help-0

[chilly dove]

my answer is 24%, is that correct?

[narrow kelp]

40/100 = 360/x

,calc 360/40

[ocean seal]

Result:

9

[narrow kelp]

900 is original

[chilly dove]

ohh

[narrow kelp]

wait

[chilly dove]

my answer was 600

[narrow kelp]

,calc 360/900

[ocean seal]

Result:

0.4

[narrow kelp]

360 * 2/5

,calc 360*2/5

[ocean seal]

Result:

144

[chilly dove]

i got 144 for michael

[narrow kelp]

$\frac{144}{900-360}$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

that will be your answer

[chilly dove]

are you sure?

[narrow kelp]

,calc 900-360

[ocean seal]

Result:

540

[chilly dove]

it asks for a percent

[narrow kelp]

,calc 144/540

[ocean seal]

Result:

0.26666666666667

[narrow kelp]

26.67%

(i believe)

[chilly dove]

could you write your equations here

[narrow kelp]

$\frac{60}{100} = \frac{x-360}{x}$

[ocean seal]

CrEpasPmkinPie

[chilly dove]

i mean the thing is 360 is 40% of 600

and 600 should be his savings

[narrow kelp]

900

[chilly dove]

could you tell me how you got that

[narrow kelp]

the previous equation can be simplified to $\frac{40}{100} = {360}{x}$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

nope wrong equatioe

$\frac{40}{100} = \frac{360}{x}$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

now do some fraction algebra to solve for x

I multiplied the left side by 9/9

[chilly dove]

ohh ok

[narrow kelp]

now the numerators are the same

and now you have the original value of 900

[chilly dove]

and for mr lee he kept 900-360 right

[narrow kelp]

$900-360=$ Mr. Lee's money

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

yrd

yes

[chilly dove]

like total money or the amount he kept

[narrow kelp]

,calc 900-360

[ocean seal]

Result:

540

[narrow kelp]

540 is the amount mr lee kept

[chilly dove]

alright

thanks

[narrow kelp]

need any more help?

[chilly dove]

nah i think im good

[narrow kelp]

woo

[lone heart]

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[dim matrix]

Is my solution correct?

[whole shell]

this part feels sussy

shouldnt it be ((a+b)^2 -2ab)^2 - 2a^2b^2

[dim matrix]

@whole shell Is it fine now?

[whole shell]

yh

that seems fine

@dim matrix yh that works

[dim matrix]

Many thanks @whole shell 👍

.close

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[lilac thicket]

Hey guys I have a question on first order logic

[pliant cedar]

[lilac thicket]

Ye one second sorry have to send the picture

But my tablwts connection got lost sorry

So given the structure A and the interpretations for the relationsymbol G and the functionsymbol dot

I need to find the formula phi such that the satisfying elements of A are all the +/- 2^k

I am struggling with describing that the elements have to be powers of two
Can someone give me a hint maybe?

So I was able to define the following formulas

but really the 2^k part is hard for me

ah nvm I think I have an idea

,close

.close

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[candid swan]

someone help

[candid swan]

i can’t understand my teacher

i need some help on these

so i can better get what is happening please

[lone heart]

@candid swan Has your question been resolved?

[lone heart]

@candid swan Has your question been resolved?

[rustic coral]

It’s just matching the form - $a=1, p=2, q=-4$ (note $p$ and $q$ are interchangeable because multiplication is commutative)

[ocean seal]

Civil Service Pigeon

[harsh swallow]

the x intercepts are the roots

where the graph intersects with the x axis

y = 0

and so when you look at the pattern

and compare it to the function you are given

you can find the values for a, p, and q

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[thorn ice]

how did they know that angle corresponds to that point?

[merry depot]

go to the line marked 2pi/3
That's the point on the circle

[thorn ice]

i have to memorize this?

[thorn ice]

what if they give me something thats not on the circle?

[merry depot]

then you probably won't be asked to find the exact value, or you'll be given triangles and use the triangle definitions to find the values

[thorn ice]

okay thanks 👍

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[bitter grail]

How would I begin this problem

[lone heart]

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@bitter grail Has your question been resolved?

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[alpine sable]

how 2 solve for x?

[alpine sable]

is it 7?

[narrow kelp]

What number minus 7 equals 3?

or

[alpine sable]

13

wait

10

[narrow kelp]

and

here's how you can do this in general

$3=10-7$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$3+7=10-7+7$

[ocean seal]

CrEpasPmkinPie

[narrow kelp]

$3+7=10$

[ocean seal]

CrEpasPmkinPie

[alpine sable]

oh wow tank u so clear

i want to finish so i can pay minecraft

[lone heart]

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[alpine sable]

sorr

sprry

sorry

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[pliant wedge]

I solved this non-homogeneous linear system and i have a free variable

Does it matter whether i take x1 or x2 as a free variable?

[lone heart]

@pliant wedge Has your question been resolved?

[old birch]

My friend sent me this question and I’ve tried my best but no luck. Is it been solvable?

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[loud thorn]

it confuses me why as isnt a shift UP 24 units

a*

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[shadow raptor]

I need to find the surface area of this trapezoid prism and i tried everything but cant get the right answer (210in^2)

[narrow kelp]

What is that 5 in in the back

[shadow raptor]

for the rectangular part

its the height of the rectangle

.close

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[tepid elk]

ANYONE NEED HELP

[shadow raptor]

i really do

[tepid elk]

ok

[shadow raptor]

ill ping you in it

[vapid shuttle]

Please read #❓how-to-get-help

This is not what these channels are used for

[wanton mauve]

i have question

[vapid shuttle]

Read #❓how-to-get-help

This channel is occupied

[wanton mauve]

oh

um bye

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[worthy cloak]

I'm trying to find C, the result of the other part (before +C) depends if it's rads or deg, so I'm confused. I'm supposed to work with radians or degrees? This is a rectilinear movement problem.

[surreal meadow]

radians

if you have an angle in terms of pi it usually means you’re working with radians

[worthy cloak]

Makes sense. Thanks!

.close

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[quasi dirge]

I need help with algebra 2 Highschool

[narrow kelp]

show problem

[alpine sable]

I’m learning how to find Domain and Range with equations and very confused. How do I find domain and range for a problem that looks like this: y=square root of x

[quasi dirge]

it's super easy but I'm struggling

[narrow kelp]

start with number 1

[alpine sable]

@quasi dirge I think we’re doing the same thing lol

[quasi dirge]

he showed us number 1 but it didn't help

[narrow kelp]

do you remember transformations?

[quasi dirge]

nope

[narrow kelp]

like

translations

reflections

rotations

dilations

?

[quasi dirge]

I think I've heard of dilations

[quasi dirge]

from what u said i think so

[narrow kelp]

thats what's happening here in question 1

[quasi dirge]

this is what he showed us

[narrow kelp]

that's $y=\sqrt{2x}$

[ocean seal]

CrEpasPmkinPie

[quasi dirge]

like I just need to know how to find range and domain

[quasi dirge]

yeah that looks about right

[narrow kelp]

Imagine you drew a box around the function

the domain is how big it is from left to right

the range is how big it is from bottom to rop

*top

[quasi dirge]

so

what would 3 be

[narrow kelp]

to graph it?

[quasi dirge]

no the domain and range

I got the graph

[narrow kelp]

so look at the graph

how far to the left does it go

or

[quasi dirge]

it goes right

[narrow kelp]

what is the point to the left most of the graph

[quasi dirge]

starts at zero and goes on

[narrow kelp]

So the the leftest point is

is

(answer)

[quasi dirge]

so it would be
X≥ 0
Y≥ 0

?????

[narrow kelp]

yes

[quasi dirge]

really????

[narrow kelp]

mhm

[quasi dirge]

danggg

okay hold on lemme see other questions to to make sure

so would it be
X≤-3
Y≥0
(edited)

wait not zeros

X≤-3

?!?

@narrow kelp

[narrow kelp]

not right

you're saying x goes infinitely left

[quasi dirge]

oh

so would the sign be hte other way around?

[narrow kelp]

yes

[quasi dirge]

X≥-3

then Y is correct?

[narrow kelp]

Y≥0

[quasi dirge]

so if it was like this it would be going left infinitely

and this Y≤0 is down infitely

[narrow kelp]

Yes

[quasi dirge]

holy, thank you so much

that actually helped so much

[narrow kelp]

np

I haven't actually done alg 2 :p

[quasi dirge]

seriously?

[narrow kelp]

nope

[quasi dirge]

what math are u taking?

[narrow kelp]

oh woops

I lied

[quasi dirge]

lmaooo

[narrow kelp]

lol

forgot it was combo lol

Im taking alg 2 trig but I do not like the teacher

[quasi dirge]

ohh

gotcha gotcha

I feel taht

that

my teacher goes insanely fast and I can't keep up

[narrow kelp]

oof

[quasi dirge]

could you help with 7-9 in a moment?

[narrow kelp]

sure

[quasi dirge]

correct?

if so then I'm ready for 7-9

[narrow kelp]

correct

[quasi dirge]

lets gooooooooo

tysmmm

[narrow kelp]

https://media.discordapp.net/attachments/490557019623915520/1078512114441912330/image.png

Question 7?

[quasi dirge]

yup

[narrow kelp]

So

Its an inequality

and it doesn't ask for the D or R

so you want to graph this

and shade the side of the equation its dealing with

and <> mean dotted line and ≤≥ mean full line

[quasi dirge]

so should I only have the line that i punch into the graph

[narrow kelp]

?

[quasi dirge]

???

[narrow kelp]

that looks wrong

[quasi dirge]

thats what i put in

[narrow kelp]

Is with the f slider?

[quasi dirge]

it told me to put the slider

[narrow kelp]

hmm

[quasi dirge]

?!?!?!?!?

[narrow kelp]

It looks more right

[quasi dirge]

I got it!!!

thank you so much for helping me

[narrow kelp]

wooo

[quasi dirge]

.close

[lone heart]

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[jagged laurel]

Ops

Lol you’re fine

[restive hearth]

You cannot distribute the 2.

It’s not -2(x^2 + 4x + 3) (multiplied by -2)

It is (x^2 + 4x + 3) - 2 (subtracted by 2)

If I understand it correctly, you are subtracting it, therefore the -2 cannot be distributed in.

What was the original question?

Are you trying to combine like terms?

A negative two that you added to the end as multiplication?

Why are you multiplying it with -2?

The original was as such:

(x^2+4x+3) -2

Correct? Before dropping the parentheses.

You cannot distribute the -2 in as it’s not multiplication.

It’s subtraction.

[lone heart]

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[worn mulch]

Hello, I am having trouble with graph sin and cos functions. I get all the information up to the point of plotting the x values. I get very confused on how to make the x values to fit after a phase shift. So I overall just need help plotting x values also I can not use a calculator for this class.

[worn mulch]

If my handwriting is to hard to make out please ask

[remote heron]

so one way to think of it is

you know where sin(x) is 0

if x = npi, where n = 0, +-1, +-2, ...

so you solve as many of these little 'sub equations' as you need to get intercepts

like one would be $\frac12t+\frac{5\pi}{3} = 0$

[ocean seal]

jan Niku

[remote heron]

where this is true, $\sin \qty( \frac12t+\frac{5\pi}{3})=0$

[ocean seal]

jan Niku

[remote heron]

hopefully that is helpful

[remote heron]

.

[worn mulch]

so would I eventually get to the end value I calculated doing this?

[remote heron]

end value?

[worn mulch]

A video showed me you can calculate the start and end value of a phase shift

so I was trying to find points in between to graph it

[remote heron]

well you could find like

where 0, pi, and 2pi get sent

[remote heron]

i feel like its easier to do this .

especially with no calculator

[worn mulch]

so I add the t value to each answer I get after the first one?

[remote heron]

If i understand your question

you are confused where like

where are the roots on the horizontal axis

of some sin function like that, with a transformation on the inside

but maybe i misunderstood

[worn mulch]

yea so 5pi/3 would be the start correct? and then I need the other 4 points going right so I can mirror the points on the negative side. so your saying if I take 1/2t + 5pi/3 and solve that I will get the shifted start point. then after how do I get the other points. or is the 1/2t + 5pi/3 gonna give me the point that goes after and I just repeat that step?

[remote heron]

What im saying is like

you solve the inner equation in a clever way to know where the intercepts are with the horizontal axis

then all you need is the amplitude and you can graph it

i think you mean start in terms of t? i dont think its very helpful

its too hard to think, for me, in terms of the linear transformation at just arbitrary places

[worn mulch]

Can I show you a picture of how my professor did it and maybe you could explain that better to me cause it may be what you are trying to say

[remote heron]

sure

or i can give u an example of what im trying to say

sometimes you have to do it in the way your teacher wants though

well any method that works is a good method so

[worn mulch]

Ok so he uses this table looking thing

[remote heron]

Ah thats one way

[worn mulch]

so I dont really understand this

[remote heron]

it looks to me like hes relying on you having some comfort with transformations already

can i show you the easy way

[worn mulch]

Yes please

[remote heron]

or do you have to understand his way

okay we have function

$\sin \qty( \frac12t+\frac{5\pi}{3})$

[ocean seal]

jan Niku

[remote heron]

do you agree that sin(0) = 0?

[worn mulch]

yes

[remote heron]

okay

then assume that $\frac12t + \frac{5\pi}{3} = 0$

[ocean seal]

jan Niku

[remote heron]

this must mean that $\sin \qty( \frac12t+\frac{5\pi}{3})=0$

[ocean seal]

jan Niku

[remote heron]

seem reasonable?

[worn mulch]

yea

[remote heron]

all were doing is using that sin(0) = 0

okay, so we can solve

$t = \frac{-10\pi}{3}$

[ocean seal]

jan Niku

[worn mulch]

10pi/3 right

yea

[remote heron]

yea

so where t = -10pi/3, sin(that whole mess) = 0

and you have a point you can plot

[worn mulch]

so the start point correct?

[remote heron]

sure, the start point

[worn mulch]

ok how do I go from there

[remote heron]

the next really easy value for sin

sin(pi)=0

so $\frac12 t + \frac{5\pi}{3} = \pi$

[ocean seal]

jan Niku

[remote heron]

we want to enforce this

what do you get for t?

[worn mulch]

uh hol up me slow

[remote heron]

youre good, do you understand why were solving this equation?

feel free to go as slow as you want to

[worn mulch]

to plot the next point?

[remote heron]

yea, and because we know that sin(pi)=0

so if some stuff = pi, then sin(some stuff) = 0

easy point

[worn mulch]

would this value change depending on the problem?

[remote heron]

it will depend on whats inside the sin

transformations inside the sin are gonna stretch and distort stuff

but this method works really well for 'simple' transformations

especially stuff like lines inside the sine

ideally you just want these equations were making to be easy to solve

if some stuff = pi is hard to solve, this method doesnt work so well

[worn mulch]

yea ill be honest with you even solving that equation up there is kinda racking my brain since im so used to a calculator

[remote heron]

lets go through it

$\frac12 t +\frac{5\pi}{3} = \pi$

[ocean seal]

jan Niku

[remote heron]

my first step, because i just hate fractions and they make me make mistakes

i will multiple everything by every denominator i see

$\frac{2\cdot 3}{2}t +\frac{2\cdot 3 \cdot 5\pi}{3} = 2 \cdot 3 \pi$

[ocean seal]

jan Niku

[remote heron]

multiply everything by the same amount, so no change in equality

and we get some really nice cancellations

can you simplify this ?

[worn mulch]

yea one sec

[remote heron]

the fractions should go away

brb

[worn mulch]

so it would be 3t + 10pi = 6pi ?

[remote heron]

yea looks good

thing you can solve this?

looking for combining like terms, then isolating t

[worn mulch]

yea so 3t = -4pi

then divide

3t/-4pi

or sorry -3/4pi

i think

[remote heron]

you just wanna strip the 3 off of the t

so $\frac{3t}{3} = \frac{-4\pi}{3}$

[ocean seal]

jan Niku

[remote heron]

divide both sides by 3

[worn mulch]

yea

[remote heron]

and we get another point

[worn mulch]

oh other way around

I see

[remote heron]

what do you think of this method

at basically every step youll have to solve an equation like this

which can be easier than understanding transformations in the other way

if youd rather avoid solving linear equations

but were basically done

[worn mulch]

so do I use this point now by doing 1/2t + -4pi/3 = 0 to get the next point?

[remote heron]

well we have a 0 now

and we know its the next one

so youre mostly done

https://www.desmos.com/calculator/x31byn4zyt

heres our two points

do you see how you can use the repeating nature of sine to help you from here?

[worn mulch]

so I can keep moving forward by +6pi/3?

[remote heron]

yup

every time you will find another x intercept

same way for going backwards

i mean i guess really they are t intercepts

this is most of the information you need to solve the problem

sorry

to graph the function

[worn mulch]

so the next one would be 2pi/3 then

if so I think im good

[remote heron]

can you tell the amplitude of this function

just by looking at the equation

[worn mulch]

its 1

[remote heron]

yup

so you know how high it goes

[worn mulch]

yep

[remote heron]

from -10pi/3 = t

is it going up

or down

as you move right

[worn mulch]

and then if it had a number at the end it would change the midline

[remote heron]

(the sign of the amplitude tells you this)

remember sinx increases to the right of x=0

and -sinx decreases to the right of x=0

[remote heron]

yup

thats gonna make this method not work so well right

you have an extra step

if sinx+a=0

then sinx = -a

its just one extra step

[worn mulch]

if its negative before the sin dont you do the inverse of it

[remote heron]

negative before the sin just flips the function

,w plot sinx and -sinx

[ocean seal]

Results provided by WolframAlpha

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[remote heron]

upside down

[worn mulch]

ok so what are you explaining now? if I had a another value to take into account?

[remote heron]

im explaining if sin(some stuff) + 5

graphing this kind of equation

because sin(0)+5 isnt equal to 0

what you reall want to solve first would be some stuff = -5

this will give you a t intercept

or x intercept or whatever

[worn mulch]

would you be able to explain this better to me if I get another example problem? I dont know if theres a time period on this but if I cant let me know.

[remote heron]

we can do an example

say like

$\sin(2x)+\frac12$

[ocean seal]

jan Niku

[remote heron]

the time limit is its my bedtime but im down to help

this is the most fun thing i will do today

[worn mulch]

Ok I really appreciate it. damn💀

[remote heron]

is this example okay?

[worn mulch]

I need to sleep in like a half hour too.

yes

[remote heron]

okay so

we know that we can solve sin(some stuff) = 0 easily

lemme think of how to say this

[worn mulch]

could this equation also be written like this hold on

f(x)=4sin(π/2(x−3))+7

like only focusing on whats inside the parenthesis wise

not the actual numbers

[remote heron]

[worn mulch]

sin(π/2(x−3))

[remote heron]

i hate it when they add on a number like this

[worn mulch]

like this part

[remote heron]

i dont really get what youre asking

[worn mulch]

oof so this is different then if it were like sin(2t +pi/4)

so that long expression is what im given

then I graph off that

but to get the t values we use whats inside the parenthesis of sin( )

[remote heron]

oh

i think i get what you mean

well $\sin(2x+\frac12)$ and \sin(2x) + \frac12$ are 2 really different graphs

[ocean seal]

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

[remote heron]

if thats what you mean

[worn mulch]

oooh yea this is the real issue im having

the two things inside

rip

[remote heron]

okay so the two things on the inside

you just do the thing we did before

set it equal to 0

set it equal to pi

then you seemed to have intuition from there

[worn mulch]

will pi ever be a different value

like replaced by something else in the equation

[remote heron]

so its pi because were solving sin(some stuff) = 0

if instead you were doing like

$\sin(2x)+\frac12$

[ocean seal]

jan Niku

[remote heron]

this will take you to different places

but the 1/2 is outside the parens

like, we are shifting the whole function

this is a way different problem

if you are graphing sin(some stuff)

you should always use pi and 0

[worn mulch]

tan is when it gets different im assuming

woah

discord just died

[remote heron]

a lot of graphing tan is just understanding the graphs of sin and cos

[worn mulch]

I meant to ask is it pi when its cos still

[remote heron]

well where is cos(some stuff) = 0

[worn mulch]

so it is alright

[remote heron]

,w graph cos x

[ocean seal]

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Requested by jan Niku#2119

[remote heron]

is cos(pi)=0?

[worn mulch]

uh

yeass?

[remote heron]

thats not what I'm seeing in the plot

im looking where x=pi

[worn mulch]

is it 1/2 pi

[remote heron]

yea

1/2 pi

3/2 pi

these are another thing to remember but

theyre really important to remember

[worn mulch]

ok so you would set it equal to 1/2 pi instead

[remote heron]

your basic unit circle stuff

[worn mulch]

im write down

[remote heron]

yea like

if cos(some stuff) = 0

then some stuff = pi/2

alternatively you can do the peaks

if cos(some stuff) = 1, then some stuff = 0

pick your poison

not to overload you

[worn mulch]

Ok I think this helps so could we run through a example real fast that had two numbers on the inside of the sin parenthesis

I write it down then we sleepy

[remote heron]

like uhh

$\sin(3x+\frac \pi 2)$?

[ocean seal]

jan Niku

[worn mulch]

yea

[remote heron]

does that example work?

okay

whats the first step

[worn mulch]

I think so

set it equal to 0

[remote heron]

right

since sin(some stuff) = 0

means some stuff = 0

and we really want x intercepts, because theyre easy to find and easy to plot

$3x+\frac \pi 2 = 0$ what do you get

[ocean seal]

jan Niku

[worn mulch]

so would you divide both sides by 3 then basically multiply I think since its dividing a fraction by 3

[remote heron]

just take it step by step

get rid of the fractions

combine like terms (usually a pi floating around), and isolate x

[worn mulch]

sorry I did it on paper and didint say it

[remote heron]

ur good

whats x?

[worn mulch]

3x = -pi/2

this is where im stuck

[remote heron]

i'd get rid of the fraction first

$6x+\pi = 0$

[ocean seal]

jan Niku

[remote heron]

since this is so much easier

[worn mulch]

so multiply everything by 2

[remote heron]

multiply everything by 2

yup

[worn mulch]

so -pi/6

[remote heron]

alright, we get x=-pi/6

how do you interpret that

what does it mean

what can we plot, is what im asking

[worn mulch]

its the start point on the graph

[remote heron]

what will be the value of $\sin \qty( 3 \frac{-\pi}{6} + \frac \pi 2 )$?

[ocean seal]

jan Niku

[remote heron]

( if some stuff = 0, what is sin(some stuff) = ? )

[worn mulch]

do we have to set that whole thing = to pi

[remote heron]

thatd be the next step, yea

as long as you got your point plotted

from the first one we did

did you get it plotted?

[worn mulch]

-pi/6 is the first point correct

[remote heron]

it is, yea

-pi/6, 0

[worn mulch]

yea I have it

[remote heron]

okay

next up is pi

[worn mulch]

so you have to put the first point into the t?

sorry c

x

[remote heron]

i was just asking like

clarifying questions

to see if you were feelin understandy

but its not important

[worn mulch]

oh

[remote heron]

the process is probably more important

[worn mulch]

aight

[remote heron]

so were solving $3x+\frac \pi 2 = \pi$

[worn mulch]

so it would just be 3x+pi/2 = pi next

[ocean seal]

jan Niku

jan Niku

[remote heron]

1. get rid of fractions
2. combine like terms
3. isolate x

[worn mulch]

so it would be pi/6

[remote heron]

allright

now you should have enough info to fill in the rest of the graph

if you understand sin well enough

[worn mulch]

then for the steps from there you do +2pi/6 for each

[remote heron]

you know its amplitude 1

damn we should have done one that was reflected

i have a feeling youd catch it though

if the very next problem was $-\sin\qty( 3x + \frac \pi 2 )$ you think youd do okay?

[ocean seal]

jan Niku

[worn mulch]

would you do the equation = to pi/2 like the cos one

[remote heron]

you do the exact same thing

except where sin goes up

-sin goes down

and visa versa

so from the starting point, it goes down

[worn mulch]

you just graph it differently

[remote heron]

not up

[worn mulch]

amplitude wise

[remote heron]

https://www.desmos.com/calculator/8q4cy7kupq

see

[worn mulch]

It does not change on the t values right

[remote heron]

same intercepts

same magnitude

just flipped

[worn mulch]

yea

I understand that stuff like inverse and what not

[remote heron]

well i might go to bed

[worn mulch]

Thank you so much

[remote heron]

hope you have luck with your problms

no problem

[worn mulch]

Have a good night

[remote heron]

you too

[worn mulch]

.close

[lone heart]

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[sage pond]

is induction how you'd prove this? https://i.imgur.com/vnDtpJC.png

[sage pond]

I mean I figure you can with induction, but I guess my question is can you without?

my book hasn't introduced induction yet

so I'm assuming the answer is yes

but I kind of don't see how since its recursive

iterative*

[alpine sable]

try it by put some value and observe

[wild trail]

start with rhs and write the product. Everything will cancel except the x^n and y^n terms

[lone heart]

@sage pond Has your question been resolved?

[sage pond]

sry guys had a work meeting lol

[sage pond]

before this, I did prove x^3 - y^3, which follows the template and is pretty simple so I'm not worried about that

my question is more about how to prove something iterative without induction

[alpine sable]

btw thats only for odd number

not odd

except 2

[sage pond]

wait wait what

[sage pond]

oh and I can just say "..." in my proof too, which is now obvious

[wild trail]

Yep, that's standard practice

[frosty arch]

Solve this for me😴

[sage pond]

answer is C

[frosty arch]

C!?

Write all evens as a sum of two primes.Solve it.

[sage pond]

alr back to my real problem

idk where I went wrong I think I don't understand how to work with the ... thing

because my stuff is not canceling out

https://i.imgur.com/VK7lJL8.jpg

so in line 2 since we're multiplying everything in the brackets by x

I turned my $...+xy^{n-2} into ...+x^2 n^{-2}$

[ocean seal]

math

[sage pond]

was that legal?

because now it's not canceling out

[fast lichen]

scoot over the bottom part slightly to the right

[frosty arch]

Did you solve it😅

[fast lichen]

and you can literally see that the thing above cancels the thing right below it

[sage pond]

D: I might be going crazy but

[fast lichen]

termwise

[sage pond]

i see a x^2y^n-2 in the top one

and I don't see that in the bottom one

[frosty arch]

Yeah

[fast lichen]

ill draw it

[sage pond]

😭

I need crayons????

[sage pond]

it's in the ...

I actually hate this notation

[fast lichen]

ye cause you wrote out an extra term lmao

for no reason but you can imagine every single term in the ... has a matching term

right below it

except x^n and y^n

[vapid shuttle]

Key to math proofs: "Imagine that the proof is correct.... therefore it is proven... Q.E.D"

[sage pond]

so in the original since +...+ stops at x^1, that means that in the ... is everything until n reaches 1?

even if we do an operation to it that is supposed to increase the exponent of that term?

[sage pond]

proof by looks about right is my fav

I don't know if I'm asking my question in the right way

so for any real n there is a finite number of elements it's going to sum up before n reaches 1, where the original expression stops

[fast lichen]

for the top one the ... contains terms n-2 to 1 for x and 2 to n-1 for y and in the bottom is n-3 to 2 for x and 3 to n-2 for y

[sage pond]

so if we multiply every element in that set by x, wouldn't all exponents increase by 1

[fast lichen]

i guess having it tilted is better for visualising it

[sage pond]

including the last one

like I don't see how the last item doesn't become x^2 :/

[fast lichen]

in the bottom part?

[sage pond]

operation of line 2

see it written out in line 4

last term after +...+ is x^2 y^n-2

oh wait that part issss correct

[fast lichen]

yea its the last term of ... in the bottom

[sage pond]

it's just included in the ... of the thing we're subtracting

right right yeah I was being dumb lol

[fast lichen]

yea they match diagonaly kinda of that makes sense

or you an scoot the bottom over 1 term and they match up and down

[sage pond]

when you say I wrote an extra term

for line 5 it was x^n-2y^2 that was extra?

[fast lichen]

yea i was wrong mb. i was looking at it incorrectly

[sage pond]

oh so it's not extra?

[fast lichen]

i mean you can write as many terms as you'd like

[sage pond]

right ik but I'm saying like

I started with 4 terms

ended with 4 terms

[fast lichen]

yea its correct nws

was my bad

[sage pond]

ok cool that was throwing me off too

I still prefer sigma notation by far

but I'm less confused by this inline notation thing now

.close

[lone heart]

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[livid mesa]

Im confused on how to do this I looked on YouTube but still confused

[tacit arch]

multiply top and bottom by 1.5

[livid mesa]

How'd you get 1.5?

[wild trail]

the point is that you need the value which sin has

ie you need 3x in denominator

you can figure out why to multiply by 1.5

[livid mesa]

wym?

[jagged cobalt]

small angle formulae

[wild trail]

$\lim_{t \to 0} \frac{\sin t}{t} = 1$

so, the t in sin(t) and the denominator must be the same

in this case t=3x

[livid mesa]

oh ok

wait but if u multiply the denominator to get to the same number as the numerator then wont you have to multiply the numerator as well which not let it be the same?

[raven rover]

This is unfortunately not true

This limit should be 1

[jagged cobalt]

is that not 1?

[ocean seal]

numbpy

[wild trail]

my bad, tying error

I should have been more careful

[livid mesa]

Is there a way to solve this problem using the squeeze theorem?

[wild trail]

I mean the fact that sint/t = 1 uses squeeze theorem so implicitly you are using the squeeze theorem

[livid mesa]

ok

So what would I then have to do after getting sin3x(1.5)/3x

[wild trail]

You can take the constant out of the limit then simplify

[lone heart]

@livid mesa Has your question been resolved?

[livid mesa]

take the 1.5 out?

[wild trail]

Yep

[livid mesa]

Would I do that by dividing by 1.5?

[livid mesa]

So then would the answer be 1? because then plugging in 0 into sin 3x/3x = 0

[lone heart]

@livid mesa Has your question been resolved?

[lone heart]

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[agile raptor]

how do you answer this huhh

[agile raptor]

my answers are x=15 and y=60 but im not sure

[modern imp]

The quadrilateral ABFE is a parallelogram?

[agile raptor]

they are parallel

so yesss..?

[modern imp]

if both the pairs of the lines are parallel

yeah ur answer is crct

[agile raptor]

EYYYY

THANK YOU

i was worrying because

I forgot to substitute after solving it

And then i substituted it again

it was asking for z but there wasnt any z variable soo.. i answered not given

[modern imp]

kk

[agile raptor]

.close

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[snow pawn]

hey

[snow pawn]

does this make sense?

I kinda know it doesnt

[vale wigeon]

,w (3n-1)/(n^3+n-1) < 3n/(n^3+n)

[ocean seal]

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[vale wigeon]

well, termwise the inequality holds for all n greater than sqrt(2)

so you're good to go

[snow pawn]

holy shit that was fast

thanks!

close.

.close

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[vivid tiger]

how do i show that $\frac{1 + n + n^2 + \dots}{(n + 1)^n}\to \infty$?

[ocean seal]

CoolShot

[vale wigeon]

is that exactly how it was written...?

[vivid tiger]

well, nothing was written it just came up in a problem i was doing

lim (n! e^n)/(n + 1)^n

i just used the power series of exp

[vale wigeon]

you screwed up using it i think

but lets see

$\lim \frac{n! e^n}{(n+1)^n}$ you say?

[ocean seal]

Ann

[vale wigeon]

i'd try looking at the log of that and stirlinging the factorial.

[vivid tiger]

how did i mess up though

[vale wigeon]

well 1 + n + n^2 + ... is sus

[vivid tiger]

$n! \sum_{i =0}^\infty \frac{n^i}{n!}$

[ocean seal]

CoolShot

[vale wigeon]

n^i/i!

not n^i/n!

[vivid tiger]

right i

lack a brain

nevermind

sry ty xd

.close

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[forest sedge]

Determine if the following either converges or diverges. I used the ratio test and got 1, as inconclusive. Would like to know what other ways I can determine. Software says it diverges to infinity but need assistance with proof.

[vale wigeon]

limit comparison with 1/k

[lone heart]

@forest sedge Has your question been resolved?

[lone heart]

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[thorn adder]

hi

[thorn adder]

I would like it if someone helped me with a math pattern

7 9 8 6 10 9 5 11 10 ? 12

my friend challenged me to solve it and i have tried a lot

[vale wigeon]

19, because there is no pattern and "guess what number the author has in mind" questions are stupid.

[thorn adder]

?

[velvet cliff]

I believe the answer is 4

[vale wigeon]

your friend sent you the following message:

here's a number sequence. i want you to guess the missing number in it, and i will make fun of you if you fail to do so.

7, 9, 8, 6, 10, 9, 5, 11, 10, __, 12

is that correct?

[thorn adder]

no?

[vale wigeon]

then how did you receive this from your friend

[thorn adder]

they sent it as a quiz to my friends and i

[vale wigeon]

a quiz.

[hard patio]

Could be 4

[vale wigeon]

could be 4, could be 19, could be 42069.

[velvet cliff]

let them have their fun

it's not that deep

[thorn adder]

its 4

[vale wigeon]

i mean ok like

if you write this sequence in 3 columns

[thorn adder]

because 19 is not there in the multiple choice

[vale wigeon]

WHY DIDNT YOU TELL US ABOUT THE MULTIPLE CHOICE

[thorn adder]

bruh

[hard patio]

42069 how?

[vale wigeon]

malicious compliance with underspecification what else

[velvet cliff]

every 3 terms the number decreases by 1 it seems

and the inbetween are consecutive numbers increasing by 1

on each cycle

[vale wigeon]

writing the sequence in three columns we see this:

7 9 8
6 10 9
5 11 10
_ 12

presumably each column is meant to be an AP

that's how one could justify 4 maybe

[thorn adder]

yes it does make sense

but its ok if i get it wrong cos i got everything else right

.close

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[jaunty rapids]

(x-6)^2

[jaunty rapids]

how to finish completing the square

is it -6^2 or --6^2

[wind cloak]

The square is complete

wdym

[jaunty rapids]

-6^2 or --6^2

to add to the end

of (x-6)^2

[wind cloak]

Can we have a look at the original question

[jaunty rapids]

complete the square for y^2-12y

[wind cloak]

Yeah so subtract 6^2 you're right

[jaunty rapids]

ok

its not --6^2

[wind cloak]

?

[flint pecan]

$-(-6)^2?$

[ocean seal]

jay.

[wind cloak]

$y^2 - 12y = (y - 6)^2 - 6^2$

[ocean seal]

NEONPerseus

[flint pecan]

$-(-6)^2=-6^2$

[jaunty rapids]

(x-6)^2 - 6^2
or (x-6)^2 - (-6^2)

[ocean seal]

jay.

[gray isle]

best not to take shortcuts and go through the intermediate steps if you're starting out

[wind cloak]

The first

I mean they're the same

[gray isle]

no they're not

[wind cloak]

[flint pecan]

No they're not

[jaunty rapids]

so (x-6)^2 - 36

[gray isle]

watch those ()

[wind cloak]

Oh yeah

I messed the order up

[jaunty rapids]

so (y-6)^2 - 36 is my final answer

[wind cloak]

Yup

[flint pecan]

There's a difference between -6^2 and (-6)^2

[gray isle]

be careful of () placement
(x-6)^2 - (-6)^2
(x-6)^2 - 6^2
if written like that, both would be fine

(x-6)^2 - (-6^2), however is not

[lone heart]

@jaunty rapids Has your question been resolved?

[lone heart]

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[desert tusk]

What am I doing wrong? I seriously can’t find where’s the mistake.

[gray isle]

doesn't look live you've done anythigng wrong

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@desert tusk Has your question been resolved?

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[woeful wind]

Im really not sure how to tackle this question

I know usually you just take the equation of y and then square it, multiply by pi and integrate

but when i dont have a single equation, but rather two different equations, im not sure what to do

[velvet cliff]

you revolve y = e^3x from 0 to 1/2

[woeful wind]

I tried setting them equal to each other but that gets me an equation only in terms of x which i struggle to integratew

[velvet cliff]

and then subtract y = (2x-1)^4 revolved around x axis from - to 1/2

[woeful wind]

ohhhh

so you do each individually

[velvet cliff]

yes 👍

[woeful wind]

that does make sense thats also what you do when integrating

[velvet cliff]

yeh

[woeful wind]

thank you1

!*

[velvet cliff]

np

[woeful wind]

.close

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[stable night]

hi can someone help me with this question

i cant figure out how to use the b^2 - 4ac thingy

[gray isle]

note that you don't actually need to find the exact solution

if they wanted that, they would've said solve

[stable drift]

You can find critical points and justify.

[gray isle]

you just need to show that at least one exists

[stable night]

right

hmm

[gray isle]

which you can do by applying stuff like ivt

[stable night]

wait so ill just brute force it? like keep trying

whats ivt

[pseudo ice]

Intermediate value theorem