help-0

[wanton hill]

i can find what each side equals

[woeful pulsar]

well that's some progress

did you know you can make a regular hexagon out of 6 equilateral triangles?

[wanton hill]

nope

[woeful pulsar]

maybe try drawing the triangles in

[wanton hill]

this makes a lot more sense now

im gonna brb im gonna see what i can do now knowing this thx lots

[fading zephyr]

you just have to substitute

[opaque carbon]

Can someone explain this please?

How does it go from left to the right

[charred flint]

that's wrong

[cunning jackal]

Can someone help me on this question? What is the probability (as a simplified fraction) of having 2 boys in a family of 4 children? (consider that there is a 50% chance of having a boy) *

Is it 1/2 times 1/3? I'm completely stuck

[alpine sable]

does the word "binomial" have any significance to you?

[cunning jackal]

honesty i don't know really know what it is

my stat teacher went over this lesson really quickly and i only understand the permutation and commutation thing

[alpine sable]

alright that's good enough

hmm not sure what explanation will be most appealing to you, but how many ways can you have a family of 4?

[cunning jackal]

16 right?

[alpine sable]

yes

how many of them will have 2 boys?

[cunning jackal]

8 of them right?

[alpine sable]

no

[cunning jackal]

oh wait is it 4

[alpine sable]

no

[versed talon]

A math problem.
Let's say there are certain values for each day of the week
Mon-6 Tues-8 Wed- 9 Thurs- 2 Fri-4 Sat- 10 Sun- 3
If the value for a particular day is missing let's say Wednesday, then we have to calculate that by finding the mean of the previous and the next day. I this case let's say Tuesday is 10 and Thursday is 12 then the valu for Wednesday is 11.
Now let's say there are two values missing Wednesday and Thursday in the sequence Mon-5 Tues- 8 Friday-12, the respective values of Wednesday and Thursday would be 8 and 10 respectively.
So how can we find the mean value when the adjacent value is also missing?

[cunning jackal]

am i braindead like i actually can't figure it out lol

[alpine sable]

it's 4 choose 2

[split trail]

can someone help with this question?

[alpine sable]

base area is 36cm so the side of base will be 6cm

also h is given which is 4cm

so apply pythagorean theorem for that

[cunning jackal]

what does that mean sorry 2 ways will have 2 boys?

[split trail]

@alpine sable would it be square root of 52

[alpine sable]

yes!!

no, it means [4 choose 2] of the 16 ways to have the family have exactly 2 boys

[cunning jackal]

um kinda confused

[alpine sable]

about what?

what 4 choose 2 is?

[cunning jackal]

yeah

my teacher never taught anything about this

[alpine sable]

lol is this application of binomial distribution?

[native yew]

hey!! where can i ask for help with calculate lim ?

[alpine sable]

yes but they have not learned binomial distribution so we are taking a more primitive approach

[native yew]

under what section ?

[cunning jackal]

i just remember about times when it says "and" and add when it's "or"

[alpine sable]

just go (c1 + c2 + c3 + c4)/16

[alpine sable]

was this meant to say "combination"

[cunning jackal]

oh yea

whoops

[alpine sable]

well that's all 4 choose 2 is

a combination

1/4 is the answer right?

no

👀

[cunning jackal]

i already got this question wrong but i just want to understand it

i just guessed and put 1/2 but idk how to do it

how do i use 4 choose 2

[alpine sable]

ok what parts of what I've said are still unclear to you

[ocean seal]

ChrisRyan

[alpine sable]

@cunning jackal oh since its only four kids you can just write total number of cases

[cunning jackal]

im looking at my notes and there's nothing about binomials it's just law of largen numbers, fudamental counting principle, permutation, combination

[alpine sable]

all we are using is combinations

and then figure out favourable cases

[cunning jackal]

er

[alpine sable]

and probably what you called fundamental counting principle, if that's multiplication principle

[amber marsh]

how do u know that x is those degrees

[alpine sable]

@amber marsh go other channel uwu

[amber marsh]

np

[alpine sable]

lemme help you there

[cunning jackal]

can you tell me the formula and i can plug in the numbers

[alpine sable]

desired outcomes over total outcomes

[cunning jackal]

is desired outcomes 1/2?

[alpine sable]

desired outcomes is an integer number

and it's 4 choose 2

4c2

[cunning jackal]

OH

IM SO STUPID LOL

so its 6

[alpine sable]

ye

[cunning jackal]

i didnt know what c was thats why i was so confused when you said choose

wait so now what

whats total outcomes

nooo its 3/8

[vagrant rover]

So I've been emailing my math teacher for the past 9 days trying to get help on one single math question that I have. The school is basically stalling since she's not responding and they won't help me. I'm emailing them because I feel like a bunch of the question on some of my tests are wrong. Now I know it's against the rules to give help for tests, but I just want someone to check if the question is just literally written wrong or if there is an actual possible answer. I don't want an answer to the question, I just want someone to make sure that the question is no written wrong. I had these troubles last year and my school is fucking me over big time, I'm falling behind and I don't know what to do.

This is the question

This is my answer.

Again, I don't want an answer. I just want someone to check if the question is written incorrectly if I'm just doing this wrong

I feel like that both B and C are wrong.

[alpine sable]

b is also true

d is correct, 2nd difference is constant so this is quadratic

ok ignore what I had actually, the way it's written is confusing

c is probably gonna be wrong, we can either continue the pattern to the 10th term or do quadratic regression to find the function and then plug in x=10

[topaz flint]

Am I good to go ahead and ask one in here?

[alpine sable]

nah I got confused by it too

[topaz flint]

Or are y'all still using it

[alpine sable]

but the indexing starts at 0

and the "tenth" term is indeed 114

x=9 is tenth term

[vagrant rover]

@alpine sable I'm confused, how is b correct? Can you explain?

[alpine sable]

oh my bad typed it wrong, 2x+6 does not fit the pattern

so b would be not true

[vagrant rover]

Oof

Okay so both b and c would be a correct answer?

Which means the question is fucked

Right?

I'm confused

[alpine sable]

yes, unless your teacher wants to argue that sequence starts with a 0th term

but that's not a very good argument

unless they have told you that's the language convention they are using

[vagrant rover]

If it does start at the 0th term would it make the question correctly written?

[alpine sable]

the quadratic that models the function is x^2+3x+6

simplify
ab + ab
ab * ab

i think by "10th term" they mean the output when the input is 10

so yeah the table would start with a "0th term"

[vagrant rover]

So the question is written correctly?

[alpine sable]

it's written unclearly

the phrasing is awkward, but it has a correct answer

[vagrant rover]

So if we sub 0 into x we get it correctly, but if we sub it for any other number its wrong

[alpine sable]

indexing doesn't really affect what the "first" term is

[vagrant rover]

So how does that make it correct?

Like shouldn't it give a correct answer for whatever number we give to x?

[alpine sable]

personally if I were grading this, anyone who ran into this issue would receive full credit

[vagrant rover]

My school teacher isn't helping

She's not responding

And the administrator is stalling and pretending like they had a different teacher check it, which I doubt.

Let me try to find another question I think is wrong.

I'll send in three of them to the principle

[vagrant rover]

And ask for help

[native temple]

diffrence between this and log(26)+1/6?

like seriously

how was I supposed to figure out dividing logarithms had some special rule?

also what even is that rule?

[alpine sable]

what specific step(s) are you confused with?

[native temple]

Dividing by 6

when I divided by six I did this

$$ /frac log(26) + 1 /6

[alpine sable]

from here to here?

[native temple]

$$ /frac log(26)+1/6$$

[ocean seal]

Nerdy_Coder

[alpine sable]

well you need to divide all of the right side by 6

you only divided the last term by 6

[native temple]

but putting everything over a fraction does that

doesn’t it

that’s how fraction bars work

other wise the quadratic formula is invalid

[alpine sable]

@native temple

[native temple]

Then hownis there a difference in my ti-84?

I thought I got the answer wrong

[alpine sable]

what is the right answer supposed to be?

[native temple]

it’s in this picture

0.4025

my ti-84 returns something different

my scientific calulator online returns the right answer

[alpine sable]

did you give the base values right?

[native temple]

Oh snap

it doesn’t return a different answer I just entered it wrong

i do know how to solve this

hate the fact I have to simplify these answers

[paper temple]

Can anyone explain why for 5bi it’s 2x+8 and not 2x+4 inside the bracket

I know it’s 2x+8 as I check the answers

[scarlet flax]

someone has a idea how i can multiply two big numbers? for example 11111...(42 ones) x 11111...... (47 ones)

[native temple]

by pain

that’s how

[scarlet flax]

i mean i just need the result , is there any solver who can do that

[native temple]

sure a ti-84

[alpine sable]

Right

[native temple]

1.234567901e87

sorry that was wrong

1e89

[scarlet flax]

did u find a online solver or did u just put it into your ti-84 xd

[native temple]

ti-84

figure out how to inpit scientific notation

apparently you can just add the exponents

ehhhh

like 42 + 47 = 89

also

What’s continuous interest?

sighno likewhat is it intrest gained every second?

[final crest]

Is it correct

[native temple]

I asked a question

[final crest]

So?

[native temple]

move

[warm stirrup]

im confused by D here
the hint would seemingly suggest that he does not want us to use a normal distribution to solve this?
however if thats the case what other assumption about the distribution could we make?

[velvet pelican]

@warm stirrup I think its about using the Central Limit theorem, because that is valid when the random variable is not normally distributed.

[warm stirrup]

ahh okay that makes sense

thanks ❤️

[alpine sable]

that would just be 1

oh crap wait

itd be 15 i think

$\sum _{k=1}^nk=\frac{1}{2}n(n+1) \$
$\frac{1}{2}\cdot 5(5+1) \$

[ocean seal]

square

[alpine sable]

u would write that

1/2 * 5(5+1)

[abstract sundial]

For -2 is the range 0?

Is the answer 3?

[misty roost]

tf is that notation

[dire wren]

fr

[misty roost]

"Can we have closed intervals?"
"No we have closed intervals at home"
Closed intervals at home:

Like is that supposed to denote a set?

[delicate pendant]

can someone explain this to me?

[misty roost]

Just how to expand that?

[delicate pendant]

simplify.

[misty roost]

Just do (3h+2)(3h+2)

And then distribute

Do you know how to do that?

[formal swift]

I recommend you to memorize this

[delicate pendant]

lol for some reason I just learned it today.

[misty roost]

Eh I don't think that's neccesary yet

[delicate pendant]

i got 9h^3+4

[misty roost]

I still don't know difference and sum of 2 cubes

[delicate pendant]

i dont even know why

[misty roost]

The answer is 9h^2 + 12h + 4

Unless I'm dumb

[delicate pendant]

well I added the exponents and squared

[delicate pendant]

no ur good thats it

so 2 squared and 3 squared

ok thanks.

[tranquil tulip]

Open?

if it’s open can someone help me write 4x^2 + 17x - 15 as a sum

[alpine sable]

wdym it's already written as a sum

[tranquil tulip]

i meant product

[alpine sable]

oh ok so you need to factor it

[tranquil tulip]

how do u do that??

[misty roost]

1(4x^2 + 17x - 15) 🧠

[alpine sable]

this one factors nicely

[tranquil tulip]

lmao i don’t think my teacher will allow that

[alpine sable]

so the easiest way is just to find the zeroes

then write it as 4(x-r1)(x-r2)

[misty roost]

Is it?

[alpine sable]

well you could do factor pairs and all that stuff

i find it easier to just use the quadratic formula

[tranquil tulip]

what’s r?

[misty roost]

I generally find most problems like this are easier to solve by inspection but I guess it's ultimately personal preference

[alpine sable]

zeroes are r1 and r2

[delicate pendant]

(4x−3)(x+5)

[tranquil tulip]

how did u get that?

[alpine sable]

so set 4x^2 + 17x - 15 equal to 0 then plug and chug into quadratic formula

[abstract sundial]

Can someone check my work? This is inverse functions and excuse my bad hand writing.

[tranquil tulip]

i don’t know how to get rid of 4x ^2

[alpine sable]

channel is occupied, repost elsewhere

[abstract sundial]

I was here first tho

[alpine sable]

oh wait

[abstract sundial]

sorry I'll wait

[alpine sable]

well btw your work is correct

[tranquil tulip]

4x^2 + 17x - 15 = 0?

[alpine sable]

yes

do you know how to solve quadratics?

[tranquil tulip]

i think so let me try

[delicate pendant]

bad at explaining but I learned from this guy. https://www.youtube.com/watch?v=apCmfszdXZA

[abstract sundial]

Ty and when you're done I have another question

[tranquil tulip]

thx

what do i do after 4x^2 + 17x = 15 ? @alpine sable

[alpine sable]

oh you want to solve by completing the square?

then divide both sides by 4

[tranquil tulip]

x^2 + 17/4x = 15/4

@alpine sable is that right

[alpine sable]

yeah

the coefficient on the "x" term is 17/4

so halve that, then square it

(17/8)^2

add that o both sides

then factor on the left side

[tranquil tulip]

what will that make the equation?

actually nvm i figured it out, tysm

[wild talon]

Any help simplifying this down to prove its an identity?

im just not rly sure where to start

[cerulean ingot]

Divide numerator and denominator by Cos(x)Cos(y) and u are done

[wild talon]

oh thanks xd

[abstract sundial]

Is this right or no? This is inverse functions.

[clever parcel]

Does anyone know how to calculate the doppler effect?

[dreamy epoch]

what is 1 3/4 x 1 1/6

[sly coral]

how do you solve this one ?

Let X be a normal random variable with mean 0 and variance 1. The random variable Y is given by Y = 3x + 2. The probability density function of Y is given by...

[ionic jewel]

mean 2, variance 3?

[strong cobalt]

I want to post my problem but it is a wall of text bc it deals with compound probabilities. I hit a wall. If anyone can help me i would appreciate it
I need help determining prizes (number value) for each multiplier bonus while maintaining 50/50 odds. Willing to paypal/venmo/cashapp $2 .
(for a minecraft casino project)

[crystal cape]

how do i solve this?

[ornate hinge]

How does sqrt(m/n) simplify to msqrt(n)/n?

I have sqrt(9/2) which simplifies to 3sqrt(2)/2 but im not sure how.

[ionic jewel]

i dont think thats true

,calc sqrt(9/2)

[ocean seal]

Result:

2.1213203435596

[ionic jewel]

,calc 3sqrt(2)/2

[ocean seal]

Result:

2.1213203435596

[ionic jewel]

oh im dumb i guess

you can pull out the 3 easily

[ornate hinge]

Mathway has the steps but you have to pay which is dumb

[ionic jewel]

3sqrt(1/2)

it doesnt work in general

just does here

sqrt(1/2) just happens to equal sqrt(2)/2

[ornate hinge]

Ah thanks, kinda stupid that that solution is unique to those numbers.

[ionic jewel]

... wait let me make sure it is

might be being dumb again

LMAO

no it always works

$\sqrt{\frac{1}{n}} = \frac{1}{\sqrt{n}}$

[ocean seal]

bunny

[ionic jewel]

multiply the top and bottom times \sqrt{n}

and you get $\sqrt{n}/n$

[ocean seal]

bunny

[ionic jewel]

@ornate hinge

[ornate hinge]

Thanks.

[ionic jewel]

yeah my bad got confused at the beginning

hopefullt that helps

[ornate hinge]

👌

[solid orchid]

please tell me this channel is in reference to the unit of measurement

[ashen wave]

Im really bad at determining if we are doing a quadratic equation or linear etc in a word problem could anyone help me with that (in general)

[ionic jewel]

do you know what vertex form is?

[ashen wave]

are you talking to orbs?

[cunning lily]

i finished it

but i have a new one

[ionic jewel]

fascinating, why did you ping me for that

[alpine sable]

so where did the 0.25 come from?

[glass lichen]

$\frac{1}{2+2i}$

[ocean seal]

moshill1

[alpine sable]

how does \frac{1}{2+2i} = \frac{1}{4} - \frac{i}{4}

[glass lichen]

realize the denominator

$\frac{2-2i}{(2+2i)(2-2i)}$

[ocean seal]

moshill1

[alpine sable]

oh i see thx

[cunning lily]

i need someone smart to do this for me please🥺

[manic quail]

I could tell you how to do it, if that is okay for you too.

As a first tip, how about you create a parabola that is shifted up by 4.

[umbral folio]

Given f(x, y) = z as z = 1/x+3y
find the trace of f(x, y) in the xz-plane then draw the graph on
the domain of x E [−3, 3]

how do I go about this?

[slender marten]

The trace basically means the slice of the three-dimension plot on the y = 0 plane. In a sense you will have just z = 1/x in the three-dimensional space with the desired domain, I suppose you could just have z = 1/x on a xz plot.

[umbral folio]

so I just take out the y and plot 1/x

[slender marten]

Here we are basically asked for the intersection of y = f(x,z) and y = 0, so yes.

[high sandal]

can someone help me find the equation?

[umbral folio]

how do I chart 1/3y?

[slender marten]

You don't.

Let me graph it for you, so you understand what it's asking for.

Also I misread the question.

Actually, it doesn't matter.

[final crest]

How

[umbral folio]

what doesnt matter?

[slender marten]

I read the question wrong.

It's fixable.

[umbral folio]

so I just graph right?

it wants me to graph on the yz axis too

[alpine sable]

is this answer correct?

[umbral folio]

I have no idea how to graph this

[slender marten]

I've not done this in Mathematica before, so I can't just instantly hand it out.

[ashen wave]

Is anyone good with quadratic equations/word problems

The length of a tropical garden at a local conservatory is 5 feet more that its width. A walkway 2 feet wide surrounds the outside of the garden. If the total area of the walkway and garden is 594 square feet, find the dimensions of the garden

I need help with this i have noo idea what to do

[alpine sable]

should just be this no? @ashen wave

[ashen wave]

yeah! actually the teacher said that was how you do it

but i just dont get it

[alpine sable]

what part dont u get

not trying to be condescending w that question btw

[ashen wave]

uhm theres a lot but can I start with that is this a quadratic equation? or like a standard or linear

[alpine sable]

its a curve so standard

yea it should b a quadratic equation

if u move the 594 to the left side its just a standard curve graph

im getting a negative number for this

what am I doing wrong

[ashen wave]

how did you know that tho? when we talk about the rectangle with an outside rectangle is it most likely going to be a quadratic equation?

[alpine sable]

can u show me how ur getting that

95 + 5x = 180
5/x = 180/5
95 + x = 36
-95 = 36 - 95
x = ?```

[alpine sable]

no but for this specific type of question it is, because when you graph it and list out the variables it turns into (x+4)(x+9) and you have to distribute the variables inside it properly, turning it into a a^2+ba+c type of equation

[gray isle]

what's happening from the second to third line?

[alpine sable]

ur supposed to subtract 180 with 95 first

ikr lol

@gray isle

[ashen wave]

ok hold on let me right this down

[alpine sable]

how come

90 + x + 5 + 4x = 180 95 + 5x = 180 5x = 180 - 95 5x = 85 x = 17

[alpine sable]

bc pemdas

oh

thanks

np!

[gray isle]

if you were attempting to divide both sides by 5, you should actually divide both sides by 5

[alpine sable]

mfw trying to get my own help turns into helping ppl

[gray isle]

instead of phase out the 95 and being it back

later

[ashen wave]

Vlyni, how do you know what the x and y represent?

[alpine sable]

im not sure what you mean, the x represents the width in this and the y is just f(x) if you put it into a graphing calculator

[ashen wave]

yeah but how did you know that by just looking at the word problem

[alpine sable]

i have to solve it by setting a certain value as x. you don't really know it would be a quadratic equation until you actually do the problem and then solve for x

like you see my graph up there

initially the equation isn't a quadratic formula

but after i listed out the length and width lengths

i then moved it to (x+4) (x+9) = 594

like i think the key to this problem isn't thinking "oh how can i apply the quadratic formula to this" its "ok im gonna set a side as my variable then visualize the problem and then write out an equation and start from there"

if that makes sense

[ashen wave]

alright ill try using that mentality from now on xD

[alpine sable]

yeye lol

[slender marten]

@umbral folio Finally managed to figure out why it kept plotting z = 0 instead of y = 0. The trace is in red.

[umbral folio]

so what if I set x to 0?

[slender marten]

What do you mean?

x = 0 is undefined.

I had to exclude this from the plot since it just produced a weird plane on the plot.

[umbral folio]

oh

so thats the chart for 1/3y?

[slender marten]

Damn, that's a beautiful plot.

[umbral folio]

how come it looks the same as if I did it for x

[ionic jewel]

what software is that?

[slender marten]

Mathematica.

[ionic jewel]

why do my mathmatica plots look ugly

thanks

[slender marten]

It's effectively the plot of z = 1/x + 3y (excluding x = 0), the parametric equation <x,0,1/x> and the plane y = 0.

I went through extensive effort to make it not ugly.

[umbral folio]

hmm

maybe im overthinking it but I'm confused

[slender marten]

A trace is just the intersection of the plane y = 0 and the surface z = 1/x +3y.

The intersection is the curve in red.

[umbral folio]

I get that the chart is the red lines

but if I did the opposite it still looks the same?

im lost the more i think about it

im use to just plotting stuff as y = rather than having a z access

[slender marten]

@ionic jewel This is the bog standard lol.

[umbral folio]

so im probably just not understanding anything

[ionic jewel]

yeah thats what mine look like lol

[slender marten]

z = 1/x + 3y just allocated a z value to each coordinate (x,y) on the xy-plane

[umbral folio]

I see

so if y is always 0 then

what happens when y is 0

[slender marten]

the xz plane is the flat surface where y = 0 on the entire surface.

[remote hound]

can someone hel;p

pelase

HELP

PLS

[slender marten]

This is the case for y = 0.

[umbral folio]

then the points never go above 0?

wouldnt that be a straight line

i dont know why im not understanding

[narrow vector]

I need some help on trying to find the inverse for this.

I have it right now as

[umbral folio]

whats a good graphing tool

[narrow vector]

x-3=-3/4(2^x-5)

[slender marten]

Since we can never have x = 0, we effectively have a plane, x = 0, where no point exists.

@ionic jewel If you wish to have the code to manipulate it in the future, sadly Mathematica refuses to use proper axes, so I have to force the axis origin to be (0,0,0) and manually plane the x,y and z as text on the plot.
function =
Plot3D[{z = 1/x + 3 y}, {x, -3, 3}, {y, -3, 3}, PlotPoints -> 50,
ExclusionsStyle -> {None, Black}, ClippingStyle -> None,
PlotStyle -> Opacity[0.3], Mesh -> None, AxesOrigin -> {0, 0, 0},
Boxed -> False, Exclusions -> {x == 0},
ExclusionsStyle -> {None, None},
AxesStyle -> Directive[Opacity[0.9], AbsoluteThickness[2]],
Ticks -> None]
intersection =
ParametricPlot3D[{x, 0, 1/x }, {x, -3, 3}, PlotStyle -> Red]
axes = Graphics3D[{Text["x", {3.5, 0, 0}], Text["y", {0, 3.5, 0}],
Text["z", {0, 0, 31}]}]
plane = ContourPlot3D[y == 0, {x, -3, 3}, {y, -3, 3}, {z, -30, 30},
Mesh -> None, AxesOrigin -> {0, 0, 0}, Boxed -> False,
ContourStyle -> Directive[LightGray]]
Show[{function, plane, intersection, axes}]

[slender marten]

I guess Geogebra, it's easy to use but won't be able to make it perfect.

[ionic jewel]

thank you!

ill go ahead and steal that

[slender marten]

If you get stuck on anything, you'll just have to ping me.

It took me a while to figure out that trick.

[umbral folio]

im using geogebra but dont get it

it just makes a red square

nvm fixed it

or maybe not

im confused

[slender marten]

The best you can do I think is plot z = 1/x + 3y and y = 0.

[umbral folio]

1/3x gets me a straight line

any number I add makes it a line

is that right?

because just 1/x isnt a line

[slender marten]

1/3x?

What are you doing?

I found a way to do parametric curves in Geogebra though: (x,0,1/x)

[umbral folio]

idk..

im trying to graph with y = 0

[slender marten]

Are you using Geogebra 3D?

https://www.geogebra.org/3d?lang=en

Just input these three things:
z = 1/x + 3y, y = 0 and (x,0,1/x).

[umbral folio]

I see

how do I make sure its facing the right way

i want it flat

[slender marten]

A trace is the intersection of two planes. the zx plane the question mentions is the plane y = 0.

You want to view the trace is 2 dimensions?

If so just plot z = 1/x on a 2D plotter.

[umbral folio]

why does 1/x and 1/y look identical

[slender marten]

It's just effectively a different letter.

z = 1/x and z = 1/y will not be the same though.

[umbral folio]

it does look the same for me

on a 2d grapher

which is probably wrong

[remote hound]

help

[umbral folio]

but idk what to use

[slender marten]

No, that's to be expected.

[umbral folio]

ok so thats right?

[slender marten]

In my view, it doesn't really make sense to view the trace on a 2D plot.

[umbral folio]

well Im suppose to draw it

[slender marten]

With pen and paper?

[umbral folio]

yes

in 2D

it says to sketch it in 2D on the domain -3, 3

[slender marten]

Best we can do really.

[umbral folio]

so both would look similar

thats weird..

[slender marten]

I wish I knew what was going through your mind.

[umbral folio]

same

whatever

if I wanted to do z = 1/(x+3y) what shape would that be

[slender marten]

Plug it into Geogebra and see.

[umbral folio]

it gives me nothing

[slender marten]

Yes it does. Just give me screenshots of what you are entering.

It's the only way I can figure out what is going wrong.

[umbral folio]

and I get a blank graph

[oak chasm]

,w plot 1/(x + 3y)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

@umbral folio ^

[slender marten]

z = 1/(x+3y).

1/(x+3y) alone gives me a graph though.

[umbral folio]

what shape is that

im doing this all wrong nvm

[slender marten]

Am I the only one mind boggled?

[umbral folio]

no

i am too

[slender marten]

I mean with what you're doing.

[umbral folio]

ok ill explain since im lost

z = 1/x+3y I have to set z to 1 then solve for y and find the object

[slender marten]

Why?

[umbral folio]

I dont know...

[slender marten]

The xz plane is y = 0.

[umbral folio]

its what it wants me to do

its a 3 part question

[slender marten]

Is this a new question?

[umbral folio]

yes

[slender marten]

Well, you can not expect me to know you've changed question.

[umbral folio]

sorry

[slender marten]

Now it wants the trace generated by the intersection of the surfaces z = 1/x + 3y and z = 1?

[whole dagger]

how

how am i here

oh wait nmv

[umbral folio]

z = 1/x + 3y is the original

its asking for the level curve when z = 1 and solve for y

and wants to know the shape

it says it will be a two dimensional object

[slender marten]

z = f(x,y) = 1 is what it's asking for.

It's basically asking for the surface where f(x,y) is one all over it.

1/x + 3y = 1, solve this 3y = 1 - 1/x, simplify further to give y = 1/3 - 1/(3x) = (1/3)(1-1/x).
Basically we will have the surface y = 1/3 - 1/(3x).

[umbral folio]

well z = 1/(x+3y)

[slender marten]

Just modify the logic then.

[umbral folio]

so y = (1-x)/3 I think

[slender marten]

z = 1/(x+3y) = 1, for x + 3y not equally zero. This implies that x + 3y = 1 or x = 1-3y.

Yes, that too.

[umbral folio]

thats not really a shape though

I graph and its just a line

,w plot y = (1-x)/3

[ocean seal]

Results provided by WolframAlpha

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

Requested by Elissa#3564

[slender marten]

You can plot this line on the usual xy plane but then in three dimensions it will just be extended vertically upwards and vertically downwards and see where it intersects your original plot of z = 1/(x+3y).

[umbral folio]

so I need to do this on a 3d plot

[slender marten]

Yes.

[umbral folio]

I just get a square

is that right...?

its a flat square

[slender marten]

See, where they intersect, the value of f(x,y) is always one.

[umbral folio]

so its a square?

[slender marten]

I'm literally doing nothing special. Ensure you are not trying to do this on the 2D version.

[umbral folio]

yeah thats what Im doing

[slender marten]

Do you see where they intersect?

[umbral folio]

I just dont know what I'm looking at

[slender marten]

The light blue plane intersects the orange curved surface on a infinitely long line.

[umbral folio]

so..

I get that theres an intersection but this doesnt look like a shape at all

[slender marten]

A line is a shape.

The level curve is this intersection.

[umbral folio]

so I need to plot z = 1/(x+3y) and y = (1-x/3) and the shape is formed from that

which is a ... triangle? im not sure

[slender marten]

Yes. The key to this is the term "level curve" the surface of intersection is a straight curve, a straight line.

[umbral folio]

so this is my shape?

or maybe not

this isnt working

i guess ill just give up

thanks for the help

[slender marten]

Plotting in 2D again.

[remote hound]

stabulo can you help me next please

Im sorry for spamming

[umbral folio]

isnt it asking for a 2 dimensional object

What type of two dimensional object is this (parabola, circle, etc.) is what its asking

[slender marten]

A curve can exist in three dimension space.

[umbral folio]

when I plot in 3d its just a mess im not sure what im looking at definitely no shape

[slender marten]

It's not the prettiest plot but this is what it's after.

[umbral folio]

but how is that a shape

[slender marten]

It's a line. A 1 dimensional line existing in three dimensions.

On this 1 dimensional line, f(x,y) always has the value of 1.

[balmy oxide]

can you guys help me with a form?

https://forms.gle/JjVQwXdigQGt7Bu39

[slender marten]

Hmm.

[native temple]

how to solve using gauss elimination?

[slender marten]

Write it in matrix form, then perform row operations until you reduce the matrix to row echelon form, meaning below the diagonal you have zeroes. Then perform back substitution.

[indigo glade]

You can also use the reduced row echelon form and have the solution directly within the matrix

[slender marten]

That would be Gauss-Jordan elimination though.

[indigo glade]

Yup

[slender marten]

I guess both is definitely viable, you could even calculate the inverse matrix, assuming it exists.

[native temple]

I wanted reduced row escelon

form

[native temple]

back what?

[slender marten]

Start performing row operations then.

[native temple]

i’m stuck

I have it in echelon form

(this seems harder then just elimination

[slender marten]

It means when you have it in row echelon form, you can read off the z value directly, the you use the second line and input the value of z, working backwards in a sense, hence the name back substitution.

[native temple]

I have faith this will get easier....

oh

okay how to get this to reudueced row esxhelon

this eliminations seems difficult

like solving a rubik’s cube without a guide

anyway

ummm an you help

like from my textbook

(Unrelated to acellus)

It used the analogy of a game to explain how to solve this

and said the operations you can do are addiction, multiplication, and swapping rows

by extension of this you can suntract divide and idk what swapping rows can do

so help

I’m not sure how to get this to all sides have 0s

except for the diaganol

did someone leave?

[slender marten]

I do.

Paul's online notes used to have Linear Algebra too. This is the document of it that was given to me a while ago. I got through about a third of it and it was very good @native temple .

[alpine sable]

Does anyone here study pure math?

[slender marten]

Everything is divisible by 5 and n, factor out 5n, maybe you can do more after this step.

[native temple]

you left?

[slender marten]

No.

[remote shard]

can someone explain why they used the taylor approxmation of e^x

and not plugged in the numbers to the taylor approx formula

[slender marten]

They used $y(x) = \sum_{n=0}^{3}f^{(n)}(0) \frac{x^n}{n!}$.

[remote shard]

no i get that

but why

[slender marten]

The end of the question says use a third order Taylor approximation.

[remote shard]

yes taylor approximation

taylor approx =an x^n

that's the taylor approx of e^x no?

[slender marten]

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$.

[ocean seal]

stabulo

[remote shard]

i know they used e^x

but why

[ocean seal]

stabulo

[remote shard]

why not plug in the values into the formula

[slender marten]

e^x has f^(n)(0) is one in every case but in yours it's not.

[remote shard]

?

[slender marten]

Do not offer to pay, this is bannable.

[flint remnant]

?

[slender marten]

It's fine, you can delete it, just beware.

[remote shard]

why would you use the equation of e^x in the first place

[slender marten]

They didn't, it's just similar.

[remote shard]

oh it represents position pretty well

[slender marten]

All Maclaurin series will be similar just with different constants.

[remote shard]

they used e^x but plugged in the f values at each derivative

[slender marten]

e^x has a Maclaurin series with every constant being one.

They didn't.

Ok, I see your confusion now.

A Maclaurin series assumes every series can be written in this form:

[remote shard]

taylor, yup

maclaurin is when a=0

[alpine sable]

@slender marten

Your a professor???

[slender marten]

For f = e^x it just happens that every constant you would get from every derivative of f you will get 1, therefore you get x^n/n!. For yours you need to find f(0), f'(0), f''(0) and f'''(0) but these do not give one like e^x does.

I'm not, no. @alpine sable

[remote shard]

yes i get that

but it follows the pattern

but why are they trying to mimic graph of e^x

thank you whoever deleted that

[slender marten]

They aren't.

[remote shard]

isn't that what a approximation is for?

[slender marten]

The taylor series basically assumes you can write every equation as a power series of the form: $$\sum_{n=0}^{\infty}a_n x^n.$$

[ocean seal]

stabulo

[remote shard]

yes exactly

[slender marten]

You can find that a_n is given by f^(n)(a)/n!.

It just happens that e^x gives the term a_n x^n/n!.

[remote shard]

so my question is

why e^x

where in my question does it point to using e^x

where it has /n!

wait

i read that wrong sorry

so lets start over

[alpine sable]

Wait stabulo isn’t emeritus a former professor

[remote shard]

we need to find a_n

nevermind

everything just came at once

thank you

[slender marten]

Nice. 🙂

[remote shard]

that was very helpful

[slender marten]

They made new roles for recognition or something.

[alpine sable]

Oh

Are you a college teacher

[remote shard]

he just said no

stabulo

why are you using that formula though

isn't to test for radius of convergence

f^(n)(a)/n!

oh nvm

i'm thinking of the wrong thing

you're right

[slender marten]

Just give this a quick scan: https://tutorial.math.lamar.edu/Classes/CalcII/TaylorSeries.aspx .

[slender marten]

I'm nothing.

[native temple]

hello stabulo

while nothing is happening

ummmmm to get gaussian elimination do i just have to practice to get to unit diagonal form or eschelon form?

because it seems complicated to do so

as I have to figure out

like how that works

[tender saffron]

good morning

how to do this

[native temple]

Umm ask somewhere else

thanks

[ionic jewel]

yes get it in row reduced echelon form

[native temple]

oh it seems difficult

like with the regression problem I’m doing

[ionic jewel]

practice makes perfect

[native temple]

it said use a calulator but I want to quic=ckly solve 3 systems by hand

[ionic jewel]

just use a calculator lol

[native temple]

so maybe matrices will work

sigh

maybe later

@ionic jewel ummm how to solve this

I suck at solving three equationmms

so hard to keep track

on paper

(not on whiteboard thoug h

[slender marten]

On a tricky multi variable question at the moment.

[amber mountain]

is anyone good with trig and the trigonometric functions?

ive been on a problem for 40 mins and cant find anything to help me with it

[alpine sable]

[woeful pulsar]

try drawing the unit circle

and plotting where theta seems to be

[amber mountain]

its quad 1 i think

but i looked up a problem similar and they said 3

[woeful pulsar]

draw a diagram?

[alpine sable]

do you know pythagorean identity + quotient identities and the relationship between the quadrant of the angle and the signs of the trig functions?

[amber mountain]

I plotted (pi,3pi/2)

Not too sure what that means dan

but im familiar with unit circle

[alpine sable]

these aren't the right coordinates on the unit circle

the unit circle has a radius of 1

[amber mountain]

Oh ok so it is quadrant 3

which makes sin negative i think

[alpine sable]

cos(theta)=-3/4 means the x-coordinate of the point on the unit circle is -3/4

Oh ok so it is quadrant 3
which makes sin negative i think
correct

[amber mountain]

I'm just so confused with how to find the other trig functions

since cos is negative

am I suppose to square cos to rid the negative?

[woeful pulsar]

you reference your unit circle diagram

[amber mountain]

in what way?

so do I not square cos to get rid of the negative?

[woeful pulsar]

the unit circle diagram tells you if the sin or cos is negative

[amber mountain]

I already know the cod is negative

its given in the problem

-3/4

however since thats all im given i'm not sure if the A or H is negative

im just gonna leave it blank its too confusing and not worth working another 20 mins for the pt

[woeful pulsar]

what do you mean A or H?

the sin and cos are just coordinates of the point

[amber mountain]

Adjacent and hypotenuse

[woeful pulsar]

from your unit circle all we have are the coordinates of the point

there's not really adjacent and hypotenuse

the point is always distance 1 from the origin

[amber mountain]

is it the x,y,r then?

[woeful pulsar]

given a point (cos(theta), sin(theta)) on the unit circle

well x=cos(theta) and y=sin(theta), that's all to it

[amber mountain]

but since cos is negative how do i know if x or r is negative

[slender marten]

The theta angle giving you a negative cos output will be the part of the circle in either the second or third quadrant.

[amber mountain]

I know its in the third

[slender marten]

It's between pi and 3pi/2 then.

[amber mountain]

I just dont know if the numerator or denominator is negative

in cosine theta

[slender marten]

Oh, do you mean via SOH CAH TOA?

I don't think you give A and H a negative sign, they are lengths so they are always positive. You just use this additional knowledge to determine the angle it corresponds to and the sign it gives.

[amber mountain]

But it says in the given that cosine is negative

meaning either the denominator and numerator is negative, right?

is this problem complicated or easy because I've spent too much time on it to want to spend a lot more

[patent burrow]

i have the formulas and all but I'm a little confused on how I would convert this

[alpine sable]

r^2=x^2+y^2
x=rcos(theta)
y=rcos(theta)

so solve for r and cos(theta) then plug in

[patent burrow]

how would i do that?

just

sqrt(x^2+y^2) = 5cos(theta)

[alpine sable]

then use cos(theta)=x/r=x/sqrt(x^2+y^2)

now you have everything in terms of x and y

[patent burrow]

so cos(theta) = x/sqrt(x^2+y^2)?

oh i see what you mean

so now there's sqrt(x^2+y^2) = 5(x/sqrt(x^2+y^2))

and then x^2+y^2=5x

[alpine sable]

perfect

[patent burrow]

is that it?

oh i guess it was

thank you :D

[slender marten]

Then (x-5/2)^2 + y^2 = 25/4 and you have the form of a circle!

[upbeat isle]

is 3sin(x)+7=0 undefined or am i dumb

like what is arcsin -7/3 thats nota thing rite

[slender marten]

If in serious double plot it. 🙂

[lusty tiger]

I need some help with rational expressions
I'm feel like I'm doing it right until I realize I can't cancel stuff
Heres an example:

fuck wrong image

i mean i feel like i'm simplifying it right but im supposed to cancel it out and make it one fraction

sorry for the handwriting im on a mouse

[ocean seal]

Chai T. Rex

[oak chasm]

@lusty tiger OK, so first, you have $$\frac{36x^2 - 25}{12x - 10} \cdot \frac{x^2 + x}{24x^2 + 20x}$$

[ocean seal]

Chai T. Rex

[oak chasm]

What's the GCD of 36 and 25?

[lusty tiger]

ohoooo
lmfao

[oak chasm]

If you get stuck, let me know.

[lusty tiger]

i thought it was -20

so i was doing 4x6 and 4x5

so 1

[ocean seal]

Chai T. Rex

[oak chasm]

Right, so you can't pull out a factor that way.

[lusty tiger]

yeah i see that

[oak chasm]

OK, so do you have a difference of squares?

[ocean seal]

Chai T. Rex

[lusty tiger]

(6x +5)(6x - 5)

[oak chasm]

Right!

[lusty tiger]

so that cancels out the denominator: (6x-5)

[ocean seal]

Chai T. Rex

[oak chasm]

OK, factor the denominator.

[lusty tiger]

2(6x-5)

[ocean seal]

Chai T. Rex

[lusty tiger]

right

[oak chasm]

OK, what about the right part?

[ocean seal]

Chai T. Rex

[lusty tiger]

x(x+1)

[ocean seal]

Chai T. Rex

Chai T. Rex

[lusty tiger]

4x(6x+5)

wait you dont need to flip the other side?

[oak chasm]

No, we still haven't combined them. See the dot in the middle.

$$\frac{36x^2 - 25}{12x - 10} \cdot \frac{x^2 + x}{24x^2 + 20x}$$
$$\frac{(6x + 5)\cancel{(6x - 5)}}{2\cancel{(6x - 5)}} \cdot \frac{\cancel{x}(x + 1)}{4\cancel{x}(6x + 5)}$$

[ocean seal]

Chai T. Rex

[oak chasm]

So let's cancel what we have so far.

[ocean seal]

Chai T. Rex

[oak chasm]

Now, this is multiplication (the dot in the middle) of two fractions.

[lusty tiger]

x+1/8 ?

oh

[oak chasm]

Yes, that's right.

You multiply the numerators together.

You multiply the denominators together.

No flipping (that's dividing two fractions, you flip the second one).

[lusty tiger]

I see

Now that I know that let me try one real quick

[ocean seal]

Chai T. Rex

[oak chasm]

That's the full working.

[lusty tiger]

ok that makes so much more sense

thank you so much

[oak chasm]

You're welcome.

[lusty tiger]

So wait, I also have division ones on my worksheet
For those I would just flip the second side and do the same thing?

[oak chasm]

Yes, $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc}$

[ocean seal]

Chai T. Rex

[oak chasm]

Wait

[lusty tiger]

like this correct?

thats supposed to be (x+1)(x-1)

[oak chasm]

@lusty tiger Almost.

You have the right idea.

[ocean seal]

Chai T. Rex

$\frac{x(x + 1)}{6x^2} \cdot \frac{(x - 1)(x + 1)}{(x + 6)(x - 1)}$

[lusty tiger]

idk why i added x^2 either

[gusty pawn]

btw you can use \divisionsymbol

[oak chasm]

@gusty pawn Oh, OK. Thanks 🙂

[lusty tiger]

Why is this just the same as multiplication?

[oak chasm]

It is, after you flip the second fraction.

Division is just multiplication by reciprocal.

[lusty tiger]

but what you wrote is not flipped

[ocean seal]

Chai T. Rex

[lusty tiger]

I'm not even going to try to use the math bot, but the origional was:
x^2-1 / x^2+5x-6
so wouldnt it be:
x^2+5x-6/x^2-1

[ocean seal]

Chai T. Rex

[lusty tiger]

so then (im going to try this)
$\frac{x}{6x^2} \cdot (x+6)$

[ocean seal]

F4ZR

[oak chasm]

$$\frac{x^2 + x}{6x^2} \divisionsymbol \frac{x^2 - 1}{x^2 + 5x - 6}$$
$$\frac{x^2 + x}{6x^2} \cdot \frac{x^2 + 5x - 6}{x^2 - 1}$$
$$\frac{x(x + 1)}{6x^2} \cdot \frac{(x + 6)(x - 1)}{(x - 1)(x + 1)}$$
$$\frac{\cancel{x}\cancel{(x + 1)}(x + 6)\cancel{(x - 1)}}{6x^{\cancel{2}}\cancel{(x - 1)}\cancel{(x + 1)}}$$
$$\frac{x + 6}{6x}$$

[ocean seal]

Chai T. Rex

[oak chasm]

You're almost there.

[lusty tiger]

ah i get it

the x cancels out the x^2 making it 6x

[oak chasm]

Yes, that's right.

[lusty tiger]

ok this is easier than I thought

thank you

[oak chasm]

You're welcome.

[plucky cipher]

Can you help me with this

I’m confused anf just need references because all the questions next are like this

<@&286206848099549185>

[upbeat gorge]

Do you know trigonometric functions

Are you allowed to use calc or not

Also analyze the figure

(You don’t need calcu btw if you know sum and difference identities)

[plucky cipher]

I am aloud to use a calc

[alpine sable]

theta=75 degrees
opposite side=12
adjacent side = ?
can you come up with an equation using a trig function that relates theta, opposite, and adjacent?

[upbeat gorge]

ah ok

ye follow dans

[plucky cipher]

No I think I know the answer just every single time I put it in it’s wrong

[alpine sable]

what did you try?

[upbeat gorge]

What’s your solution

[alpine sable]

do you have your calculator set to degrees?

make sure its in degree mode not radian mode

[plucky cipher]

I do

[upbeat gorge]

i bet ik your mistake but i don’t want to guess

What function did you use

actually just show your solution

[plucky cipher]

I got 44.78 etc

[upbeat gorge]

ye definitely not

what did you do

[plucky cipher]

Idk bro I’m really tired

I did 12tan(75)

[alpine sable]

ok so we know that tan(theta)=opposite/adjacent

plug in what we know

[alpine sable]

here

for problems like this always use the definitions of sin, cos, tan, and plug in what you know, don't just try to guess the formula

[plucky cipher]

So can you like write down what to do

I’m a visual learner anf my brain hurts rn so I’m having a very hard time understanding lol

[plucky cipher]

Ok so it’s tan

Right?

[worthy verge]

Ye

[upbeat gorge]

it is tan

[worthy verge]

Look

Every time

[upbeat gorge]

so derive an equation for the adjacent

[worthy verge]

Slanted =hypot

The side which is directly opposite of the angle is the "opposite side

[worthy verge]

And the closest side is adjacent

[alpine sable]

plug and chug into the tan formula

[worthy verge]

Just do tan75=x/12

[plucky cipher]

Yeah I know that but now how do I find my formala to get my answer

[worthy verge]

Thats ur missing side

Idk what the number is

But thats your side

[alpine sable]

tan75=12/x

[worthy verge]

Right

Oops

[oak chasm]

@worthy verge No, "the hypotenuse is across from the right angle" is a better way to remember it. Sometimes, diagrams can make the hypotenuse nonslanted.

[worthy verge]

Tan(?)=opp/adj

[worthy verge]

Yeah

Sorry worded it wrong

It takes practice

After awhile it'll be a breeze

Trust trust

[alpine sable]

SOH CAH TOA will solve all problems of this type

[lapis fjord]

X= 12/tan(75)

I think

[upbeat gorge]

ye

[plucky cipher]

Thank you

I deadass got the answer first but forgot to round

Holy fuck I’m a dumbass

[lapis fjord]

How do you make it a radical tho

🧐

[alpine sable]

wdym

[lapis fjord]

Like that one box arrow thing

/-----

@alpine sable

The square root thing

[alpine sable]

how do you make what a radical?

[oak chasm]

$\sqrt{x}$

[ocean seal]

Chai T. Rex

[oak chasm]

@lapis fjord You mean that? ^

[lapis fjord]

Yep

How would you make the answer of this in that thing.

X= 12/tan(75)

[oak chasm]

,w tan(75 degrees)

[ocean seal]

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Requested by Chai T. Rex#7323

[oak chasm]

@lapis fjordI think this way:

$$x = \frac{12}{\tan(75^{\circ})}$$
$$x = \frac{12}{2 + \sqrt{3}}$$
$$x = \frac{12(2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})}$$
$$x = 12(2 - \sqrt{3})$$

,w 12/tan(75 degrees)

[ocean seal]

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Requested by Chai T. Rex#7323

[oak chasm]

Hmm, that's interesting.

No, it's $12(2 - \sqrt{3})$. For whatever reason, it's not being exact.

[ocean seal]

Chai T. Rex

Chai T. Rex

[lapis fjord]

Is the square root of 10.3 a rounded answer?

[oak chasm]

,calc sqrt(10.3) - 12*(2 - sqrt(3))

[ocean seal]

Result:

-0.0060290019972311

[oak chasm]

Yes, if you want something inside a square root, that seems fine.

[lapis fjord]

Ok

[narrow vector]

i need help on a question

im trying to find the inverse of this equation

[oak chasm]

Solve for $y$:
$$x = -\frac{3}{4}\left(2^{y - 5}\right) + 3$$

[ocean seal]

Chai T. Rex

[worthy verge]

Why would you change the x value on left to y

[narrow vector]

to find the inverse

[worthy verge]

Oh right

[narrow vector]

right now I have my equation set up as

x-3=-3/4(2^y-5)

i don’t know what to do afterwards

[ocean seal]

Chai T. Rex

[narrow vector]

would that be