precalculus

[spring thunder]

the LaTeX

[small grail]

esketit

anyway

[full garden]

that is the god?

[small grail]

solve for y

[full garden]

ya

[small grail]

such that 7^y = 49

[spring thunder]

yes it's the god which helps us create pretty math

[full garden]

ohh

i thought he created the earth

[spring thunder]

ok i'll stop

[small grail]

$\log_{0.5}(0.5^x) = y$

[spring thunder]

_{}

for the base

[full garden]

@small grail do you know Khan Acadmy

[obsidian monolith]

8BitRobot:

[small grail]

thank you onion_art

yes I know Khan Academy

[full garden]

should I check it out for log

[small grail]

yes

[full garden]

is that were you learned it from

[small grail]

so in the second one I sent

[full garden]

?

[small grail]

with the 0.5

no I learned it in school

it means

[full garden]

bec you sound very good at it

ok my bad

continue

[small grail]

what is the value y such that 0.5^y = (0.5^x)

[full garden]

wholly that sounds so hard

[small grail]

it's just backwards exponents

[full garden]

ya

[small grail]

$\log_b(n) = y$

[obsidian monolith]

8BitRobot:

[small grail]

basically means

$b^y = n$

[obsidian monolith]

8BitRobot:

[full garden]

ohh

thats acctually so helpful

it makes life easy

[small grail]

yea

that's not all though, there are also a bunch of rules that you use when solving equations

like

$\log_b(nm) = \log_b(n) + \log_b(m)$

[obsidian monolith]

8BitRobot:

[full garden]

your very good at coding btw

[small grail]

$\log_b(\frac{n}{m}) = \log_b(n) - \log_b(m)$

bruh I picked this up like 10 seconds ago

[obsidian monolith]

8BitRobot:

[small grail]

$\log_b(n^m) = m\log_b(n)$

[obsidian monolith]

8BitRobot:

[small grail]

$b^{\log_b(n)} = n$

[obsidian monolith]

8BitRobot:

[small grail]

those are the rules I remember off the top of my head

[full garden]

thank you bro

not to annoy you but jsut one more question

what does it eman when a question asks " find the equation of the curve of best fit"?

[small grail]

basically

[full garden]

is that the same as asking for equation?

[small grail]

find an equation for a curve that gets as close to all the given points as possible

[full garden]

but how do I do that

[small grail]

I don't know how to do it manualy

manually*

whenever a question asks that

I always use my calculator

[full garden]

but this does not require logs right?

[small grail]

there are higher level methods to do that

such as cubic splines and lagrange interpolation

yeah no logs there

[full garden]

the question is giving me a table of calues

[small grail]

but I wouldn't advise trying to learn how to do that in a precalculus class

[full garden]

year - population

oh

[small grail]

you can probably do it

[full garden]

is that that hard

[small grail]

with the means you have available

I mean

those are like

unnecessarily complicated

for a precalculus class

[full garden]

are you a PHD math?

[small grail]

no

I'm a high school student

[full garden]

oh

[small grail]

lmao

[full garden]

waaat

whcih grade

[small grail]

10th

[full garden]

ohh

in your country the tests are harder?

the circulum

[small grail]

idk how tests are in your country

[full garden]

the circulum

[small grail]

so i don't know

yeah same with that

[full garden]

what country are you

[small grail]

I don't want to say

[full garden]

oh oki

[spring thunder]

and he's not a country

[full garden]

dude i hate english

[small grail]

I am the senate

[full garden]

how are you good in the math?

just school

or extra circular activities?

[small grail]

just school

[full garden]

oh

so your grade 10 doing calc 2?

[small grail]

yep

[full garden]

you are very smart man

good for you

[small grail]

thanks

[full garden]

people in Canda are dumbasses then

@small grail

what do you think ab the carreer of a pilot

[small grail]

I know nothing about being a pilot besides pushing buttons and flying a plane

[full garden]

oh

your gonna becom a phd math guy right?

[small grail]

nope

cs probably

[full garden]

what is cs?

[small grail]

computer science

[full garden]

ohh

I dont thin k you need much math in cs right?

[small grail]

you need a bit

depends on the field

[full garden]

are you cybersecuity?

[small grail]

nope

I don't know yet

but probably not that

[full garden]

ok bro could you just help me with that curve fit question please

[small grail]

maybe a bit later

I was supposed to be working

on hw

but I kinda got sidetracked

sorry

[full garden]

its ok thank you for your help and cool converstaion

[small grail]

yep

nice talking to you

[spring thunder]

try posting a pic of the question (i gtg real soon so i guess i won't be able to help you )

@full garden

[full garden]

@spring thunder yes bro I dont have a phone so I am begging for a camera

[spring thunder]

well repost your question at least ^_^

[full garden]

B)?

@spring thunder

[full garden]

#Helpers

guys

someone help please

[viscid thistle]

@full garden we need the answer to a first

[full garden]

finally

yes man

[viscid thistle]

-_-

That's not an answer to a

[weak helm]

I dont really undestand Synthetic Division

https://www.reddit.com/r/learnmath/comments/azlean/help_with_understanding_synthetic_division/

theres a problem that ive done like 4 times but i dont know how they got the correct answer

[viscid thistle]

What is it

[full garden]

@viscid thistle The ratio of successive first differences in constant in exponential functions

[weak helm]

F(x) = 6x^3-19x^2+5x+8 = 0

[full garden]

idk what that means

[viscid thistle]

Why pung

That is not the answer to a.

[full garden]

how do I answer a

[weak helm]

and then the roots are 1 , -1/2 and 8/3 but i dont understand how they got the answer

[viscid thistle]

@full garden you have to actually make the scatterplot

[full garden]

whats scatterplot

[weak helm]

oh lmao

put those x and y values into desmos graph

[full garden]

like graphing witout connecting the dots?

[weak helm]

and itll show a scatterplot if you put it as that type

yea

basically

[full garden]

how do I connect them

?

[weak helm]

click that plus

[viscid thistle]

No no no no no no no no no

Make a table

[weak helm]

and make ^

[viscid thistle]

Just listen to Zemah

[weak helm]

then put those in

[viscid thistle]

https://youtu.be/bZoMz1Cy1T4
https://youtu.be/1byR9UEQJN0
https://youtu.be/FxHWoUOq2iQ

@Zemah

5 min, 5 min, 10 min

[full garden]

what do I do after

[weak helm]

ive watched 2 of them so hoping the third does the trick

[viscid thistle]

@full garden click the magnifying glass

[full garden]

yes I did

[weak helm]

oh lmao its super zoomed out i was confused for a sec

[viscid thistle]

Yeah The Organic Chemistry Tutor is the best channel on YouTube

[full garden]

what do I do

[weak helm]

oh thanks for recommending it then

ill watch it

[full garden]

better than Khan Acadamy?

[viscid thistle]

@full garden so is it linear or not

[full garden]

yes it looks like y=x

[viscid thistle]

Then type y_1~mx_1+b

Tell me what m, b, and R² are

[full garden]

does r^2 mean radious

[viscid thistle]

It's not linear

[full garden]

yes its no

t

but how did you know that

[viscid thistle]

Type y_1~ab^x_1+c

Because R²≠1

[full garden]

what does the r^2 mean

[broken minnow]

r ^2 is a measure of how close the data are to the fitted regression line

[full garden]

ohh okay

@viscid thistle are you there?

[viscid thistle]

Chill the fuck out

@broken minnow R² is a measure of how much the variation in y-values is accounted for by the model.

As a %

[broken minnow]

Disagree

those are big words for no use

[viscid thistle]

@full garden type y_1~ab^(x_1)+c

@broken minnow your words are factually incorrect. All three times.

[broken minnow]

They are not

it's legit the same definition on the internet

SO check your facts

thank you

[viscid thistle]

Are you typing or copy-pasting

[full garden]

copy pasing

[viscid thistle]

Then type it

[full garden]

one sec

[viscid thistle]

And then tell me what a, b, c, and R² are

@broken minnow don't spread falsehoods

[broken minnow]

Alright. I won't pass on your knowledge

[weak helm]

hey lets not get aggresive

😃

[viscid thistle]

Maybe I'm getting my terms swapped

[full garden]

idk what the fuck i am doing

[viscid thistle]

Type y_1~ax_1^b+c

[full garden]

what does that even mean

[viscid thistle]

The question is broken

[full garden]

so b) y_1~ax_1^b+c?

[viscid thistle]

No. We're still on a.

[full garden]

wholly crab this sounds hard

[viscid thistle]

Type y_1~ax_1^2+bx_1+c

[viscid thistle]

I'm going to smack your teacher with a waffle iron

[full garden]

man I wish I had one

i'm jsut using a book

[viscid thistle]

Okay well the question has no correct answer. Skip it

[full garden]

ok thank s for your contributions

[rocky bison]

What was the question?

[viscid thistle]

y=Asin(x)=Acos(x+pi/2) ?

cos(x) is just sin(x) phase shifted to the right pi/2 right?

I just wanted to make sure

So if you're modelling some sort of wave

if the y-int is 0 you'd use sin,

if the max or min is the y-int you'd use cos?

So if I want to have the y-int be the minimum

I'd do like

y=cos(x-pi/2)

one sec

y=cos(x-pi/2) doesn't have local max at x = 0?

oh yeah mb

yeah

I'd just do y=cos(x-pi)

oh

yeah true

I got a bit confused by looking at sin graphs

if you take -2sinx and 2sinx

is there a different between the two?

Huh... I was doing some online homework and maybe I got confused

like -2sin(x) is sin with an amplitude 2 reflected over x-axis, yeah?

Maybe the buttons confused me because that's what I thought as well

I was probably just messing up the graphing tool instead of the maths

Oh also, if it's a question on trigonometric functions should it be asked in geometry-trig or in precalculus?

[alpine basin]

I got this from my class notes but I am little confused, do I need to find the y intercept in order to graph this as well?

I see how they get all the points but I was wondering why the line goes so far down the y axis on the y intercept

[willow bear]

f(0) = -56 🤷

[alpine basin]

@willow bear Does it not matter or?

[willow bear]

i mean idk if you want to mark it on the y axis go ahead

[alpine basin]

Okay just to clarify, if i were to graph this specifically, would this part be intercepting at -56?

[viscid thistle]

yes

[alpine basin]

okay thanks

[alpine basin]

One more question if you guys dont mind, Why is it the line on the right of this graph goes up and through the vertical asymptote but the one on the left doesnt?

When I graphed the function on my calculator the line didnt do that either

[viscid thistle]

which asymptote and which part of the function do you mean

for the asymptote on the left, it's because when -6 < x < 0,
(x-1) is negative
(x-3) is negative
(x+6) is positive

negatives cancel, so it will become positive

and for the left side of the left asymptote, ie x < -6
(x-1) is neg
(x-3) is neg
(x+6) is neg
and therefore the whole thing is negative

[alpine basin]

wait you referenced the left side twice

What is x on the -6<x<0?

[viscid thistle]

negative

i referenced the left side twice because the function is defined on both sides of the asymptote x=-6

[alpine basin]

Why does the line on the right of the x=1 asymptote go through the x-axis though?

[viscid thistle]

consider x = 3

or rather f(3)

it will make the numerator 0

[alpine basin]

hm

[viscid thistle]

oh btw

a function can cross it's horizontal asymptote any number of times

even infinitely many times

[viscid thistle]

As long as there exists some x=c such that once x>c, it never crosses again on (c,∞). Or negative. Don't matter

what do you mean

@viscid thistle ex plane

yo

ex plane yourself pls

also hi tadders

x plane

Hey tadders

helloo kronk

As of yesterday, 9/10 people who were on the top-10 list this time two weeks ago on HWH have left the server. Everyone but zav.

oof

i wish i was zavzav

but you still haven't explained yourself

"As long as there exists some x=c such that once x>c, it never crosses again on (c,∞). Or negative. Don't matter"

basicallyo

prove $\sum_{n=1}^{\infty}n^{-n}$ is transcendental

[obsidian monolith]

tadders:

[viscid thistle]

@viscid thistle

No

The proof is trivial

See Champernowne constant etc

if its trivial do it

Frik u class bouta start

how is champernowne related to this

lol my school finished

[half axle]

Anyone trying to do my precalc hw for 60$ lol

just need a tutor for it

[opaque bay]

:/

no ones gonna do ur hw

for u

[serene heath]

read #rules

[half axle]

Asked for a tutor

@opaque bay

[viscid thistle]

Lmao

[earnest finch]

When your class does physics application problems for the vectors and matrices unit but you're in chemistry

[viscid thistle]

How did he do the third equal sign? It is on the fourth row.

Plz tell me

[echo plaza]

uh

this one?

[quick river]

You have 2 cos at the bottom

One of them is gone because there is a cos at the top

@viscid thistle

[viscid thistle]

Oh so the first equation cancels the cos at the top?

[quick river]

And for the tan

@viscid thistle

[viscid thistle]

Sin theta/cos theta makes a tan theta then. Thanks.

[quick river]

Yeah your welcome

[short sorrel]

Yeah, recall that sine is opposite/ hypotenuse

And cosine is adjacent / hypotenuse

Therefore, $\frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{opposite}{hypotenuse}}{\frac{adjacent}{hypotenuse}} = \frac{opposite}{adjacent} = tan{\theta}$

[obsidian monolith]

Namington:

[short sorrel]

This can also be derived from the unit circle definition of tan, too

@viscid thistle

[viscid thistle]

Ahh xD k

[quick river]

Damn nice bot

[viscid thistle]

Im trying to understand this problem and the way to set it up.

[patent beacon]

Rational root theorem tells you everything you need to know about the possible rational roots

@viscid thistle

[viscid thistle]

Okay thank you

[patent beacon]

The possible rational roots are
±8/2, ±4/2, ±2/2, ±1/2
±8/1, ±4/1, ±2/1, ±1/1

That is, any of the factors of 8 divided by any of the factors of 2

[viscid thistle]

Ok...my instructor included synthetic division into this type of problem. Is that also apart of the theorem..?

[patent beacon]

That was just the answer to a)

[viscid thistle]

Ok

[patent beacon]

The rational root theorem says that any rational root will be in that form

b) says to use graphing to find approximately what the roots are

[viscid thistle]

Ok

From third to fourth row, the denominator is changed from 1- sin theta to cos theta. How?

[serene heath]

using sin^2+cos^2=1

[viscid thistle]

Thx

[viscid thistle]

What would sin theta times cos theta equal?

[thick kayak]

you can cancel $ \sin \theta \cos \theta$ from top and bottom

[viscid thistle]

Then it would -2?

[thick kayak]

yes @viscid thistle

[viscid thistle]

No because the answer to the problem is 1/2

[thick kayak]

wait it would be -1/2

oops 😃

[spring thunder]

-sin * cos-sin * cos = +2sin* cos

[viscid thistle]

No. Positive 1/2 is the answer

[spring thunder]

That's what you wrote :/

[viscid thistle]

Onion. How did the fraction turn into positive 1/2?

[spring thunder]

I'm showing you where you screwed up dem

[viscid thistle]

Where? The simplification of the 1-(1+2 sin theta cos theta)?

[spring thunder]

before

2 steps before

[viscid thistle]

Oh

Then what should I have wrote for the second row?

[spring thunder]

$$\frac{\sin(t)\cos(t)}{1-(\cos^2(t)+\sin^2(t)-2\sin(t)\cos(t))}$$

[obsidian monolith]

emeric75:

[spring thunder]

such a sport doing TeX on phone

[viscid thistle]

Ah thx

Did the next step I did correctly?

[serene heath]

[viscid thistle]

Multiply the quotient and the denominator (divisor). You won't get the numerator (dividend) back.

@viscid thistle

[half axle]

are these functions inverses of eachother?

i dont believe so

[viscid thistle]

So do I have to multiply the same fraction by itself?

Or do I just multiply it with sin^2 theta and sin theta/sin^2 theta and sin theta?

[patent beacon]

@half axle
Yes they are, but only on specific values. What is g(5)?

[viscid thistle]

@viscid thistle multiply the quotient and the denominator.

[viscid thistle]

K

[viscid thistle]

What did they do to make it through that step?

[short sorrel]

Multiply the numerator and denominator by the conjugate of the denominator

That is, multiply the entire thing by (8 - 15sqrt3)/(8 - 15sqrt3)

[viscid thistle]

Ah kk

[weak helm]

Hey I've got a question about Synthetic Division

so im supposed to find the roots to this polynomial

y=x^5-6x^4+11x^3-2x^2-12x+8

and when I did it, i could only find the roots of 1 and -1 even though i know that there was a root of two

is there an order to what numbers you are supposed to divide when doing it because I divided that polynomial first by 1

and then divided the remainder by -1 but on the homework it shows that the teacher divided it by 1, then 2, then -1 even though it works doing -1 first?

[patent beacon]

@weak helm
Order doesn't matter

[weak helm]

oh thanks, that just means im doing something wrong

[weak helm]

Ok I don’t understand what I’m doing wrong

I got this answer but if you put the function into Desmos it there is a (x+ .5) x intercept but I didn’t get any

[full garden]

guys do i have to memorize this in order to know trignometric rations?

[charred hull]

you need to know angle 0 to 45 and remember sin represent y and cos represent x

cos 30 is sin 60 so if you remember up to 45, all the values p much repeat

[full garden]

do you think class exepectations are limited to 0, 90, 180 and 270?

or do I have to know all of them?

[charred hull]

what do you mean?

remembering them all is probably a good idea tbh

some times itll come into play

[full garden]

i am lil new to this could you please explain to me why they are important

so like its smoother to work at?

[charred hull]

it's kinda expected to know i think for a good amount of math out there

[full garden]

ok thank sbro

[full garden]

guys i have one question

an equilateral triangle has a height of 3 times square root of 3 . what is the premier?

[fading token]

Premier...?

[full garden]

perimeter*

[full garden]

guys anyone help

[willow bear]

what have you tried so far?

[full garden]

i tried a+b+h=p

but thats wrong

I thought it was some speacial angle thing but idk

if the traingle is equilateral does that mean its 30, 40, 90

[willow bear]

"30, 40, 90" is not a valid set of angles in a triangle (in euclidean geometry, anyway)

you probably meant "30, 60, 90", but even then, an equilateral triangle does not have those angles

[full garden]

does it have 45, 90, 45?

[willow bear]

do you know what an equilateral triangle is

[full garden]

if two angles are equal then the traingle is equaliateral

its like all the same sides

[willow bear]

no

[full garden]

but those are angles

so what is it

[willow bear]

no, two angles being equal gets you an isosceles triangle

an equilateral triangle is a triangle in which all three sides are the same length]

[full garden]

yes

so what are the possible set of angles

60,60,60?

i never seen that before

[gilded jewel]

[willow bear]

yes, in an equilateral triangle all three angles are 60°

[full garden]

so how do i solve this question

[willow bear]

consider drawing the triangle

this is a geometry problem

[full garden]

yes but what formula/principal should I follow to find the Perimeter?

[willow bear]

if you knew what perimeter was in the first place you wouldn't be asking that question

[full garden]

budy

its giving me the height not the sides

[willow bear]

yes, but you can find the side length from the height

[full garden]

using sine law?

[willow bear]

draw the thing

don't try to do this blindly

[full garden]

yup

[weak helm]

what does it mean when doing synthetic division and you get zero while there are still numbers

do you keep on going or just stop

[rugged bolt]

What are the components of a vector with the magnitude of 7 and the angle of 240?

[weak helm]

ok this is my last question about synthetic division sorry for asking so many

[rugged bolt]

oh, sorry

For interrupting your question

[hard dragon]

anyone can help me with my precalc hw

<@&286206848099549185>

[viscid thistle]

1: You didn't even post a question
2: Wait 15 mins to ping helpers

[hard dragon]

oooo mb

[viscid thistle]

Where da question at fren

[viscid thistle]

So set y=0

then 0=x^5+5x^3+17x^2+85

[hard dragon]

o then what

[viscid thistle]

solve for x

[hard dragon]

whats x

[ornate helm]

Are you trolling?

[severe verge]

3. we're not doing your work for you, or spoonfeeding you.

you need to demonstrate actual effort

[hard dragon]

spoonfeed me dad

[severe verge]

no

[viscid thistle]

Can somebody please help me with this?

[hexed ermine]

With which parts

[viscid thistle]

So im having trouble factoring the bottom because when i graph it, it never touches the x-axis

when the top is factored its (x-3)^3

im very confused

[rugged bolt]

hat are the components of a vector with the magnitude of 7 and the angle of 240?

[weak helm]

honestly MrMeltz i dont feel like you should ask all of these pretty easy questions

you might learn bad habits that dont help with learning

[patent beacon]

@rugged bolt
You asked me this question in DM, and I answered you. If there was something wrong with my answer, then you should have said so rather than state "How long did it take you to look that up?" This is a waste of the server's time imo. Please be more professional in the future.

[serene heath]

kek that's like the 5th channel they post that in

[full garden]

guys could someone help me with this question

i can't figure it out

Determine another angle that has the same trigonometric ratio as each given angle

a) Sin 45

b) sin 150

[viscid thistle]

Start by evaluating the given expressions

[full garden]

like the y/r=sin

sin 45= squre root 2/2

360-45=315

wait ok I think i got part a

but part B is not working w me

can someone help

[serene heath]

what property of sin do you know?

[full garden]

its positive in the first and second quadrants

[serene heath]

yea but also sin(x)=sin(180-x)

[full garden]

i never saw this before

is the 180 bc of the first quadrant + the second one?

is it wrong if I do 360-150= 210?

[serene heath]

think of the uni circle

sinx is the y coordinate

so a point on the unit circle would have the same y coordinate as the point across it horizontally

[full garden]

does that mean cosx=(360-x)

because of the x/r

[serene heath]

yea

[rare zephyr]

3(a)

Im supposed to proceed but all I end up is nonsense and "???"

[rare zephyr]

<@&286206848099549185>

[limber bone]

how would u solve that

https://media.discordapp.net/attachments/363224154469826562/555543577522864138/unknown.png

with graphing?

[willow bear]

this factors

(x^2 + 5)(x^3 + 17)

[rare zephyr]

Help with mine too please

[limber bone]

oh by grouping?

didnt see that 1 ty ann

[willow bear]

@rare zephyr line 3: 1/(x+y) is not 1/x + 1/y

[rare zephyr]

Oh

I see now

[steep sparrow]

hey

u still need help?

nvm i see u said u got it

[rare zephyr]

I actually dont tbh@ @steep sparrow

[steep sparrow]

oh

ok

what part dont u undertand

understand

@rare zephyr

[rare zephyr]

I continued the problem by myself and end up with this

Which I am sure is not what I'm supposed to get

Problem is, I can't pinpoint what my mistake was

[steep sparrow]

hmm

ugh i think its been too long since i did this

ill have to call in the big kahoonas

<@&286206848099549185>

[rocky bison]

CATTO INBOUND

[viscid thistle]

lol

[rocky bison]

[remote musk]

ETA

5

4

3

2

1

[rocky bison]

oof

[remote musk]

That's an abort mission

Roger that Houston

[serene heath]

I wasnt actually typing there was a message in the box earlier that I didnt send

anyway 3a?

[rare zephyr]

Idk how im supposed to get this

[serene heath]

yup

now turn the top into cos

and use diff of 2 squares

basically just take ur initial fraction

[rare zephyr]

Pressed edit by mistake

[serene heath]

and multiply top n bottom by sinx

[rare zephyr]

This is referring to which part?

[serene heath]

the very first fraction

provided by the question

[rare zephyr]

ok

Wait you can add in some stuff

I didn't know that

[serene heath]

hm?

[rare zephyr]

you said to multiply top n bottom with sin x

[serene heath]

yea

so multiplying by sinx/sinx

ie multiplying by 1

[rare zephyr]

oh

Now I actually get it

thanks

[raven hearth]

So the equations are y is less than or equal to -x-1

And

Y is greater than or equal to (x+3)^2-4

But how do you find the vertices of the solution/shaded region of the system?

[willow bear]

the what?

[raven hearth]

The vertices of the double shaded regions, so the solution?

[willow bear]

can you show the problem exactly as stated?

[raven hearth]

So I got it graphed

But what do I label

[willow bear]

okay so ig by vertices they mean the intersection points of the boundary curves

[raven hearth]

Is there any special notation for the dotted lines (greater than vs greater than or equals to) than the regular lines?

[willow bear]

wdym special notation

like

you draw dotted lines to exclude points on them from your region

[raven hearth]

Yah

Or are vertices just the same either way

So if ie (0.0) is in your data set as a vertex but (3.0) is not a part of the dataset but is a vertex

[willow bear]

i mean

that parabola is still a boundary curve even if it itself isn't included

[raven hearth]

K guess I get it

[deft flume]

Any help would be appreciated! Thx

[patent beacon]

x be number of standard
y be number of stainless

2x + 4y = 40 (melting times)
4x + 6y = 48 (hardening times)

@deft flume

[deft flume]

ohhhh ty! @patent beacon

[alpine basin]

I think I understand most of the problem but what do they mean by that -13/2 doesn't exist? because from what I can tell they are both the same solution

[limber bone]

which problem

oh

log(-13/2) doesnt exist

becuase

domain of log function is from 0 to infinity

u cant put in negatives

and think about it this

let for example log(-13/2) = a

that means 10^a = -13/2 right?

there is no number such that ^ this is true

got it?

[alpine basin]

oh yeah that makes sense, thanks

[limber bone]

np

[alpine basin]

I have one more quesiton if you dont mind, how would I solve this problem? The answer turned out to be 4 but i dont have any work shown for it

[tawny nacelle]

Let, $c = 5^{\log_5 4} \implies \log_5 c = \log_5 4 \cdot \log_5 5 = \log_5 4$

[obsidian monolith]

soap:

[tawny nacelle]

so c = 4

is that enough explanation ?

[knotty spear]

or $y = \log_5(4) \implies 5^y = 4$ per definition of logarithm

[obsidian monolith]

BewareillEatYou:

[knotty spear]

$5^{\log_5(4)} = 5^y = 4$

[obsidian monolith]

BewareillEatYou:

[knotty spear]

[tawny nacelle]

ok u win

[knotty spear]

[alpine basin]

wait wut, which one do I look at? 😮

[tawny nacelle]

second one

[alpine basin]

where did the variable come from and how does 5^log5(4) turn into 5y?

[knotty spear]

y is just a temporary variable

to use the definition of the logarithm

and in the second part i just substitued log5(4) with y because i chose y to be equal to log5(4) in the first part

[alpine basin]

Yeah I guess that part doesnt make much sense to me

if it was just log_5(4) it would be 5^x = 4 right?

[knotty spear]

thats the definition of a logarithm, yes

[alpine basin]

Yeah Im just confused why you would substitute it with y

[knotty spear]

well whether its x or y doesnt really matter

[alpine basin]

yeah

[knotty spear]

but logarithms are made so that if 5^x = 4, then x = log5(4)

so if you put those two expressions together

you get 5^(log5(4)) = 4 right?

[alpine basin]

I think.. its still weird because its confusing me with the exponent

[knotty spear]

well logarithms are kind of the inverse of exponents

which is exactly why exponents and logarithms cancel out

[alpine basin]

What would happen if it was log_4 instead of log_5, cause what I can see it seems like they just cancel out like you said

[knotty spear]

well if you have $5^{\log_4(4)}$ they dont cancel out anymore

[obsidian monolith]

BewareillEatYou:

[knotty spear]

since log4(4) is now when 4^x = 4

it doesnt use base 5

but instead, you could see that log4(4) = 1

since 4^1 =4

and you'd get 5^log4(4) = 5^1 = 5

[alpine basin]

oh ye

Okay I think I got it, so if i just see that the base and the log_# is the same, I can just cancel them out right?

[knotty spear]

yes

[alpine basin]

Alright thanks

[twin shuttle]

can someone help , why is f(x)=a^cosx an even function 🤔

looks to me as if its neither unless im doing some mistake

[eternal lotus]

f(x) is an even function if: $f(-x)=f(x)$

[obsidian monolith]

stephen:

[eternal lotus]

$f(-x)=a^{\cos(-x)}=a^{\cos(x)}=f(x)$ \
$\therefore f(x)$ is an even function

[obsidian monolith]

stephen:

[alpine basin]

When trying to write this as a single logarithm, on the second line log_a(2x+3)^5 joins (x-2)^1/3 on the denominator, but with the quotient rule shouldn't log_a(2x+3)^5 become a new denominator and by itself? Hopefully that made sense

What Im trying to ask is why wouldn't it change to log_a((x^2) / (x-2)^1/3) / (2x+3)^5) ?

[willow bear]

$\frac{\frac{a}{b}}{c} = \frac{a}{bc}$

[obsidian monolith]

Ann:

[alpine basin]

Oh yeah I forgot, thanks

[weak helm]

for the equation x^2 = -4

is +-2i the same as sqroot(-4)?

[viscid thistle]

the sqrt symbol usually means principal root

so you have to do +- sqrt(-4)

[weak helm]

yea but you cant sq root -4

so wouldnt it have to use an imaignary number?

or are they two different things

[tawny nacelle]

what do u think i is

[weak helm]

i feel like they are the same

but then that wouldnt work

so im confused

[tawny nacelle]

$i = \sqrt{-1}$

[obsidian monolith]

soap:

[tawny nacelle]

u know this ?

[weak helm]

yea

[tawny nacelle]

k

[weak helm]

doesnt that only work with one though?

[tawny nacelle]

$x^2 = -4 \implies x = \pm \sqrt{-4} = \pm \sqrt{-1}\sqrt4 = \pm2i$

[obsidian monolith]

soap:

[weak helm]

oooooh

ty

[tawny nacelle]

np

[viscid thistle]

🅱uper moe

[full garden]

guys please someone help me with this

[full garden]

<@&286206848099549185>

[willow bear]

what have you tried so far?

[viscid thistle]

@full garden The best thing to do is use trigonometry. You can use the side measurement of 230 m to find the base of the second triangle (Pythagorean theorem)

[full garden]

@willow bear well i assumed that its a 90,60,30 traingle

[viscid thistle]

why

[full garden]

and it says that the bases are in square shape so I assumed that all of the sides are 230

@viscid thistle idek man I am so confused

[viscid thistle]

@full garden try using the Pythagorean Theorem to solve for A

[full garden]

@viscid thistle I'll try

@viscid thistle I dont know how

i dont know whats a or b

[viscid thistle]

Oh I manually put that in there

[full garden]

how does the 230 measurement help? @viscid thistle

@viscid thistle please help

[viscid thistle]

The yellow sides both measure 115 m because they are half the side measurement of 230 m

[full garden]

yes sir

[viscid thistle]

You can use the Pythagorean theorem to solve for A

[full garden]

but what is the b?

a^2+b^2=115^2?

[viscid thistle]

Oh, no not that

115^2 + 115^2 = a^2

[full garden]

a=162.6

[viscid thistle]

Ok, that’s good. The next step would be to find the height of the pyramid

Which we can definitely do

Try using trigonometry to find the height

[full garden]

i got 199

[viscid thistle]

Oh, that may be a bit off

How did you find it?

[full garden]

Pythagorean

[viscid thistle]

Can’t do that just yet

[full garden]

i honestly dont know how to find it

[viscid thistle]

trig

[full garden]

sine law?

[viscid thistle]

you have an angle remember

52

Use trigonometry, if h is the OPPOSITE, and the ADJACENT is 115m, then we can use tangent

@viscid thistle I got this, ty though

tan = O/A, so tan(52 degrees) = h/115

[full garden]

h=147.1?

[viscid thistle]

Yes, good work!

[full garden]

so theta is 47 degreees?

[full garden]

can i use tan=162.23/147.1

[viscid thistle]

I didn’t check yet, but we can use inverse trig. The height is our adjacent and length a is our opposite (Sorry should have used a different variable)

The best bet is to use inverse tangent

[full garden]

yes

[viscid thistle]

tan^1(162.63/147.19)

That should be your answer

[full garden]

@viscid thistle thank you so much for taking initiative into helping me with this

[viscid thistle]

No problem!

[tawdry sedge]

Can someone please help me with evaluating a fraction like this?

[echo plaza]

for which x

[tawdry sedge]

I'm sorry? What do you mean?

I tried doing this but I don't know how I can put the 2 in

[willow bear]

...

[tawdry sedge]

Oof

[willow bear]

can you post the problem you're doing exactly as stated?

[tawdry sedge]

Ahh

Ah the question is find the domain and range of the function

[willow bear]

okay

[echo plaza]

factorise that boi

[tawdry sedge]

Ohhh

[willow bear]

find when the denominator equals zero

those values of x are going to be not in the domain

and since there are no roots or logs there is nothing else that could exclude points from the domain

[tawdry sedge]

Hmm okay

If I got you correctly, I should put in numbers in x to see which numbers will not equal to 0 right?

Since x/0 is undefined?

[willow bear]

no, you should solve the equation x^2 - 3 = 0.

[tawdry sedge]

Alright I tried to plug in some numbers in x but anything I plug into x does not equals to 0

[willow bear]

no, you should solve the equation x^2 - 3 = 0.

[echo plaza]

Have you done much on solving quadratics?

[tawdry sedge]

Is x^2 - 3 still factorable?

Ah it's been a long time since I have

[echo plaza]

not with integers

but there's quite a simple way to solve this one in particular

[tawdry sedge]

How to?

[echo plaza]

||add 3||

[tawdry sedge]

You mean on x^2-3 = 0 right?

Or on x^2 - 3 only?

So it's either x^2-3 = 3 or x^2=0 right?

[echo plaza]

3=0

add it to both sides

[tawdry sedge]

Omg

Dang I'm sorry

I forgot to

Alright so x^2 = 3?

[echo plaza]

yes

[tawdry sedge]

Alright so the x^2 - 3 is equals to 3?

Would that mean the range is 2/3?

[willow bear]

no

x^2 - 3 = 0

[tawdry sedge]

Shit sorry for the lag

[willow bear]

x^2 = 3

x^2 - 3 ≠ 3

[tawdry sedge]

Ah hmm alright if only x^2 is 3 then it will become 2/3-3?

[willow bear]

you'd benefit from going back and reviewing your algebra

$x^2 = 3$ has solutions $x = \sqrt{3}$ and $x = -\sqrt{3}$

[obsidian monolith]

Ann:

[tawdry sedge]

Yeah I'll do that first

I'm really going no where right now

Thanks for the help though

[alpine basin]

How would I determine the function f(x) = 3x^3 + 2x - 4 is one to one?

[fading token]

Hmm the easiest way I can think of is proving that f is continuous as well as strictly increasing

over the real line

[echo plaza]

I get strong continuous vibes from this one

[fading token]

[echo plaza]

hmmm no calculus...

well you can write it as x(3x²+2)-4

[alpine basin]

In my notes it says "By using the horizontal line test on a cubed function, it proves it is a one-to-one", but they didnt actually show the work 😦

When I try to graph it tho it looks scuffed

[echo plaza]

let's see

are you supposed to use graphing software

[alpine basin]

were allowed to use graphing calculators

I tried inputting it into mine and it didnt look right I think

[echo plaza]

what did it look like?

I'll try something on the side

suppose 3a³ + 2a - 4 =3b³ + 2b - 4

then 3a³+2a=3b³+2b

3(a³-b³)+2(a-b)=0

3(a-b)(a²+ab+b²)+2(a-b)=0

3(a-b)(a²+ab+b²+2/3)=0

so a=b or a²+ab+b²+2/3=0

uh

can I make a square

how about

(a+b/2)²-b²/4 + b²/2 +2/3=0

(a+b/2)²+b²/4+2/3=0

ok and everything on the right is >=0 with 2/3>0

so a=b

which means f(x) is one to one

does it look like this @alpine basin

[alpine basin]

yeah

[echo plaza]

that's right

[alpine basin]

i think i had the display settings messed up cause it looked like a straight line

until i zoomed in

so it is a one to one right? since it passed the test

[echo plaza]

yes

[alpine basin]

mkay thanks man

[weak helm]

hey how would i find the zeroes of x^4-22x^3+121x^2 ?

wouldnt they all be zero?

[echo plaza]

take out a factor of x²

and when I say take out I mean keep it there but use brackets

[weak helm]

yea i understand

but it would still be x^2(x^2-22x +121)

[echo plaza]

yes

[weak helm]

how could i get the zeroes from that?

i know its something witll 11

[echo plaza]

solve x²-22x+121=0

[weak helm]

oooh ty

so just ignore the outside x^2?

[echo plaza]

factorising is a good choice

well also solve x²=0

but I don't think that should be a problem

[weak helm]

oh ok, yea lol

ty!

wait @echo plaza i ended with x(x-22) = 121

that seems wrong

[echo plaza]

I mean it's right but not helpful

[weak helm]

but what would i do then?

because 121 / 22 is 5.5 and thats wrong

its not even an option on the answers

[echo plaza]

get it into the form (x-a)(x-b)=0

[weak helm]

oooh and get the roots

lmao im dumb thanks for helping

[swift glacier]

I can't seem to figure out how to calculate interest rate is the time is more than one?

Is it the same, but rooted to the amount of time?

[weak helm]

well if this is a math problem, it might depend on the variables? idk

[half axle]

these are the options for the second and third inout

input*

kind of confused on what the correct answer is

anyone know?

[waxen yoke]

second is the growth/decreasing factor and third is initial value

[dapper forge]

Anyone here very good at calc

[tawny nacelle]

@dapper forge yea dude

[willow bear]

[viscid thistle]

@dapper forge

Wat

5$ I'll be good at it

[tawny nacelle]

@dapper forge

4.99$ and i'll be gud at it

[dapper forge]

Alright so

I’m gonna need help at around 2 PM EST

@tawny nacelle @viscid thistle

I’ll msg you guys around then

[tawny nacelle]

y r u specifying time

[dapper forge]

Lmaooo

😈

[viscid thistle]

Wheres the question

[viscid thistle]

Who ping and not post question

[dapper forge]

Oh sorry

I’ll ping when I’m ready

[tawny nacelle]

i dont understand time

[dapper forge]

I do t have my book on me that’s why

[tawny nacelle]

concept of time is confusing

[viscid thistle]

Or just post question and wait 15mins to ping helpers

That's about the only rule here and u missed it m8

Bop

Bring in another bop

@tawny nacelle

[tawny nacelle]

heh ?

bop ?

[viscid thistle]

+1 woog bop

[tawny nacelle]

t!wiki bop

[brisk mica]

📖 | ** https://en.wikipedia.org/wiki/Bop **

[tawny nacelle]

naruhodo

balance of payments

i think i decoded the msg

bepis wants me to add 1 to woog's balance

t!credit @severe verge 1

5289

[brisk mica]

➡ | Transaction completed! soap, 💴 1 has been deducted from your balance.

[tawny nacelle]

@viscid thistle yo i did wat u asked for

[viscid thistle]

t!crrdits

t#credits

Fuck

t!credits

[brisk mica]

💳 | Babowwz, you have a balance of 💴 117663 credits!

[viscid thistle]

Give those to woog

[royal gull]

t!credits

[brisk mica]

💳 | dog, you have a balance of 💴 7355 credits!

[viscid thistle]

t!daily

[brisk mica]

🏧 | Babowwz, you received your 💴 200 daily credits!

[royal gull]

t!daily

[brisk mica]

🏧 | dog, you received your 💴 200 daily credits!

[royal gull]

how do you hacve so much money m8

[serene heath]

#bots

[viscid thistle]

[dapper forge]

Aight I’m ready

@viscid thistle

[viscid thistle]

whats the question

Im not reading an essay

[dapper forge]

What’s the standard form of f(x)=x^2-4x+3

Express f in standard form i mean

[viscid thistle]

(x-3)(x-1)

I think

idk

fren whats standard form

[fresh crow]

that is standard form

descending degree order (x^4+x^3+x^2), constants at end, alphabetical order

i believe

but thats algebra I, not precalc

so idk

[brave frigate]

https://gyazo.com/00ba958f8e90fe0f8b42f183ea57ea48

why does cos become squared?

[winter tide]

In order to make the terms have a common denominator of cos(x) we need to multiply the cos(x) by cos(x), making it cos^2(x)

Because cos(x) = cos^2(x)/cos(x)

[brave frigate]

where do you get the other cos from?

[viscid thistle]

multiplying and dividing by cos x

[winter tide]

^^