help-19

[clever fjord]

MæthIsAlwaysRight

MæthIsAlwaysRight

MæthIsAlwaysRight

MæthIsAlwaysRight

[tepid pelican]

So we get $\frac{4x}{3\cdot19}+\frac{x}{19\cdot23}+\frac{x}{3^{3}\cdot23}$

[clever fjord]

MæthIsAlwaysRight

[tepid pelican]

etc, i gtg now

but it all simplifies nicely

[small fulcrum]

noice

[odd edge]

@hoary cape Has your question been resolved?

[hoary cape]

I solved this like an accountant...sorry

[small fulcrum]

xD

[small fulcrum]

wdymmm ais aprox 729 xD

[hoary cape]

https://tenor.com/view/pepe-cry-reading-pepe-the-frog-sad-gif-17607942

[small fulcrum]

you shouldve kept them as prime factors lol

[tepid pelican]

Holy

That's a whole another level of brute force

[odd edge]

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[finite oxide]

How do I find the direction of the forces perpendicular and parallel to the slope

[stable wave]

Ur asking how to resolve mg?

[finite oxide]

no

F

[odd edge]

@finite oxide Has your question been resolved?

[finite oxide]

<@&286206848099549185>

nvm

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[velvet olive]

okay,

[velvet olive]

i initially answered A and said 4 months

[lavish osprey]

Were you able to extract a formula for Carrier A?

[velvet olive]

I think so

[lavish osprey]

what'd you get?

[velvet olive]

y=50x

idk why I answered A was more expensive

B was obvious

Wait no

[lavish osprey]

Not quite

[velvet olive]

yeah

[lavish osprey]

you foudn the slope which is correct

but remember that a linear line has a y intercept

y = mx + b

so you gotta find the b

[velvet olive]

how do I get the b

[lavish osprey]

well you know your m, which is 50. And you know some x,y values from the chart, so plug in a pair and solve

[velvet olive]

Oh

I got that b is 350

[lavish osprey]

and remember that the "initial fee" here will be the y intercept for both equations, so pick whichever one is lower

very good

so you have:
A = 50x + 350
B = 55x + 300

So which one has a cheaper initial fee?

[velvet olive]

b

[lavish osprey]

very good

now the months where they will cost the same will be where both lines intersect

how do we solve for that?

[velvet olive]

by adding it until its the same?

[lavish osprey]

not quite

the way we find the intersection of 2 equations is by setting them equal to each other and solving for x

[velvet olive]

No way

can you actually do that

[lavish osprey]

not only can you

but you should!

for example

[velvet olive]

Ok

[lavish osprey]

say if we had:
y = 3x + 2
y = 2x + 3

then they intersect at 3x + 2 = 2x + 3 --> x = 1.

[velvet olive]

I got that the months is 10

Thanks a lot

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[lavish osprey]

Yep nice work!

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[compact steppe]

I'm asked to approximate $\sqrt {1+x}$ with Maclaurin polynomial of the 2nd degree and estimate the error, for $x \in [0, 1]$

[clever fjord]

atif

[compact steppe]

I guess maclaurin polynomial is just Maclaurin series?

I can calculate the first 3 terms, up to the 2nd derivative, but idk what to do about the error and the fact that x is in 0,1 interval

[low locust]

well only the first few terms of the series

hence, polynomial

[compact steppe]

yes makes sense

do u know what should i do about the error

[low locust]

you will have some theorem which expresses the error

compute that expression and check how big it can be

that will tell you how big your error can be at most

[compact steppe]

ok thanks i ll look for the theorem. i guess i use x in [0,1] for that part

[low locust]

yes

[compact steppe]

@low locust i don't have the thing for computing the error, it's missing from all the notes i have

i mean i can google and search on internet

or wait for someone else to pop in, in case u dont know how to do it from top of ur head

for new people coming: I'm asked to approximate $\sqrt {1+x}$ with Maclaurin polynomial of the 2nd degree and estimate the error, for $x \in [0, 1]$, I got the polynomial but idk what to do about the error. if you know a hint let me know, thx

[clever fjord]

atif

[fossil hawk]

The error is due to the remainder

Ul have to calculate a 3 fold integral

[compact steppe]

no waz

no way

but ok thx i m looking into it

[fossil hawk]

Or use this

[compact steppe]

yes i think im supposed to use that

[fossil hawk]

but then the prob will be to find z

[compact steppe]

whats z?

[fossil hawk]

Random constant that exists between x and c

[compact steppe]

well its maclaurin so theres no c here i suppose?

its just x everywhere instead of x-c

oh c is just 0

[fossil hawk]

yea
The better way would be to do the integral tbh
U can look more into taylors theorem for more detail

[fossil hawk]

Yes

[compact steppe]

but do u kno perhaps if it helps that im given that x is in [0,1]

for this z thing

[fossil hawk]

Since c = 0 try taking z as x ig

[compact steppe]

ah perhaps i dont need any particular z, i can try myb just bounding it

[forest sky]

the error is higher the farther away from the center (x = 0) your input is, so this is useful for bounding the error

[compact steppe]

i see, thx

so using this, and im asked for the 2nd degree plynomial, then i need to find the third derivative right?

do i have R_2 is what im asking

[forest sky]

yes

[fossil hawk]

Or u could evaluate this

[compact steppe]

ah ty but i think im asked to do this remainder stuff. thanks for letting me know that it's doable like that

and good to see we got same numbers

@forest sky can u take a look at the tex compilation below. i need to bound that right?

[fossil hawk]

ok your welcome

[forest sky]

where did the x+5 come from?

[compact steppe]

ah typo

i got $$R_2 = \frac{1}{16} \frac {x^3}{\sqrt{(1+z)^5}}$$

and i probably shouldnt put x

[forest sky]

note that the remainder formula says that the remainder at x is dependent on (x)^3 as well as f'''(k), where k is some number between c = 0 and x

[clever fjord]

atif

[compact steppe]

ok this is with the 3rd derivative and x^3 included

i just used z instead of k

[forest sky]

ok. so now we can create a bound by choosing the value of z between 0 and 1 that makes the formula largest

[compact steppe]

it's 1 right?

z=1

the degree in the numerator is higher and $z \leq x$

[clever fjord]

atif

[compact steppe]

so the whole fraction is increasing

[forest sky]

well note that if the denominator is increasing then the fraction is decreasing

[compact steppe]

ahhh

i got stuck with the x, the variable editing confused me

yes

z = 0

[forest sky]

so we can now say that $$R_2(x) = \frac{1}{16} \frac {x^3}{\sqrt{(1+z)^5}} \le\frac{1}{16} \frac {x^3}{\sqrt{(1)^5}}$$

[clever fjord]

cloud

[compact steppe]

and we are done?

like, this is the approximation of the error

[forest sky]

yes, i believe so

[compact steppe]

im asking bcs i never saw this done before

ok great

thanks for the lesson

much appreciated

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[pale holly]

when going into this problem are the ones under the x axis going to be negative?

or should i just add them all up since they were given to me all positive and divide by 3?

[jade kelp]

So let's try to reason. Choose a point between -2 and -1 what do you think the value of f(x) is

[pale holly]

just 9/4 since they cancel out?

negative

[jade kelp]

yes it is 9/4 you are right

but you see the reaosn why right?

[pale holly]

yes

like f(-1.5) = (-)

right?

[jade kelp]

yes

[pale holly]

so from [0,1] it's actually -9/4

[jade kelp]

exactly

you can think of it like this

uhm actually I think you got it 😄

[pale holly]

yes

thank you very much

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[icy egret]

8x-2=7(-3y)

[icy egret]

solve for x

dunno if im dumb but i literally cant???

[mystic saffron]

it depends what "solve for x" means

if you're solving for a numerical value then yeah you can't

but "solve for x" can also mean isolate x

like if you have 2x=4y, it would become x=2y

thats also solving for x

[icy egret]

oh yeah ik that

okay ig the question is just weird a lil thx

[mystic saffron]

yeah

[icy egret]

btw

[mystic saffron]

i feel like textbook questions are notorious for crappy wording

[mystic saffron]

mhm?

[icy egret]

yeah fr

is calc hard

cuz im going into junior year and ive heard too many horror stories

[mystic saffron]

couldn't tell you
also going into my junior year and just started AB lol

[icy egret]

really?

how was precalc

[mystic saffron]

it wasn't that bad

there were some tricky concepts sure but its not impossible

[icy egret]

hm i see

is it hard to end with an A

[mystic saffron]

¯_(ツ)_/¯

[icy egret]

lol

[mystic saffron]

dunno

[icy egret]

did u do sat or act yet?

[mystic saffron]

nope

scheduled tho

[icy egret]

r u prepping then?

[mystic saffron]

nah not really
yes and no

[icy egret]

lol

[odd edge]

@icy egret Has your question been resolved?

[vernal yacht]

!done

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[wary thunder]

Hi! i need help on this question! I don't understand where I went wrong. I calculated both -20(cos(20)) and 20(sin(20)) and put both of those answers as my vector but I'm still getting it wrong.

[viscid flint]

,calc [-20 * cos(20 * pi/180), 20 * sin(20 * pi/180)]

[clever fjord]

Result:

[-18.793852415718, 6.8404028665134]

[viscid flint]

,calc -20 * cos(20)

[clever fjord]

Result:

-8.1616412362678

[viscid flint]

your calculator was set to radians

[wary thunder]

ohh i see

thank you so much!

[viscid flint]

(you might have noticed that the x component should be absolutely much bigger than the y component)

[wary thunder]

ohh yesyes

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[velvet juniper]

diff eq question, the bottom question it shows is right but i just need help understanding how to do the top 2, because when i follow the solution curve my answer is always wrong (ill explain one sec)

[velvet juniper]

i started guessing because i was so confused my bad lol but basically

this is how you follow the curve right?? (like for y(0) = 0)

because if thats how you do it, then for part a) y(1) should = something positive like 1
and y(-1) should = something negative like -0.5?

I tried 0 but its wrong.. and also I tried -0.5

and -1

i only have 15 attempts left lol

ikr im so lost

idk wth it wants from me

kk one sec

yeah i tried both 0 for a

i posted it on my class discussion board and i got a not very helpful answer lol

yeah

but i think i know what its getting at actually....

because for c), the solution line gives the equation y = -x - 1

and then you plug in the points

so maybe i have to find the equation for the solution line and then plug in the points?

bc thats what i did to solve c

nah no equation given

im not sure how to find an equation for a im ngl...

i got one of them

its ok i got extra credit i give up lol

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[viral arrow]

hello! i need help on 12 i get u have to use law of sines but im having trouble with how to use the angles to plug into sin

[steep mantle]

try drawing it first

[viral arrow]

i have!!

i get completely different answers

[topaz ibex]

sum of 3 angles in a triangles alway equal 180

[viral arrow]

yes the other angle is 47

[topaz ibex]

bet

[steep mantle]

can you show your work?

[topaz ibex]

and the longest side always face the biggest angle

[steep mantle]

ah sorry, misread the question

[viral arrow]

ohhhhh

thank you !! is there a specific reason why?

[topaz ibex]

Law of Sines state that: in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant

so if one side of a triangle is longer, the sine of the opposite angle must also be larger, meaning the angle itself is larger

[viral arrow]

OH so you would use angles 47 and 82??

[topaz ibex]

yep

[viral arrow]

why not 51

oh no nvm

thanks!!

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[topaz ibex]

ok bro

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[radiant garnet]

what would be the LCD here?

[odd edge]

Please don't occupy multiple help channels.

[radiant garnet]

trying to figure it out

im not great with this my guess was 2 3(1x+1) i have no real clue

ahh

[wind basalt]

it is

6(x+1)

[radiant garnet]

oh

so i was right or

i mean my guess was

[wind basalt]

ur right

[radiant garnet]

2*3(1x+1)

but thats not exactly 6(x+1)

okay so i can use that to cancel it all out?

alright

that seems cool thanks

ah shit im a bit lost again, so i tried doing the amth i got x = 11 @wind basalt

but i tried plugging it in the equation and it didnt work

i did the cancelling out and shit and ended up with 7(6) - 1(3x+1) = 4(2) simplified to x = 11

[nimble blaze]

7(6) -** 1(3x+1)** = 4(2)
middle part is incorrect

[radiant garnet]

oh

i thought if 1/2 then the 2 would cancel out to make it 3(x+1)

im not sure

[nimble blaze]

yes, but that's not what you had

3(x+1) isn't the same as 3x+1

[radiant garnet]

oh

wait

i think i know what you mean

i gotta subtract the 3 with the 42

[wind basalt]

😩

[radiant garnet]

or um

jesus im not great with this

[wind basalt]

thats correct

[radiant garnet]

42 - 3(x+1) = 8

so 39 (x+1) = 8

[wind basalt]

what

[nimble blaze]

poor wording

[wind basalt]

sir

[radiant garnet]

yeah soz

[nimble blaze]

and you're disregarding order of operations now because of it

[radiant garnet]

im sorry yeah it doesnt look right to me either ive been at this for like 8 hours today cuz its all review stuff from way back when i was in high school 😭

[nimble blaze]

multiplication takes priority before subtraction
you can't subtract the 3 like that before multiplying

[radiant garnet]

im a bit burnt out tonight

yeah youre right

so

-3(x+1)

-3x-3

[wind basalt]

👍

[radiant garnet]

holy crap

im so sorry

thats just a simple mistake

wow

i think i just need to go to sleep and finish it tomororw

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[cerulean garden]

What does it mean to take the derivative both sides?

[cerulean garden]

I mean if two functions are equal, ofc their derivative will be equal makes perfect scence

but how do we know that the lhs and the rhs would always have functions

for example x^2+y^2=10

If we take derivative both sides

the logic here is?

like say, f(x) = g(x) so f`(x) = g`(x), makes perfect scence, if two functions are equal for all valuse of x, then their graphs will be equal and derivative will be equal and anti-derivative will be equal

sure

Here we are treating 10 as a function of x?

and is this always true, can you always take derivatives of both sides?

[sand horizon]

Anti derivative would not be equal cuz of that +c

[sand horizon]

It is just a constant which become 0 in derivation

But you can see it like a constant function of x

[cerulean garden]

oh ok yes

[cerulean garden]

alright

and can we always just call both sides as functions of x?

and say that they are equal?

cause what dose equality mean

[sand horizon]

Well, i have a doubt, cuz the example you gave has y in it

[cerulean garden]

like when I say x +1 = 10, find x, I am asking someone to find x for which this is true

[sand horizon]

It would be treated like a constant wrt x

[sand horizon]

Yeah

[cerulean garden]

It does not mean that for all values of x, x+1 will be equal to 10

[sand horizon]

No

[cerulean garden]

So here in x + 1 = 10, if I take the derivative of both sides, I get 1 = 0

so we can't always take derivative both sides?

Why is calculus so hand wavy

lol

[sand horizon]

Derivatives is a deal with function, not equation i don't think you can use it like that

Cuz derivatives work in a cases of all x

[cerulean garden]

oh yeah got it, a relation is a subset of the cartesian product of two sets, and cartesian products relate TWO things in a tuple and functions is a subset of relations so one would need two variables

[cerulean garden]

Got it

[sand horizon]

Oh, yeah thoses are the words

[cerulean garden]

That also explains why you can take derivative of relations, cause after all they are two things related to each other by some relation

That is a very circular statemetn

lol

But you get the idea

Ok thank you got it

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[merry finch]

Draw a circle centred at the centre with radius of 2?

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[paper moth]

Can someone tell me how to study without getting distracted?

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@paper moth Has your question been resolved?

[paper moth]

<@&286206848099549185>

[green elm]

help channels are for help with specific hw questions, try asking in #math-discussion

[paper moth]

sorry

i will

[green elm]

nw, good luck!

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[broken oyster]

this might be a dumb question but for part a) why is the surface area 2000h

[marsh sorrel]

Well firstly it's wrong because surface area is measured in length², not length, but let's assume they mean 2000cm rather than 2000

Secondly, do you agree that the surface area is the product of these two lengths?

[broken oyster]

u don't hv to add the area of the other sides?

[topaz ibex]

thats the Lateral Surface Area

[marsh sorrel]

It says that it's a water trough so it's safe to assume they just mean the surface exposed to the air

[topaz ibex]

or

total area i guess

[broken oyster]

it's not the same thing?

[broken oyster]

oh ok

[broken oyster]

then yes i agree

[marsh sorrel]

Well now you have one length, so how do you find the other?

[broken oyster]

oh so it's just 2h*1000

[marsh sorrel]

Yes (except with units)

[broken oyster]

righttt alr tyvm

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[ebon sparrow]

help

[ebon sparrow]

help me please

i dont understand how to get the values

[odd edge]

@ebon sparrow Has your question been resolved?

[odd edge]

@ebon sparrow Has your question been resolved?

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[mystic sable]

halp

[elfin zodiac]

Did you try anything?

@mystic sable

[mystic sable]

no

i kinda got stuck

very fast

[elfin zodiac]

What is the probability you get 2 sixes if u chose the biased die?

[mystic sable]

uh

4/5

[elfin zodiac]

No

How did u get that

[mystic sable]

random

[elfin zodiac]

? What do u mean random?

[mystic sable]

bro

idk how to do these types

of problems

[elfin zodiac]

I am asking for the very basic step

[mystic sable]

fine

[elfin zodiac]

If you can’t do this very first step

You are not ready for this exercise

[mystic sable]

kk

inna roll

there are 6 diff possibilities

[elfin zodiac]

Try other easier exercises first and learn some basic

[mystic sable]

this problem like hard?

[elfin zodiac]

No, but is more advanced for your current knowledge

[mystic sable]

it seems hard compared to the permutation and combination ive dun at school

[elfin zodiac]

You know permutations but not how to get probability of getting 2 sixes in a die?

[mystic sable]

is it

1/12

wai

1/36

[elfin zodiac]

That would be the normal die

And the biased?

[mystic sable]

4/9

wai no

[elfin zodiac]

You tell me

[mystic sable]

https://tenor.com/bpwvw.gif

[mystic sable]

its 4/9 right

[elfin zodiac]

Ok

So how much probable is that you got the biased die to get 2 sixes with respect to the normal die?

[mystic sable]

its

1:16

?

[elfin zodiac]

What do you mean with that

16 times?

[mystic sable]

wai

the probability that i got the biased die

is 1/2

[elfin zodiac]

How so?

[mystic sable]

cuz there are 2 die

[elfin zodiac]

But you got 2 sixes

[mystic sable]

im comin to that

[elfin zodiac]

You have extra information

[mystic sable]

and the odd that i got the 2 sixes with the biased die is 4/9

so its 4/18?

[elfin zodiac]

Keep going

1/16 vs 4/9

How much bigger is the second one?

[mystic sable]

wdym

odds of the normal die/

?

[elfin zodiac]

2 vs 4, how many times is 4 bigger than 2

[mystic sable]

2 times biger

[elfin zodiac]

Now here

[mystic sable]

0.14 times bigger?

[elfin zodiac]

4/9 is bigger than 1/16

[mystic sable]

ye

[elfin zodiac]

How many times

How do you get 0.14?

[mystic sable]

64/9

[elfin zodiac]

Can you put your thought process?

[mystic sable]

so

if i divide 4/9 with 1/16

its 4/9/1/16

can be written as

4/9 times 16/1

which is 64/9

[elfin zodiac]

Wait, sry i am dislexic so i didnt notice your mistake

[mystic sable]

shit

its 1/36

[elfin zodiac]

exactl6

[mystic sable]

i was wonderin

[elfin zodiac]

Lol

[mystic sable]

then

its just

144/9

which is just 16

[elfin zodiac]

Ok so

The probability of getting the second die is 16 times greater than getting the normal die

So the total is

[mystic sable]

wait bro

the odds of gettin 2 sixes with the second die

is 16 times greater

not gettin the die itself rite

[elfin zodiac]

Yes, getting the biased die

Is 16 times

Getting the normal

[mystic sable]

alr

[elfin zodiac]

So the total would be

1/17 + 16/17

Right?

[mystic sable]

wait

why 1/17

where that come from

where the 16/17 come from

[elfin zodiac]

Because that would be the total, you dont know which die u cchose

16/17 is 16 times bigger than 1/17

[mystic sable]

heh

[elfin zodiac]

Out from 1

[mystic sable]

😕

[elfin zodiac]

1 is the totality

[mystic sable]

ye

[elfin zodiac]

Chose normal die and biased

[mystic sable]

y

e

[elfin zodiac]

1 = 1/x + 16/x

x = 17

[mystic sable]

ye

16 or 36?

[elfin zodiac]

16 times bigger

Dont get confused again with chances of getting to sixes with normal die

So ok

We got 2 sixes

And we want to know the third six right?

[mystic sable]

ye

[elfin zodiac]

Ok, we dont know which die we chose, but we know the probability

1/17 and 16/17

If the die is normal

The probability pf getting one six is…

[mystic sable]

1/6

[elfin zodiac]

1/17 * 1/6

And the other?

[mystic sable]

16/17*2/3

[elfin zodiac]

Ok give me the result

Sum those

[mystic sable]

its

1/102

and 32/51

[elfin zodiac]

So the total probability

What would be

[mystic sable]

holy

its 65/102

[elfin zodiac]

Now you do what the exercise is asking you

In the end

[mystic sable]

add those two

its 167

[elfin zodiac]

Perfect

[mystic sable]

goat

tysm

im stil kidna cnfused in that 1/17 and 16/17 bit tho

[elfin zodiac]

Ok so

Lets use other numbers

Imagine the probability of using one die is 1/2

[mystic sable]

k

[elfin zodiac]

And the other die is 1/4

So the first die would be twice as big

Right?

Twice means 2 times

2 times and 1 time

[mystic sable]

ye

[elfin zodiac]

That is a total of 3 times

So out of a total of 3 times

2 times will be one die

1 time will be the other

2/3 + 1/3

[mystic sable]

alr

[elfin zodiac]

Same in the other example

[mystic sable]

ALR

i got it

thx

[elfin zodiac]

!done

[odd edge]

If you are done with this channel, please mark your problem as solved by typing .close

[mystic sable]

.close

[odd edge]

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[mystic sable]

.reopen

[odd edge]

✅

[mystic sable]

.close

[odd edge]

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Closed by @mystic sable

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[mystic sable]

.close

.close2

[vernal yacht]

it's closed

[mystic sable]

goit

gotit

[odd edge]

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[timber patio]

guys, how do i do this?

[austere blade]

Try to make a sketch

My hint : Vectors

[nimble blaze]

Do you know properties related to diagonals of a parallelogram?
Apply the same formula as you did in a)

[lethal spoke]

The distance from A TO B SHOULD BE THE SAME AS THE DISTANCE FROM C TO D

I suppose

[nimble blaze]

true but not really what you want to apply to efficiently calculate the coordinates of D

[odd edge]

@timber patio Has your question been resolved?

[timber patio]

which property? is it the 2 equal sides?

[nimble blaze]

which equal sides

[timber patio]

AB is equal to CD

and AD is equal to BC

[nimble blaze]

true, but not the property most useful here

[timber patio]

ohhh

[nimble blaze]

focus on the properties relating to the diagonals

[timber patio]

is it the diagonals meet at one point

the 2 diagonals meet at a point which is the midpoint of AC

[nimble blaze]

missing the other half of that property

[timber patio]

hmm

BD's midpoint is the midpoint of AC

[nimble blaze]

yes

or in short, diagonals of a parallelogram bisect each other

[timber patio]

yes

ohhhh

okaayyy i get it now

[timber patio]

thank you so much

[nimble blaze]

np

[timber patio]

thankyouuu

[timber patio]

thank youuu

.close

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[timber patio]

.reopen

[odd edge]

✅

[timber patio]

btw parallelogram should have 2 parallel lines right?

AB parallel to CD, and AD parallel to BC

and parallel lines are supposed to have the same gradient right, why is my gradient of AB and CD different

[weary pelican]

the opposite sides are parallel to each other, even more so that the opposite sides have opposite vectors (vector AB = - vector CD)

[weary pelican]

what gradients did you find?

[timber patio]

oops wait

i just realised i haven't gotten the D

is the line for AB and BC supposed to be right angled?

[weary pelican]

no, that's in a rectangle

[timber patio]

ohhhh

i seeee

[weary pelican]

rectangles are parallelograms but not the converse

[timber patio]

okayy thank you so much. i thought they're right angled

[weary pelican]

tho I haven't checked if this one is a rectangle

[timber patio]

okayyy thanks again

.close

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[weary pelican]

quick update it isn't xd

[timber patio]

thanksss hehee

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[grave barn]

hello

[grave barn]

can i get help why is this equation non linear

i think its cus of the cos( r+ u) but an not sure

oh ok i was just making sure

thx

.close

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[neon yew]

So far I have that $\sigma^i:k\rightarrow(k+i)\text{mod m}$ where k is an element in the m-cycle

[neon yew]

I wrote out an example of \sigma = (1 2 3 4 5) and \sigma^2, \sigma^3, \sigma^4 but not sure how to start the proof

[clever fjord]

Soap_Opera

[mystic saffron]

does m cycle means it repeats every m elements?

[sweet dagger]

So write the condition i relatively prime to m

What does it mean in terms of the gcd?

[neon yew]

gcd(i, m) = 1

[sweet dagger]

So, use that

[neon yew]

correct

[neon yew]

How does that definition fit into cycle notation?

[bleak rock]

Solve for x
Sin x= cos x

[neon yew]

Are you hinting at cancellation property?

[neon yew]

gcd(i, m) = 1 implies that for some integers x and y, 1 = xi + ym. How do I use that to help with this proof?

[odd edge]

@neon yew Has your question been resolved?

[neon yew]

$\sigma^i : k\rightarrow k+i, \sigma^i : k+i\rightarrow k+2i, ..., \sigma^i : k+(m-1)i\rightarrow k$ So there are m mappings that are distinct if and only if each k + ai is distinct

[clever fjord]

Soap_Opera

[neon yew]

Since we are working with modulo m, that means each k + ai is distinct if $(k+ai)mod m\not\equiv (k+bi) mod m$

[clever fjord]

Soap_Opera

[neon yew]

So then, can I write ((k + ai) - (k + bi)) mod m $\equiv$ 0 so i(a - b) $\equiv$ 0

[clever fjord]

Soap_Opera

[odd edge]

@neon yew Has your question been resolved?

[odd edge]

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[timid saddle]

i cant even get the starting approach of these questions

[odd edge]

@timid saddle Has your question been resolved?

[timid saddle]

<@&286206848099549185>

<@&286206848099549185>

[whole steppe]

Please only ping us once, we'll help you soon!

[timid saddle]

sry

[whole steppe]

It's fine.

[timid saddle]

.close

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[shut flame]

I need to use Riemann Sum to solve this question, but how do i know what the function is?

[lavish osprey]

You don't need a function, you just need to pick out 5 rectangles that are equidistant apart and then sum them up. They're just asking for an estimate from x= 0 to x = 10.

Remember that your delta x is going to be (b - a)/n. So in this case, what is b, what is a, and what is n?

[shut flame]

delta x is 2, right?

[lavish osprey]

yep bingo, since (10 - 0)/5 = 2

[shut flame]

im just stuck on the step right after with summing it and multipling each by delta x

[lavish osprey]

Can you elaborate? show your wokr

*work

[lavish osprey]

,rccw

[lavish osprey]

Ok that looks fine. What are you confused about? That you don't have a defined function?

[shut flame]

yes!

[lavish osprey]

You can just estimate the value based on where it is on the graph.

f(2) is easy : f(2) = 3
f(4) is a little trickier so at this point you'll have to do your best to look and check. f(4) ~ 1.9 give or take

since they didn't give you the actual function, you'll just have to do your best to interpret what the y value is for each of your points

[dusk fractal]

since dx is 2
because (10 - 0)/5 = 2
we look at the graph and find those values

[lavish osprey]

Hi there please to just flat out provide the answers. We want students to do their own work

!nosols

[odd edge]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[dusk fractal]

Ah my bad, only trying to help

[lavish osprey]

of course! Glad to have your help 🙂 Just a rule of the server

[dusk fractal]

Sami, I can help you follow the lines to the very end answer (Total area)
Without calculations, would you like me to?

[lavish osprey]

But i would check these values again, they're off a bit.

[shut flame]

so i have to manually check them ?

[dusk fractal]

Yeah, tired I am (that's my bad)

[lavish osprey]

With nothing else provided? Yes.

But it's not hard. Just look at your x values and then determine what the y would be based on where it lands

[shut flame]

okay, thank you

[odd edge]

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[lethal pond]

what've u tried

[sleek moth]

Assume that g has maximal domain

i.e. you can't just assume the domain is [0, 8] because you can do better

assuming maximal domain is also crucial for finding the range of the function

[cinder moat]

How does the 1/3 affect the domain or range

[sleek moth]

maybe you could try coming up with a concrete example of f and then plot the function and see?

[cinder moat]

Is it negative infinity , 18?

With ( ]

[sleek moth]

the range? nope

[cinder moat]

But the 1/3 affect the y values right?

[sleek moth]

sounds like a reasonable claim

[cinder moat]

So the range is affected

[sleek moth]

indeed g does not have the same range as f

at least assuming a maximal domain

[cinder moat]

So what does the 1/3 do?

[sleek moth]

for a given input x, it divides f(x) by three

recall that every real number can be divided by any other real number

except zero

[cinder moat]

Im confused 😕

[sleek moth]

So let's say when you plug in 1 to f you get 3, i.e. f(1)=3

Then g(1) = f(1)/3 = 3/3 = 1

[cinder moat]

So is the domain [-12,24]

[sleek moth]

Are you sure you mean the domain or the range?

[cinder moat]

Domain

[sleek moth]

That means that -10 belongs to the domain

How would you define g(-10)

[cinder moat]

I've got to go sorry thx for the help

[sleek moth]

np! cya

(did I take the right pedagogic approach or was I just being deliberately obtuse? who knows! :P)

[odd edge]

@cinder moat Has your question been resolved?

[cinder moat]

Yes

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[hollow jewel]

Is undefined ≠ 6 is considered false?

[hollow jewel]

Or true?

[fair prism]

That statement just doesn't make sense

[hollow jewel]

Oh I'm sorry, I'm solving rational inequalities

Then we need to check it in a number line

[fair prism]

You should send the entire context but I don't mean it makes no sense without context, that just is not a valid statement so you cannot say its "True" or "False".

You cannot say undefined = or != number. You would need to word it differently (I would need the context to give a more specific way of how you should word it)

[hollow jewel]

Sorry for that, I'm solving this one

Number 2

Then

[fair prism]

What do the instructions say at the top

[fair prism]

You would say (2x-3)/(x+7) is undefined at x=-7 (and hence not draw it on the number line)

[hollow jewel]

Ohh, thanks!

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[noble anchor]

Need help with college algebra! I need to complete the piecewise functions for this graph. The first and third are getting marked as incorrect. I've tried using the formulas for slope and point slope form but I can't get the right answers.

[mint mirage]

It's how you are factoring out the term, y = (1/2)x - 5.5 is the correct equation but when you factored out the 1/2, that was where the mistake was

[noble anchor]

Can you elaborate? sorry, very rusty with math

[mint mirage]

So from y = (1/2)x - 5.5, you are trying to factor out 1/2, correct?

Also, as a note on how to check your work, take the current equation you have, y = (1/2)(x - 5.5) and distribute the 1/2 and you'll see that it's not equal to y = (1/2)x - 5.5

[noble anchor]

I see my mistake now! thank you so much for the help!

.close

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[woeful aspen]

my friend was having some trouble with this and he sent it to me but I wasn't able to solve it. Could anyone explain how to solve it?

[tepid pelican]

this one?

[odd edge]

@woeful aspen Has your question been resolved?

[woeful aspen]

last one

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@woeful aspen Has your question been resolved?

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[wide drift]

Im not really sure what to do here

Like I know we need it in the form a < p < b

Or p < a

And im guessing I need to get the discriminant of some quadratic and set it > 0

But im not sure specifically what to do

Just have these ideas

[mighty rose]

Cant you just set fp = 1 then solve for p as indeed the discriminant > 0

[wide drift]

Watskeburt thijs 😄

[wide drift]

Oke I will try

(2x^2 + 9x + p)/(x + 3) = 1

(2x^2 + 9x + p) = x + 3

2x^2 + 8x -3 + p = 0

Discriminant is b^2 - 4(a)(c)

8^2 - 4(2)(p - 3) > 0

64 - 8p + 24 > 0

-8p + 88 > 0

88 > 8p

p < 11

So thats my answer?

[mighty rose]

Seems right to me

You could check with desmos

[wide drift]

Wait I just checked the answer sheet

How come its != 9?

[sand horizon]

The thing austin explained last time

[wide drift]

This is different tho, no?

[sand horizon]

You found p = 9 for no asymptote

Then p != 9 for one or more asymptote

[wide drift]

Ohhhhhh

[wide drift]

So we have a hole at p = 9, right?

[mighty rose]

Aaaaaa

[wide drift]

Yeah sry you didnt know cause it was a part of a previous question

I didnt think it was important but I see now it was

So my bad

[mighty rose]

Yeah still should have known but i also didnt pay attention to it so also my bad haha

[wide drift]

But am I correct?

theres a hole at p = 9?

Removable discontinuities are always holes right?

[mighty rose]

Sortof

Yes there us a hole at x= -3 but it isnt the cause here

Because it is a ‘removable’ diacontinuity youll see that the graph turns into a linear function

For p = 9

Therefore there is only 1 intersection point by definition do you know what I am trying to say?

[wide drift]

I think so

[sand horizon]

If you can factor when p=9, then f_p would just be a line equation

And two lines can have only one point of intersection

Or infinity

[mighty rose]

Screenshots from desmos as illustration

[wide drift]

Ok I see now

That makes sense it cant intersect a line equation twice

Alright I think I understand everything now haha

Thank you so much everyone!!

❤️

.close

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[peak lake]

Can you add two piecewise functions?

In some sort of "piecewise function arithmetic"?

I am asking because the general solution to the 1D wave equation is $\frac{f(x-ct)+g(x+ct)}{2}$

[clever fjord]

normalAtmosphericPa=101,325

[peak lake]

and when I apply the initial condition, which is a piecewise function, I will get two piecewise functions $f,g$

[clever fjord]

normalAtmosphericPa=101,325

[peak lake]

So, by D'Alembert's formula, how do I complete the solution?

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[celest monolith]

Hello im trying to solve problem 14

this is trignometry similar right triangles

all i need to figure out is how to find either the missing leg or hypotenus so i could solve for pythagoerean theorem

any help is appreciated

[pale atlas]

You can probably use sin, cos, tan to find the values I think

[celest monolith]

ohh ok we havent went over that and its been a few years since ive used sin cos tan

[pale atlas]

Like cos25 = b/c
b is given, you know what is the value of cos25 so find C

[celest monolith]

one sec

[nimble blaze]

use the triangle given to you

[pale atlas]

@celest monolith find sin25 and cos25 value from 1st triangle
Then use those values to find a and c in second triangle

[celest monolith]

ok ill do that rn

[celest monolith]

yea im having trouble figuring out how it correlates i understand the sides are equal but what the 0.47 etc is for

[nimble blaze]

sides are not equal

[pale atlas]

@celest monolith try this
sin = p/h
cos = b/h
p,b,h are given in first triangle

[nimble blaze]

ratio of corresponding sides are equal

[celest monolith]

ok

[nimble blaze]

you could incorporate trig into this, but not explicitly needed

[celest monolith]

oh ok so this geometry?

the course is trignometry with analytic geometry

[pale atlas]

Or you can directly do as @nimble blaze said
p/b of first triangle= p/b of second triangle

But for your understanding I said try with sin, cos etc

[celest monolith]

ok

@pale atlas hey im getting 21.5 as one of sides is that correct?

[pale atlas]

Which side

[celest monolith]

b

side opposite to the hyp

[pale atlas]

b is already given 51

You need to find a and c right?

[celest monolith]

yea i meant c

sorry

i used sin

to find 25

i think i shouldve done cos instead

[pale atlas]

Its should not come 21.5

Can you show what you did?

[celest monolith]

yea ill do a paint thing rq i dont have discord on my phone

[pale atlas]

Ohkk

[celest monolith]

i was following a video that used cos sine so i prob did the whole thing wrong

[pale atlas]

No worries, show what you did , I will help

[pale atlas]

Don't find sin value . Look at first triangle what are p,b and h in first triangle can you write them down here in chat

[celest monolith]

h 1.1 b 1.0 p 0.47

ohh right i just checked

[pale atlas]

Let's take cos25 , it will be b/h right

[celest monolith]

right

[pale atlas]

so cos25 = 1.0/1.1 from first triangle

Now in 2nd triangle what will be cos25?

[celest monolith]

cos25 would be 51/1.0?

no not 1.0

[pale atlas]

51/c

[celest monolith]

51/c ok

[pale atlas]

So can you write
1.0/1.1 = 51/c ?

As both are cos25

[celest monolith]

yea

[pale atlas]

Now find C

Follow the same for tan25 = p/b in first triangle, and in second it will be a/b. You can find a from that

[celest monolith]

im getting 76.5 but i dont think thats right

cross multiply

1.0c=76.5

[pale atlas]

Wrong calculation

It should be 56.1

[celest monolith]

yea im trying to figure out i miscalculated that

[pale atlas]

1.1*51 I don't know how to use calculator in this bot server

[celest monolith]

yea i see what i did i had 1.0 instead of 1.1 thank you

i multipled the 1.5 with 51

i appreciate the help!

[pale atlas]

No worries

[pale atlas]

Use this to get a

[celest monolith]

oh ok ill write that down in my notes i have to get ready for school thanks again!

[pale atlas]

Your welcome

[clever fjord]

Result:

56.1

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[restive night]

Asymptotes

[restive night]

So I'm confused about the range

Cause I was told

range:｛y | y ≠ H.A. values}
H.A = Horizontal Asymptotes

is this not accurate

[pastel orbit]

it is not, unfortunately

the range (or image) of a function is the set of all outputs the function produces

the f(x) shown has a hole at x = 3, where it would be equal to 1 without the hole

[restive night]

hole?

[pastel orbit]

yes, a removable discontunuity if you prefer

[restive night]

I have no idea what is that also

[pastel orbit]

it also outputs a value of 1 nowhere else, so the range does not include 1

[pastel orbit]

ah, my mistake

[restive night]

Well my teacher didn't even explain how to graph it or anything so yeah

[pastel orbit]

there's a hole at x = 3 because f(3) = 0/0

[restive night]

Can I interpret the "hole" as restriction?

[pastel orbit]

this is indeterminant, so the function does not exist at that point

[restive night]

I see

The range will be what got plugged in for x

[pastel orbit]

the range is the set of all output values of f(x), yes

[restive night]

With that known..

hmm its not clicking

[pastel orbit]

hm, what is not clicking?

[restive night]

The concept

[pastel orbit]

of range?

[restive night]

yea

So Rational Function's Domain are the restricted values of what "x" cannot be that makes the denominator 0 since that will be undefined

[pastel orbit]

correct