollars, what do you do

winged mirage
proven zephyr
#

yes

#

so what's the price for each book

winged mirage
#

uhm

proven zephyr
#

it's y cents for each book

#

you divide by 100 to make it dollars

winged mirage
#

so y divided by x?

#

y/100

#

?

proven zephyr
#

and since that's price per book

#

and there is x amounts of books

#

how do you find the total price

winged mirage
#

y/100 times x?

proven zephyr
#

yes

winged mirage
#

is there a better way to write that

#

or would that be the answer

proven zephyr
#

or you can just...

#

xy/100

#

you multiply it into 1

winged mirage
#

thank youu

#

.close

obtuse pebbleBOT
#
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proven zephyr
#

np

obtuse pebbleBOT
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ionic whale
#

im using dlh to find a limit

obtuse pebbleBOT
ionic whale
#

and im about to finish the exercise

uneven wolf
ionic whale
#

how to do this simple algebra😂

random ocean
sweet ember
#

Limit tending to what?

ionic whale
#

nah i found it all

#

i just need b

random ocean
#

what's this

ionic whale
#

idk how to do this i swear lol

ionic whale
#

do i put 6 * 0

wild swallow
#

yes

ionic whale
#

and then move 27 to the rhs

wild swallow
#

yes

ionic whale
#

Ok

#

.close

obtuse pebbleBOT
#
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stable rain
obtuse pebbleBOT
stable rain
#

hi sorry how does this work

wild swallow
#

so for the z/πn π(1/z - n) thats just factoring out z/n from the bracket

#

then the denominator you have

#

$\sin(\pi/z) = (-1)^n \sin(\pi/z - n\pi)$

warm shaleBOT
#

夢雪

wild swallow
#

$\qty(z - \frac1n) = -\frac z n \qty(\frac1z - n)$

warm shaleBOT
#

夢雪

wild swallow
#

@stable rain

stable rain
#

sry im

#

looking at the top part..

wild swallow
#

i thought you were gonna say you're in teyvet kekw

stable rain
#

LOL

#

no i was watching my lect

#

no idea whats gg on

stable rain
#

i got the same but negative?

wild swallow
stable rain
#

i was at the top man

stable rain
#

@wild swallow

wild swallow
#

it popped out of the top of my empty head

stable rain
#

OHH

#

yea

wild swallow
#

thats just

stable rain
#

sin repeats

wild swallow
#

shifting

#

yeah

stable rain
#

every pi with neg

#

ok

wild swallow
#

pi periodic

stable rain
#

ok so

#

what happened

#

@wild swallow

#

wait wrong

#

how did we get that

#

i thought we would sub z=1 into the holomorphic part or smt

#

idk what they got or how

wild swallow
#

not sure why they rewrote it with (z - 1)

wild swallow
stable rain
#

im also not sure whats gg on

wild swallow
#

you can launch into residue theorem immediately

#

dont need the (z - 1) thing

stable rain
#

ok..

#

but for understanding

#

whats he doing

#

or what did he do

#

w8w8

#

wrong example

#

w8

#

wtf

#

sry

#

i

#

yea i got the right one deleted it n sent the wrong one

wild swallow
#

whats wrong with it

stable rain
#

yea nvm

#

idk both

#

yea

#

:c

wild swallow
#

sadge

stable rain
#

so howd he get -1^2/pi

wild swallow
#

?

stable rain
#

aka howd he get to the 2nd last step

wild swallow
#

n = 1

stable rain
#

ok..

#

well

#

im done for now

#

imma review it later

#

so messy

#

sien

#

.close

obtuse pebbleBOT
#
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stable rain
#

thanks

obtuse pebbleBOT
#
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timid silo
obtuse pebbleBOT
timid silo
#

Not quite sure how to do that

#

So I was able to get the speed using pythagors

#

But I'm not sure how to work out the angle

#

can someone explain the process needed to find the angle

lyric kelp
#

If you consider the speed of the current adds up to that of the yacht use vectors

timid silo
#

how would it work

lyric kelp
#

Try creating one movement vector for the yacht and one for the current

#

Because you know the "length" of these and the angle

timid silo
#

haha sorry I'm still quite confused

#

is this a vector of the yacht

lyric kelp
#

Sorry i have trouble reading this

timid silo
#

if it's going south east, wouldn't it be 315 Degrees

lyric kelp
#

Try getting south east direction as an oriented angle

#

Yes exactly

#

Now i believe you can calculate what that vector wiln be

timid silo
lyric kelp
#

Answer using complex numbers
||v= cos (315) *10 + i sin (315)*10 ||

#

Since i dont know how to wrute a vector here

timid silo
#

would we need unit circle trigonometry

lyric kelp
#

Then 9nce you know both vectors you should be able to solve it

lyric kelp
#

Like thats what cos and sin are based on

#

But apart from that i dont think so

timid silo
#

I see

lyric kelp
#

Just try to understand rhat every force and movement is a vector

timid silo
#

i see

lyric kelp
timid silo
#

ooh wow

lyric kelp
#

Hence this if youve seen it already

#

Otherwise dont worry avout it for now

timid silo
#

never seen it tbh

lyric kelp
#

Just now once you have them is vectors you can add up every force with eachother or every movement with eachother

timid silo
#

This vector unit was taught to me when I was 14, i'm currently revising it about a year later, so I'm not sure if that rule would be needed

lyric kelp
#

But dont forget to follow your teachers method

#

Ooh

#

Then im giving you the idea of how to solve it

#

But use your teachers method

timid silo
#

alright

#

I'll ask him for it again

#

Thank you for the advice

lyric kelp
#

Just in the formula i gave you the "i" is somethign youll see later

#

Just dont forget to keep the two dimensions separatr

#

Dont add x coordinates with y coordinates

timid silo
#

oh right that is true

#

.close

obtuse pebbleBOT
#
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dreamy current
obtuse pebbleBOT
dreamy current
#

im on part D

#

wouldnt it just be 23+2.4sin(πt)≥24.2

#

in the domain of 0≤t≤8

#

but im confused on how to do this without a calculator (even with a calculator my calculator doesnt give any values, it just says [6.283constn(1)+3.665≤x≤8 and x≤6.283constn(1)+5.759])

#

my calculator is the Casio Classpad fx-CP400

obtuse pebbleBOT
#

@dreamy current Has your question been resolved?

covert salmon
#

You are correct with 23+2.4sin(πt)>24.2

#

From that, you get 2.4sin(πt)>1.2

#

Then, sin(πt)>0.5

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Sin(πt)> 0.5 when 5/6>t>1/6

#

Using the fact that the period of sin is 2π, we know that every 2 hours the cycle will repeat

#

Since the total timeframe in the question is 8 hours long, from 9am to 5pm we can figure out that there will be a total of 4 repetitions of the cycle

#

Therefore the total amount of time Freddy feels thirsty will be equal to (5/6 - 1/6) x 4 hours

#

which is equal to 8/3 hours or 160 minutes

obtuse pebbleBOT
#

@dreamy current Has your question been resolved?

obtuse pebbleBOT
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lusty steppe
#

why is this false but when i remove the t it will be true

lusty steppe
#

this only works with constants?

obtuse pebbleBOT
#

@lusty steppe Has your question been resolved?

lusty steppe
#

<@&286206848099549185>

timid silo
#

t is not negative

#

So it doesnt get pulled to the bottom

#

for example, raise the inside to the -1/15 power first and leave the T outside

#

Simplify inside then bring the T in

hallow mesa
#

Does'nt this only work when t>0

#

Or am I am just doing something wrong

#

Never mind

timid silo
#

yes, you dont know right now if the integer value of t is + or - so you treat it based on its sign

hallow mesa
#

Ok

lusty steppe
#

but now when i make t negative

#

it still doesnt make it an identity

timid silo
#

Try -ln([7/2]^t)

#

There may be some rule with negatives going into the power with ln's that I might be forgettinf

lusty steppe
#

okkk

lusty steppe
# lusty steppe

can someone explain why this rule doesnt apply with variables but it does with constants?

#

i cant figure it out

timid silo
#

If t = 0

#

Wait nvm

#

Ln(1) becomes 0 also

#

hmm

lusty steppe
#

yea...

timid silo
#

I will try something one secend

lusty steppe
#

alrightttt

#

idk is it because the actual variable t could be negative so -(-t) = t

#

and it would only apply if the variable t is >= 0

#

i cant think about anything else

timid silo
#

They are equal

#

all values are defined

#

And equal

#

Try typing ln([7/2]^(-t))

#

Might be because it doesnt want u to simplify?

lusty steppe
#

it doesnt work either

#

it doesnt make sense

timid silo
#

it looks like your on mathway

lusty steppe
#

i am

#

i got wolfram too

timid silo
#

what does it say is the rigjt answer?

lusty steppe
#

it doesnt say anything, i am just comparing two sides and "verifying the identity"

#

am i missing something

#

how is this not an identity

timid silo
#

Mathways is bugging

lusty steppe
#

yea...

#

i need to look more into wolfram to see if theres some identity verifications

lusty steppe
#

mathway is weird

timid silo
#

I see

glossy loom
timid silo
#

never used it so never knew

#

Wolfram on top

obtuse pebbleBOT
#

@lusty steppe Has your question been resolved?

obtuse pebbleBOT
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sharp iron
#

is this question broken? how do you prove its arithmetic

obtuse pebbleBOT
#

@sharp iron Has your question been resolved?

sharp iron
#

<@&286206848099549185>

obtuse pebbleBOT
#

@sharp iron Has your question been resolved?

sharp iron
#

<@&286206848099549185>

obtuse pebbleBOT
#

@sharp iron Has your question been resolved?

timid silo
obtuse pebbleBOT
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formal parrot
obtuse pebbleBOT
formal parrot
#

I'm having issues trying to graph and also write in interval notations

#

the solutions I got was x is less than or equal to 12 and x is greater than or equal to 0

robust junco
#

Hey guys. Can someone help me or give any advice on modeling differential equations. Ik its a big part of theoretical physics but im just not getting it. I never got stuck like this in any topic of math like tensor calc, mult. calc or anything. Any tips cuz im clueless

formal parrot
#

.close

obtuse pebbleBOT
#
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uneven niche
#

Hello, when dealing with conics - what does it mean when they say a conic (e.g elipse or hyperbola) in 'standard position and orientation'? I'm not sure what the bolded term means.

obtuse pebbleBOT
#

@uneven niche Has your question been resolved?

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vivid creek
#

Are you able to use the quick method to solve this quadratic equations since I tried and couldn’t. Are there certain equations that you can’t use it in and have to use the method? Since I don’t know why I can’t

zenith raft
#

quadratic formula?

#

what's the "quick method"?

vivid creek
#

Yes it that.

#

It when you find the factors of 3. Then you choose which number you have to times by 8 aka 3 or 1. Then you have to add them to get 10

#

But it doesn’t work for this equation

zenith raft
#

oh

#

it's probably the 8 in front of the x^2

vivid creek
#

Wdym?

zenith raft
#

actually it sounds like you are looking for a facorization over the integers

#

since you say factors of 3

#

but that might not exist

vivid creek
#

So that why it doesn’t work?

zenith raft
#

,w factor 8x^2+10x-3

zenith raft
#

yes, it does not factor over the integers

vivid creek
#

Wdym by factor over the integers

zenith raft
#

you can't write it as (x-a)(x-b) for integers a and b

vivid creek
#

Oh ok thanks I understand now

#

Thanks for the help

zenith raft
#

but I'm still not sure exactly what your initial method was

warm canopy
#

this is the method

vivid creek
#

I know that the method. But there a video that has a shorter method so I can skip all that

#

But for some reason it doesn’t work for all types

warm canopy
#

what is the shorter method?

vivid creek
#

What this video then skip to about 15:43

#

That the method I’m talking about

#

I tried that method for the problem I showed up top

#

But it doesn’t work

#

I don’t know why tho

#

That my question

warm canopy
#

its because when you have 8x^2 you dont know how its going to split in the brackets

#

it might be (8x+stuff)(x+stuff)

#

or (4x+stuff)(2x+stuff)

vivid creek
#

Is there away for me to know or no

warm canopy
#

not really, the reason it works for his example is because (2x+stuff)(x+stuff) is the only way to get 2x^2 out

vivid creek
#

Oh ok

#

So does it only work for odd number and the number 2?

warm canopy
#

not going to work for 15x^2 is it

vivid creek
#

Ok well I kinda under stand it a little bit better now

#

Ty

#

.close

obtuse pebbleBOT
#
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hard citrus
#

Can someone help with question 3b

obtuse pebbleBOT
hard citrus
#

cyclic quadrilateral means that all the points lie on a circle

#

wait nvm

#

.close

obtuse pebbleBOT
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timid silo
#

i have an abs value limit

obtuse pebbleBOT
timid silo
#

its lim x--> -1 x^2-2/|1+x|

#

this is how i approached it

#

or how i was taught to evaluate these limits

#

for approaching from the left, i was taught to do x^2-2/-|1+x|

#

and from the right x^2-2/|1+x|

#

and substitute