help-28

[hot bone]

well the firs tthing that pops into my eye is 3 right triangles

one belonging to the 2cm square, 3 cm squre, and 5 cm square

[lofty shuttle]

Wait wdym

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@lofty shuttle Has your question been resolved?

[tulip marlin]

3 similar triangles

[hot bone]

it actually occured to me

it's not a given that the green area is a square

[tulip marlin]

it might be in the text

[hot bone]

no luck

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[frigid bolt]

I am trying to finish this problem. The propose of this problem is to prove that inverse matrix is smooth. I did (a) and (b). I think I did (c) and I showed that matrix multiplication is smooth by showing it is just a polynomial. Now i am stuck at (d). I can't see exactly how can i use chain rule to show this. Also, how to use this to show that inverse is smooth. I know we can use cofactor defintion of determinant to show that inverse is smooth, but I think here i should show in a different way

[tulip marlin]

one of the uni channels probably best

[frigid bolt]

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[hazy rune]

Prove <2 and <6 are supplementary

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Please don't occupy multiple help channels.

[light sonnet]

As the bot stated, don't open multiple channels

[hazy rune]

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[regal orchid]

John has 4 apples, his train was 7 minutes early, calculate the mass of the sun?

[terse karma]

Sun is massless

[slender onyx]

@regal orchid pls dont troll

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[vapid finch]

hey, ive got these equations above, the lowest one is solved already

[vapid finch]

could someone help me how to solve it for v, given you have m1 m2 v1 v2 and alpha

so you have to eliminate beta somehow

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[torn jolt]

nah im clueless

tried the basic stuff, like distribution and splitting the integral, but couldnt do anything

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[rancid elbow]

divide by (z-x)(z-y), split the right quotient into two parts and then you can use the mean value theorem

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[torn jolt]

How do I make an equation

[hot bone]

1=x+1

[torn jolt]

My zeroes are

2, 2/3 and 3

Abs it passes through 1,6

Pls send exact questions

Picture

Uh I just came up with a random example

Lol

I just don’t know how to fit Zeppo’s

Idk where it goes

What is a Zeppo

If I know it passes through 1,9 or whatever

Where do I put that

Uh

[torn jolt]

y = 0 at those values, since they're the roots of the equation.

So:
(x-2)(x - 2/3)(x-3) = 0

=> (x^2 - 5x + 6)(x - 2/3) = 0
=> x^3 - (2/3)x^2 - 5x^3 + (10/3)x + 6x - 4 = 0
=> -4x^3 - (2/3)x^2 + (28/3)x - 4 = 0

A cubic equation :p

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[torn jolt]

but im unable to form an inequality from that

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[torn jolt]

anyone know where i can find all proofs for derivatives?

[torn jolt]

(tag me)

[gritty rose]

what do you mean "all proofs" this is such a weird request.

[torn jolt]

i dont understand the derivative of fuctions

i know the proofs of d(x^2)/dx=2x for example but i struggle to understand derivatives in fuctions

like this one df(g(x))/dx

[gritty rose]

you want an introduction to derivative rules

any calculus book will have it

which one are you using in class?

[torn jolt]

its greek book from my school :/

so it doesnt give all proofs

[gritty rose]

this is a start. https://math.dartmouth.edu/~m35w18/math35_lecture20_w18.pdf

if you want more, you should find a different calculus textbook from your professor as a recommended supplement.

[torn jolt]

ok bro thanks for the help

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[rough notch]

these are the values

52, 47, 82, 76, 45, 51, 88, 83, 54, 62

[little dust]

if you know the mean already, there's not really any thinking to do except completing the table. If you do not know the mean, you can find it using the values.

[rough notch]

i know the mean

it is 64

but i dontr know what to write in the table

[spare abyss]

this is called a data set

[rough notch]

i know

[spare abyss]

you know the formula for variance?

[rough notch]

yes

[spare abyss]

what is it?

[rough notch]

would this example be a sample or a population?

[rough notch]

isnt like findning the mean of the data set, and then Adding all data values and divide by the sample size n.

[spare abyss]

put the data point in the data column

calc the sample mean

{52, 47, 82, 76, 45, 51, 88, 83, 54, 62}

[rough notch]

the mean is 64 correct?

[spare abyss]

yep

[rough notch]

do i put 64 in every single one for the 2nd coloumn?

[spare abyss]

nope

so you know the formula for variance?

[rough notch]

i think

[spare abyss]

go ahead

[rough notch]

findning the mean of the data set, and then Adding all data values and divide by the sample size n.

^

[rough notch]

oh ya

ik this

[spare abyss]

so you see xi - x bar?

[rough notch]

ya

[spare abyss]

you know what x bar is?

[rough notch]

no

[spare abyss]

it denotes the mean of the data set

xi ?

[rough notch]

oh ok

[spare abyss]

so as the head says
(data - mean)

which would be

this part

at every point in the data set

right?

[rough notch]

so i would subtract every number by 64?

[spare abyss]

yep

[rough notch]

but it would be negative

is that fine/

[spare abyss]

ofc mean cant always be bigger than the number right?

[rough notch]

yes amkes sense

[spare abyss]

then in the third column

which would just mean

this part in our equation

[rough notch]

square it

yup

[spare abyss]

yep

you know what sigma means?

this symbol?

[rough notch]

yes

and for the total

i just add everythin

[spare abyss]

correct

[rough notch]

There

Now what do we do for the variance and standard thing

[spare abyss]

you should always arrange your data in ascending

assuming you havent made any calculation mistakes

[rough notch]

i havent im sure

[spare abyss]

2472 will be

[rough notch]

yup

i got that

[spare abyss]

what is n?

[rough notch]

what do we do for variance and standard deviation

[spare abyss]

you know n?

[rough notch]

uh

[spare abyss]

s^2 stands for variance

[rough notch]

ah

so multiply 2472 by 2?

[spare abyss]

no

how?

[rough notch]

oh wait nvm

srry im slow

[spare abyss]

its okay

do you what is n in the formula?

[rough notch]

no

[spare abyss]

n is the number of data points you have in your set

how many did you count ?

[rough notch]

10

[spare abyss]

yep

n-1?

[rough notch]

10-1

9

so

[spare abyss]

now

by this formula

what you gonna do next?

[rough notch]

divide it by 9?

[spare abyss]

yep

[rough notch]

2472 divided by 9

[spare abyss]

are you confident your calculations are right?

[rough notch]

yea

[spare abyss]

alright

then 2472/9

[rough notch]

274.6

[spare abyss]

274.67

stands for variance

so you just calculated your variance

[rough notch]

then whats for standarf

deviatin

[spare abyss]

do you know the formula?

[rough notch]

oh ya

i know

i alr did it b4

[spare abyss]

😄

show me

[rough notch]

it would be 16.57 as the standard deviation

you just square root

[spare abyss]

nice

do you know what variance means?

[rough notch]

yes

[spare abyss]

good good

good job man. you solved the whole thing yourself

[rough notch]

thankyou so much

you are so helpful

im about to submit this

[spare abyss]

i didnt do anything

[rough notch]

but i just have on elast TRUE or FALSE question

the question

was

[spare abyss]

good luck . id double check the calculations if i were you

[rough notch]

The heights of a population are an example of a normal distribution

I put TRUE

but i just want to make sure

[spare abyss]

what do you think?

[rough notch]

i think true

[spare abyss]

[rough notch]

is that correct?

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[calm trail]

can someone explain the pasting lemma to me intuitively?

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[hot bone]

do you understand what it says?

I mean the elements in it

@calm trail

[calm trail]

Uh sorta

[hot bone]

f|A simply means that your inputs come from A

[calm trail]

I get that its trying to show that paths and homotopies are continuous

[hot bone]

so your function is "redefined" to f: A --> Y

[calm trail]

so its like if f: A --> Y and f: B --> Y are continuous then f is continuous too?

[hot bone]

im actually not to keen on those fields

[hot bone]

Yes

But it's only true because A U B = X

[calm trail]

yea

ok that makes sense thanks

[hot bone]

so if you divide X into 2 domains

and the your function is continuous on each
therefore it's continuous on the entire domain of X

intuitively speaking

[calm trail]

ah that makes sense

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[coral mantle]

can I get some help with this one? Answer is ln(x cos(x)) + C

trying to use substitution

I said u = cos(x) and du = -sin(x) dx

which gave me (u - x(du))/x(u)

[tulip marlin]

answer kinda gives it away

The top is the derivative of the bottom (product rule)

You can 'spot' this with the substitution u = x cos x

[coral mantle]

I see where that comes from now

I was just missing the x in the u = part, thank you

[fathom saddle]

A solution that allows you to "know less" is to split the denominator:
∫ 1/x - tan(x) dx
= ln(x) + ln(cos(x)) + C

Should know that ∫ tan(x) is possible

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[wanton plaza]

Hey there! Can someone give a hint on how to go about this exercise ? I don't know where to start.

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[gritty rose]

Can you post the definitions of all the variables

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[brittle marsh]

Need help with some maths

[brittle marsh]

Why does M stand for gradient in y=mx+c

[tiny ivy]

that’s something you can just google, that’s not really a problem with a math question

[fathom saddle]

"Gradient" is just a word here

Is there a certain thing about m that isn't making sense?

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[mint raven]

hi can someone help me with the equation within angles and circles stuff

[mint raven]

If m<AOB = 140 then m<P = ?

wait let me send the uh

figure

im unsure if im just gonna do the uh

140/2 = m<P

which will be 70 since it looks like how arcs work so im indecisive whether to go for it or just ask

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[stray hornet]

Okay so, I need help on two questions.

1. I need to show if it's surjective or not: G is a group and f: G→G is defined by f(x) = x^-1
2. I need to show if this function is surjective or not: f(x) = |x|

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@stray hornet Has your question been resolved?

[tulip marlin]

@stray hornet Thoughts

or what you've tried

[stray hornet]

I started the first one off with f(x) = y, letting y be in G

But it seems, that's what I want to show

Where x^-1 = y

[tulip marlin]

Well pretty much.

The question isn't conceptually hard. It is just testing you understand what surjective means.

So for every element in the codomain

Is there something that maps to it from the domain?

[stray hornet]

What do you mean?

[tulip marlin]

What definition of surjective are you given

[stray hornet]

Uhh a function f: A → B is surjective if, for every b in B, there exists an a in A such that f(a) = b

[tulip marlin]

Do you have some intuition

for what this means?

[stray hornet]

For every element in the range, there's an element in the domain where the function of that element is equal to an element from B

[tulip marlin]

Yes alright

so for 1)

Can you see what the question is just asking ?

[stray hornet]

In a group G, find an element a and element b where the function of a is equal to the element b

[tulip marlin]

ehh

The function f

It just maps an element in G

to its inverse in G

correct?

[stray hornet]

Yes

[tulip marlin]

So combine that with surjective

The question just asks if every element in G is the inverse of something in G?

Can you see?

[stray hornet]

Ohh

So I can say x = y^-1. And plug it into the function?

[tulip marlin]

Well I guess???

But to be honest, this question feels more conceptual

Like I would personally write down in words why f is surjective

Rather than need to show it algebraically

You can solve y = f(x) if you want...

but it is slightly pointless.

[stray hornet]

I understand

I would like to show both ways

[stray hornet]

Since this is going from G→G right?

[tulip marlin]

G is a group.

Every element has an inverse

[stray hornet]

Yes

[tulip marlin]

And every element's inverse has their inverse as the element

That's why f is surjective, conceptually.

[stray hornet]

Oh okay

This makes more sense in that way

[tulip marlin]

If you understand what a group is, you would understand immediately by the inverses axiom

it is surjective

That's why I felt it was conceptual question

🙂

[stray hornet]

Ah

Thank you

So for the second, it seems simple but I feel I'm overcomplicating it

I always do this when given simple problems because I feel like I'm being tricked, if that makes sense

[tulip marlin]

Yes ok.

Well you try the method

and set y = | x |

ok?

For every y you need to find a solution to show surjective.

[stray hornet]

Mhm

So I want where x = |y|?

[tulip marlin]

? no

Perhaps you can see it if you sketch a graph

and go through the meaning of surjective

[stray hornet]

Alright

Oh so

The range are all positive numbers

So I could use a counterexample

Like -1

Which makes this function not surjective

[tulip marlin]

yh

👌

[stray hornet]

Thank you

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[spare abyss]

whats the approach

i dont even wanna knwo the answer

[regal tundra]

should be log

n is just twice smaller each time

so you just estimate how many times it must become twice smaller to get from n to 1

which is log2(n)

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@spare abyss Has your question been resolved?

[spare abyss]

so do we just focus on n?

[regal tundra]

yes, x never changes

[spare abyss]

oh wait

is that a for loop?

[regal tundra]

and it doesn't even matter

[spare abyss]

yeah coz the answers dotn ask for x

[regal tundra]

any recursion can be written as a for loop and vice versa

[spare abyss]

what is space complexity are you aware?

[regal tundra]

yes, you got me there

[spare abyss]

😛

anyway. thanks man

@regal tundra appreciate it ❤️

love you.

[regal tundra]

np

[spare abyss]

shall i close? or you wanna look at more time space complexity questions?

just for practice/fun if you have the time for it

[regal tundra]

well, if you need any help with those - sure

if you don't, there are other channels where i can try to help

[spare abyss]

sure man go ahead. thanks once again

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[quaint ice]

okay so i got more questions for finding sets of points where the function is continuous

[quaint ice]

so i know its not continious but idk how to prove its not

[meager dew]

find where it's discontinuous

[lucid granite]

Yo

[quaint ice]

idk how to do that lol

[lucid granite]

Oh mb

[quaint ice]

i only know its not cts because the top isnt a polynomial

ah nvm i got it wrong and i cant change it

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[torn jolt]

Can someone explain how to do these questions ? Trig 10

[torn jolt]

I know a and b but not after that

These are the formulas given, I don’t understand how to use 3-5

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[torn jolt]

<@&286206848099549185>

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@torn jolt Has your question been resolved?

[wise wyvern]

Alright captain cool.

Sinθ=perpendicular/hypotenuse.
Cosθ=Base/hypotenuse.
Dividing these two we get,
Sinθ/Cosθ=perpendicular/base that is tanθ.

[torn jolt]

Uh

What?

[neat jungle]

🥲

ok

sinx = op/h

cosx = a/h

=> sinx/cosx = (op/h)/(a/h)

= op/a

aka tanx

[torn jolt]

Ya lost me here

[torn jolt]

I understand what ur saying uo until this message

[neat jungle]

uhm

sinx is the ratio between the side opposing the angle and the hypotenuse of the triangle

[torn jolt]

Ah

Can someone also explain these?

Special angles

I’m lost, so if I could get a step by step that would be great.

[neat jungle]

that is why sinx/cosx = tanx

[torn jolt]

Idk why but I’ve never heard of sinx/cosx/tanx before, are these exclusive to special angles or are u from a different country?

[amber radish]

I think they mean sin(x), cos(x), tan(x) etc.

Delete this please you've got your own channel at #help-4

x is just the parameter

I usually wouldn't write sin(x) simply sin x because it's only one variable

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[coral hamlet]

Has anybody managed to create program to build 4d math models (such as x^2=y but 4d) yet?

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[torn jolt]

Working with composite functions and derivatives

I'm to create derivative of above function using the below formula

Therefore I'm to somehow guess which component is f(x) and which is g(x)

Which is easier with composites like (0.5x-7)^10 => f(x) = x^10; g(x)=0.5x-7;

But what about this one? How do I do it?

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

If the question isn't clear enough, the final goal is to find f'(x) (the derivative of function x)

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

After I got enough time to look at it again, this is what I came up with

Definitely not clean but consistent with what other tasks I've been given to solve

I'll be closing this now, then

.close

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[nocturne creek]

Pls only use the first principle

[torn jolt]

what have you tried

[nocturne creek]

Im confused what to do after

[fathom saddle]

You'll need that (e^h - 1)/h approaches 1

Pull that (e^x)/x out the limit imo

[nocturne creek]

Im done thanks

.close

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[last saddle]

could someone pls help me with this question?

[amber radish]

system of equations?

Just sub your vals and equate, make a system

simulatenous equations

$g(-2)=3\implies -\frac a2+b=3,\ g(3)=8\implies \frac a3+b=8$ \[\begin{cases} -\frac a2+b=3 \\ \frac a3+b=8 \end{cases}\]

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[last saddle]

yes thank you for your assistance

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[near island]

Cesar started an investment program by buying $ 250 worth of mutual funds on the first day of every month starting on 01 March. Mutual funds are purchased in units. Cesar purchased as many units as he could with his $ 250, including fractions of units. Unit prices for the first six months were $ 9, $ 9.80. $ 10.50. $ 8.25, $ 8.40, and $ 11.15 respectively. What is the average cost of the units purchased? Round your answer to nearest 10th

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@near island Has your question been resolved?

[near island]

<@&286206848099549185>

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@near island Has your question been resolved?

[sweet ingot]

Find out how many mutual funds he buys for each price

Then you can find avg

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[jaunty temple]

https://media.discordapp.net/attachments/641441793459748874/935913971964330034/Screenshot_20220126-2036122.png

[jaunty temple]

This from Cauchy construction of real numbers

How do I rigorously prove the limit in the last line

Nvm is it after u show this inequality relationship we know that a_n and b_n are monotonic(increasing and decreasing) and bounded so they are convergent by monotonic convergence theorem

No wait but still

[glossy valve]

whitedwarf

[jaunty temple]

still am not getting L_1=L_2

[jaunty temple]

<@&286206848099549185>

[full forum]

@jaunty temple Has your question been resolved?

[ivory cairn]

What happens if $L_1$ and $L_2$ are different?

[glossy valve]

Zybikron

[jaunty temple]

Oh wait yeah if l_1 and l_2 are different then after rearranging the inequality l_2-l_1 is a constant

Thanks 😅👍

Hmmm

[jaunty temple]

Still stuck 😅

Maybe it results in some contradiction from the was a_n and b_n are constructed?

[ivory cairn]

That's my thinking (I haven't gone down the rabbit hole yet) but if $L_1$ and $L_2$ are different then we can assume $L_1<L_2$ and we get that there's some number between them, for example $\frac{L_1+L_2}{2}$

[glossy valve]

Zybikron

[jaunty temple]

Oh hmm

Ah alright I will try this with all the hints u gave me if I am still stuck i will be back then

Thanks again

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[merry stag]

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 6.8. Find the probability that the next two months will both result in four accidents each occurring on this stretch of road

[merry stag]

I know the working and all

but i keep solving it and im getting the wrong answer

[torn jolt]

Can you post your work?

[merry stag]

my teacher has the answer on the sheet and it says (0.009846)

[merry stag]

sure

[torn jolt]

thanks

[merry stag]

for some reason i cant send pics so ill type it down

i multiplied 6.8*2 = 13.6

because 6.8 is only for one month

anyways

13.6^4 * e^-13.6/4! = the answer

[gleaming coral]

Are you interpreting this wrong?

Is it not saying that there are 4 accidents for two consecutive months?

[merry stag]

i just want to know if im wrong or if my teacher is wrong

[gleaming coral]

Life isn't that simple I'm afraid

[merry stag]

can u just tell me the final answer

it says "Find the probability that the next two months"

[gleaming coral]

This is why I dont like word problems

[merry stag]

"The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 6.8" 6.8 is for 1 month so i multiplied it with 2

[gleaming coral]

Find the probability that the next two months will both result in four accidents each occurring on this stretch of road

Is probably interpreted as $p(4) \cap p(4)$

[glossy valve]

KurtDee

[gleaming coral]

for month 1 and month 2

It's also terribly written

Given their independence, $p_{month1}(4) \cap p_{month2}(4) = p(4)^2 = (\frac{6.8^4 e^{-6.8}}{4!})^2 = 0.0098$

[glossy valve]

KurtDee

[gleaming coral]

You should yell at your teacher for writing a question extremely unclear

Hm true???

[full forum]

@merry stag Has your question been resolved?

[merry stag]

thing is

hes stupid

thank u guys

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[coarse bronze]

how do i find the asymptotes and periods of these tangent graphs

[meager dew]

took me a min to figure out your meaning of tangent line lol

where do you see asymptotes occurring?

[coarse bronze]

well i see where the asymptotes are but i don’t know the exact x value of where they are

[meager dew]

well what vertical lines are they approaching?

[coarse bronze]

wdym

[karmic coral]

what are the increments of the values on the x-axis?

[coarse bronze]

my teacher made it every 2 increments = pi/2

[karmic coral]

and what about the unmarked values?

[coarse bronze]

id guess half of pi/2?

[karmic coral]

yup

[coarse bronze]

uh

so uhh

what would (pi/2)/2 be

[karmic coral]

what is pi/2*1/2?

[coarse bronze]

wait

it would be multiplying by 1/2 instead of dividing?

[karmic coral]

they're equivalent

[coarse bronze]

oh because when i was dividing it i got pi but when i multiplied i got pi/4 which i’m pretty sure is right

[karmic coral]

multiplying by a fraction is easier to visualize

[coarse bronze]

oh

ok anyways

if each incriment is pi/4

would the asymptote be the line in the 4th quadrant or first

[karmic coral]

wydm? the asymptote goes through both quadrants. the blue lines in each quadrant approach the asymptote at a certain x-value

[coarse bronze]

wait

what’s the asymptote

or what is an asymptote in this case

[karmic coral]

an asymptote is a line that causes a function to blow up to +infinity or -infinity.

at what values of x does this happen for the blue lines? those are your asymptotes

[full forum]

@coarse bronze Has your question been resolved?

[coarse bronze]

@karmic coral so would it be like pi/4, 3pi/4, 5pi/4

so on

[karmic coral]

yup

[coarse bronze]

ok that’s one question how about the period..

[karmic coral]

The period is the interval in which your function repeats the same value

[coarse bronze]

@karmic coral is it pi/2

since it repeats every pi/2

[karmic coral]

yea

[coarse bronze]

and then the x intercepts are just the points where the line crosses the x axis right

[karmic coral]

uh huh

[coarse bronze]

thanks bro legend

[karmic coral]

np

[coarse bronze]

ok so if the line is in the middle like this

would it still be pi/2

and 3pi/2

[fossil stump]

π/2 and 3π/2 appear to be asymptotes of the graph shown

[coarse bronze]

thanks

[brave blaze]

pi/2 + k*pi, k € Z

[coarse bronze]

bro?

what are these symbols

[karmic coral]

it's shorthand notation to denote that the asymptotes occur periodically at every instance of pi/2+k*pi, where k is an integer: pi/2,3pi/2, 5pi/2... and so on and so forth

[coarse bronze]

oh

ok last question i swear

how do i find phase shift

[karmic coral]

what does the normal cosine function graph look like?

[coarse bronze]

huh

thats all that was provided

[karmic coral]

do you know how to plot the cosine function yourself?

[coarse bronze]

somewhat

but not really

im trying to catchup with my math class since i was out of school for the past 3 weeks

[karmic coral]

well, where is cosine(x) normally equal to 0?

[coarse bronze]

uh

do not know

[karmic coral]

are you in pre-calc? have you learned of the unit circle?

[coarse bronze]

yeah i have a unit circle on me rn

that i wrote down before i left school

im in math 3

or alg 2

we're in our trig unit rn

[karmic coral]

ok. look at your unit circle and see where cos(x) would be 0

[coarse bronze]

uh

90 degrees or at pi/2?

[karmic coral]

yup. now look at pi/2 in your graph

[coarse bronze]

yes im looking at pi/2 in the graph

[karmic coral]

what is the y-value?

[coarse bronze]

2

[karmic coral]

and what should it be?

[coarse bronze]

uh

1?

[karmic coral]

keep in mind it is a cosine function. what is cos(pi/2)?

[coarse bronze]

wdym

[karmic coral]

the graph itself is a cosine function

what should the value of cosine be at pi/2?

[coarse bronze]

i am not sure

[karmic coral]

you said it earlier. it's on your unit circle

[coarse bronze]

0?

[karmic coral]

yes

[coarse bronze]

what now

[karmic coral]

but the graph isn't 0 at pi/2 right?

how far did that 0(x-intercept) move from pi/2?

that is the phase shift

[coarse bronze]

uhhhh

[karmic coral]

where are the x-intercepts(zeros) located on the graph?

[coarse bronze]

0, pi, 2pi, 3pi

[karmic coral]

and what are the zeros of cosine?

[coarse bronze]

hm

wdym by the zeroes of cosine sorry

[karmic coral]

the values at which cosine is equal to zero

[coarse bronze]

like pi/2

??

[karmic coral]

yes that is one

[coarse bronze]

3pi/2?

[karmic coral]

that is another

[coarse bronze]

and 5pi/2

[karmic coral]

so you have zeros at 0,pi,2pi, 3pi on your first graph. Cosine normally has zeros at pi/2,3pi/2,5pi/2

[coarse bronze]

mhm

[karmic coral]

so how far on the x-axis did the zeros shift?

[coarse bronze]

pi/2?

[karmic coral]

yes that is your phase shift

[coarse bronze]

bruh

is it the same concept for a sine function

[karmic coral]

yes. fun fact a cos function is just a sine function phase shifted by pi/2

[coarse bronze]

wait

so the answer to this would just be pi/2 as well?

did the picture load for u

[karmic coral]

no it didn't

[coarse bronze]

oh here

[karmic coral]

yes the phase shift is pi/2. Notice how the zeros all moved by that increment

[coarse bronze]

oh

[karmic coral]

be sure to brush up on your unit circle. it will help tremendously

[coarse bronze]

alright

are u still up for one more question lol

[karmic coral]

sure

[coarse bronze]

i dont wanna be annoying or sumth

[karmic coral]

hopefully you are kind of getting the gist of these concepts

[coarse bronze]

yeah fs fs

how would i get the equation given the graph only

[karmic coral]

Well first it would help to identify the type of function this is

[coarse bronze]

cos?

[karmic coral]

yes or more generally a trigonometric function but let's use cosine

[coarse bronze]

oh lol

just so i know the basic real quick

its

Acos/sin(Bx+C)

right?

and then -+d

[karmic coral]

yea

that's the general form of a trig function

it would greatly help in this problem to plot cos so you can find A, B, and C

[coarse bronze]

kk

thats great what does it mean

[karmic coral]

to plot?

[coarse bronze]

yes

[karmic coral]

graph it

[coarse bronze]

oh

ok what now

[karmic coral]

,w plot cos(x)

[glossy valve]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Taltost#8448

[coarse bronze]

mhm

[karmic coral]

now what is different between this graph and the one you posted?

[coarse bronze]

amplitude

[karmic coral]

by what factor?

[coarse bronze]

3?

[karmic coral]

yes. So A=3

the equation will be in the form of: A*cos(Bx+C)

[coarse bronze]

what is D usually

oh

midline right

[karmic coral]

where A= amplitude, C= phase shift

D is how far up or down your shift the graph

[coarse bronze]

alright

how do we find B

now

[karmic coral]

B is related to the period

[coarse bronze]

hm

oh

is b

2pi

[karmic coral]

not quite. B=period/2pi

[coarse bronze]

oh

is B the frequency

i remember doing something about frequency yesterday

so would B = 1

[karmic coral]

yes

so now the equation is 3*cos(x+C)

where C is the phase shift

[coarse bronze]

so phase shift would be

is c 3pi/4

[karmic coral]

almost. you are off a bit

also remember when you are shifting the phase, - is a right shift and + is a left shift

[coarse bronze]

is it a right shift

[karmic coral]

you tell me. Compare the first peaks of the graphs

[coarse bronze]

the peak

is to the right

does it matter if the peak is on the bottom or top

[karmic coral]

yes

when calculating shifts, peaks should match

[coarse bronze]

so did it shift

by 3

[karmic coral]

no, that is amplitude

amplitude multiplied everything by a factor of 3

phase shifts always occur along the x-axis

[coarse bronze]

hm

[karmic coral]

you almost had it before

how far did the peak from my graph shift over?

[coarse bronze]

5pi/4??

[karmic coral]

yes!!

[coarse bronze]

so it would be

3*cos(x-5pi/4)

[karmic coral]

yup! good job

[coarse bronze]

thxx

[karmic coral]

no problem. glad to be of help

[coarse bronze]

my teacher wrote it with sin

so it doesnt matter which u write it with

right

[full forum]

@coarse bronze Has your question been resolved?

[karmic coral]

it shouldn't. If you want to use sin, add pi/2 to the phase shift we found for cos and it will be the same answer

[coarse bronze]

thanks

[full forum]

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[odd gazelle]

Someone pls help me

[plush egret]

have you tried drawing a picture?

i think that'd be my technique

i guess what have you tried?

[odd gazelle]

I tried basic multiplication

Basic logic*

I think they did miss the cafe

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@odd gazelle Has your question been resolved?

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[tardy ruin]

Can someone help me with this question? Plz

[tardy ruin]

I need to know what I should let x and y be

As well as equations

[hollow geode]

Just be patient, and dont ping random users.

[light sonnet]

Also, you don't need to keep closing and opening channels

[tardy ruin]

Ok

But I’ve waited forever

And no one is helping

[light sonnet]

Well, this server is volunteer based, people can help whoever they want

[tardy ruin]

Ok

<@&286206848099549185>

[plush egret]

oh

did you ping me

was i the random user

[tardy ruin]

Ye lol

Um can you help me if possible

[plush egret]

i can try

what have you done so far

[tardy ruin]

Ummm

About that

I have no idea what to set x as and y as

It’s so confusing

But when I get the equation I can solve it

Can you help me if possible

[plush egret]

well an equation is made up of independent and dependent variables usually

hmm

[tardy ruin]

Can we go to VC?

[plush egret]

sometimes the way they try to help you get through these is more confusing

[tardy ruin]

If it’s easier

[plush egret]

i cant tonight

[tardy ruin]

Ok

[plush egret]

my voice is gone

[tardy ruin]

Oh lol

[plush egret]

im sick on something

[tardy ruin]

Oh

Umm do you know what x and y should be though?

Cause i have no idea

[plush egret]

i feel like it should be clear

im trying to think of how to lead you to it

[tardy ruin]

Ok

X should be the 20 oz plastic cups right?

[plush egret]

what you want is

yea something like that

you ideally want x and y to be related by something

in the way that if you pick some x, you can figure out y

and visa verse

so like

one degree of freedom

[tardy ruin]

Ye

Ik that with equations

[plush egret]

so whats y

[tardy ruin]

But word problems are harder

Y is 16 oz cups

?

[plush egret]

and be explicit

like

Y is 16 oz cups

is not clear enough for this problem

or i mean

just as a loose example

x is apples is usually not clear enough

you want something like

let x be the number of bags of apples that Mary purchases

does that make sense?

[tardy ruin]

Kind of

So would I do

[plush egret]

specifically units

and relationship to the context of the problem

what 16 oz cups

dozens?

where do they come from

[tardy ruin]

Let x be the profit of a case of 20 oz plastic cups?

[plush egret]

I dont think profit is where you want to start

[tardy ruin]

Oh

[plush egret]

i dont even see a question about profit

[tardy ruin]

Ye

[plush egret]

looks like it might be extraneous

how do they measure cups in the problem

by what unit

[tardy ruin]

Oz

[plush egret]

no

[tardy ruin]

Oh is it lbs?

Or cases

[plush egret]

it is not

Let x be (units) of (things) that (where they come from)

this is what you need for x and y

[tardy ruin]

Ok

[plush egret]

you should be able to answer where they come from right

i know this seems uhh

probably seems pedantic or fussy or whatever

[tardy ruin]

They come from plastic resins

?

[plush egret]

but all of this is important

IMHO

they come from plastic resins

from the factory

[tardy ruin]

Ye

[plush egret]

and then you get to choose

they come from the factory right

theyre made at some rate

whats a sensible rate to choose?

Let x be (units) of (things) that are made by the factory in (timeframe)

[tardy ruin]

Wait so it’s

[plush egret]

its sort of your choice

you know how its gonna work though already probably

these two things are related by limitations in material and time

[tardy ruin]

Kind of

[plush egret]

so your variables need to reflect this

[tardy ruin]

Ye

[plush egret]

the definition needs to include time and units

[tardy ruin]

Wait would units be the cases?

Or just size of cups

[plush egret]

say its size of cups

[tardy ruin]

Ok

[plush egret]

what relationship are you extracting from the information

thats based on ounces

and are you able to instead extract some relationship around cases

you might try some like

[tardy ruin]

Would it be the lbs part?

[plush egret]

if youre getting lost

some sort of information sorting diagram

like

the prompts suggest that your relationships are gonna be through time and material

so group out numerical information you can extract by those two classes

we decide profit is extraneous i think

so lets see

[tardy ruin]

Wait so 15 per hour

Is time

[plush egret]

We have information about resin per case of each type of cup

and we can only use so much resin per day

we can only produce 15 cases total per hour

and we can only work for 8 hours a day

[tardy ruin]

So I times them I’m guessing

For the other question

[plush egret]

so looking at this just

whats a reasonable unit for cups

let x be (units) of 16 oz cups ...

let y be (units) of 20 oz cups ...

[tardy ruin]

Would units be 15 cases

[plush egret]

👀

you want units to be how many 15 cases you can make?

[tardy ruin]

15y?

So

[plush egret]

i dont know how youre gonna work with variables you havent defined yet 😄

[tardy ruin]

Oh lol

[plush egret]

i get the urge to push forward into the math but you arent on solid enough ground yet

[tardy ruin]

I can write the equations and solve them in just bad at word problems

[plush egret]

right

[tardy ruin]

Wait so 15 cases per hour right

[plush egret]

total

so that sort of uhh

that pretty strongly implies units and timeframe right

by what unit are we measuring cups

its not oz

16oz and 20z are just

widgets idk the word you use

they may as well be paper cranes and head gaskets

the oz is not important

[tardy ruin]

Ok

[plush egret]

what unit are they measured by

do we make sleeves of cups

[tardy ruin]

So units would be lbs

[plush egret]

no

its not lbs

we dont makes pounds of cups

[tardy ruin]

Is it cases?

[plush egret]

i dont want you to guess 😄

convince yourself of what it should be

[tardy ruin]

It has to be cases

[plush egret]

lbs is not a measurement of cups

read the sentence again that mentions lbs

[tardy ruin]

It is cause it’s the only one that makes sense

[plush egret]

lbs is a measure of resin

not of cups

[tardy ruin]

Ohhhhh

I read that weird at first

Ok

[plush egret]

you need uhh

you need to develop a system of parsing these things

idk if you want to use a diagram or

but objects usually have units

time also has units

and you need to be careful like

you see in this problem if you arent clear if you are talking about a work day or an hour

you might get numbers mixed up

SO