precalculus

[strange brook]

i have no clue what that is

my teacher never said anything about that

[sick steppe]

sum/difference identity is also called compound angle

so im assuming you have sin(a+b) in your notes. ..

[strange brook]

yep

[sick steppe]

yeah.. so use it

[strange brook]

that doesnt explain anything

i know the formula

i just dont know how to get it to equal the right side

[sick steppe]

use it. . . then simplify. . .

I cant do much in the way of helping if you're not going to listen to the instructions of the question

[strange brook]

ok then

thank you

just one more question

how do you figure out which quadrant the triangle goes in?

[sick steppe]

alpha and beta are acute

[strange brook]

ok ummm

im stupid

how does that help me figure out which quadrant

[sick steppe]

where is 0 degrees measured?

[strange brook]

idk the first quadrant?

[sick steppe]

no, which axis is an angle of 0

[strange brook]

x-axis

[sick steppe]

pos or neg

[strange brook]

pos

[sick steppe]

what about pi/2?

[strange brook]

its still positive

[sick steppe]

which axis

[strange brook]

the y-axis

[sick steppe]

right, so what quadrant is bounded by pos x and pos y?

[strange brook]

the first quadrant

[sick steppe]

yes

[strange brook]

ohhhhhhh thank you so much

[strange brook]

Can someone answer this, I want to know if I did it right.

[uncut mulch]

show your work instead

[strange brook]

4/5 x 12/13 - 3/5 x 5/13

48-15/65 = 33/65

[true sage]

can someone say if icevitals problem is right

please

[sick steppe]

why cant you?

[true sage]

um bc im stuck on the same one sweetheart

dont gotta be passive aggressive up in dis chat

that is not tolerated

[sick steppe]

I asked a simple question, no clue why you feel the need to get defensive

[true sage]

i was just playing lmao

[sick steppe]

cool

[true sage]

yeah

so cool

like you

also

mine was sarcasm lmfao

[sick steppe]

g4u bud

[true sage]

yeah

so good

oiu

[strange brook]

so ummm

what is the answer?

i got 33/65

just wanna know if its right

[serene heath]

yes

[strange brook]

ok thank you

[carmine fulcrum]

Help please 🙏

[pliant locust]

Try multiplying the fractin with its numerators conjugate

Reduce the fraction with the numerators conjugate.* excuse my English in math.

[pliant locust]

Kinda like this, now do the same limit as x approaches negative infinity

[restive bone]

Hi all, any clue what to do next?

Supposed to express in radical form

[sick steppe]

Apply exponent rule

Then revert to radical

[restive bone]

thx got it

forgot that i needed to add them

not sure how to start this

[pliant locust]

Same thing, just start with fraction first and then the whole thing

[restive bone]

k ill try it

thxx

[faint sun]

someone help me understand this

<@&286206848099549185>

[steel flare]

Hey

How would I go about solving this question? I’m pretty confused on where or how to start. Could anyone give me a detailed step breakdown (with numbers) for how to solve the question?

Thanks

[crisp quest]

Do you know what (f ÷ g)(0) = -4 and (f + g)(0) = 3 mean? Try translating that first, and then you should get a system of equations that will allow you to solve for n and m.

[viscid thistle]

help

for what value of x and y will this be maximum

xy=20

how to find this mathematically not trial and error

[past meadow]

can you use calculus?

you

if xy=20, then y=20/x. Then you can rewrite the expression in terms of x only and maximize it using calculus

I mean I'm not just doing it for you lol.

No <3

[trim pebble]

He told you how to do it - maybe try doing what he said?

[viscid thistle]

i did

idk how to

[trim pebble]

Set y=20/x and everywhere it says y replace it with 20/x

[viscid thistle]

the answer aint matching

[proper pilot]

it's like the fate got me in here with the #precalculus

How do you guys memorized the unit circle, i'm so confused and i'm just blindly going over youtube and searching for solutions

[viscid thistle]

@proper pilot i'd recommend understanding it before going with memorisation.

[ancient rampart]

for me i tried understanding it in degrees first and then converting and eventually i just got familiar with the radian values

themore you work with it the easier it gets

[storm matrix]

can someone join the call and help me with a few questions plz

[dark sky]

where is my mistake?

OHHH NVM

i see it

[steel flare]

No, I don't have a good idea of the foundation at all for this unit. Missed a few classes due to supplementary university applications as well as visiting a few schools interesting in basketball recruitment.

This is the question here. I don’t know how to do it or even where to start really. I’ve heard to use (f/g)(0)=-4 and (f+g)(0)=3 to start out with, but I don’t really know what to do with it all. Basically how

[trim pebble]

Yeah so what does f(0) mean?

[steel flare]

Represents the y-intercept I believe

[trim pebble]

So f(0) you replace all x’s with 0’s

Then do the same for g(0)

And then you have an equations that says (f/g)(0)=-4 and another one with (f+g)(0)=3

So you will end up with 2 equations with 2 unkown variables and then you can solve it

[dark sky]

not sure how to find range for this problem pls help

would it be: (-infinity, infinity) U ( -infinity, -infinity) U (infinity, 0)?

[sick steppe]

range is whatever y values you can equal

so 1st thing is fine the bottom the "quadratic" part of the graph (not an actual quadratic, but you get the idea)

[steel flare]

So, I just replace all the x variables with the value 0? Where do i go from there? And with being said am i supposed to have f(0) = 0^2 +2m(0)+m^2?

[trim pebble]

yes

[steel flare]

So then I would get f(0)=m^2?

Sorry if the questions seem a little stupid, this unit has me lost as i've fallen behind

[trim pebble]

yeah thats correct

then do the same for g

[steel flare]

g(0)=1/n

[trim pebble]

yep

[steel flare]

Okok

[trim pebble]

so what is (f/g)(0)?

using that

[steel flare]

err

What does that equation look like?

[trim pebble]

just insert what you found f(0) was

and g(0) was

[steel flare]

m^2/1/n?

[trim pebble]

yep

and that was equal to -4

so $m^2 \cdot \frac{1}{n}=-4$

[obsidian monolith]

ScapeProf

[trim pebble]

and then also calculate (f+g)(0)

[steel flare]

How can I solve for the unknown variables?

Or

How do I calculate (m^2) 1/n - -4

[trim pebble]

yep so you need both equations

then isolate either m or n and insert that in the other equation

[steel flare]

I don't understand how

I know thats very vague

[trim pebble]

what is the 2nd equation?

[steel flare]

(m^2 +1/n)(0)=3

[trim pebble]

remove the (0) now but yeah

okay so try and isolate for example n in the 2nd equation there

so n is alone on one side of the equality sign

[steel flare]

Okay thank you

Really appreciate the help

Pretty sure I got i

I might share it here in a bit

[trim pebble]

nice

[steel flare]

n=-1 and m=2

+/- 2

[trim pebble]

yep

[proper pilot]

yeah, I think I understand the unit circle very well, let me say what I understand in a nutshell, Unit circle is just combinations of 30 60 90 and 45 45 90 right triangles, AM I RIGHT

send help

[worldly radish]

supposed to find out whats wrong with this statement, i guess its the end but im not 100% on how to explain

last problem for tonight trying to go to bed early

[pliant locust]

This is how I remember them, if you have memorized the pythagoras theorem,sin x = opposite side/hypotenuse and cos(x)=adjacent/hyp

Then all you have to remember is an equilateral triangle which is a triangle where all angles and sides are equal to each other.

As to the unit circle I always just compare if the fraction is closer to pi or 2pi(zero).

[proper pilot]

thanks fam, ive been grinding youtube videos about this, your last statement, ill keep that in mind cherish it and love it, Thanks again

[pliant locust]

$$
\frac{-1}{-2}=\frac{-1\cdot 1}{-1 \cdot 2} = \frac{1}{2}
$$

The negative one factors in numerator and denominator cancel each other out

[obsidian monolith]

ds.b16rts

[signal summit]

need some help with Trig Equality

what would I do when im at 1= r/x * r/y?

[viscid thistle]

Hey i'm having a bit of trouble understanding this

ill try and write out my steps and if anyone can correct me id appreciate it

i squared what was inside the parentheses so i got
(1 - (sin^2(x) - 2sin(x)cos(x) + cos^2(x))/2cos(X)

i end up with (2sin(x)cos(x))/2cos(x)
I don't know where to go from there because the answer is supposed to be sin(x) but im not sure what im doing wrong

[proper pilot]

Where should I study precalculus?, from start to beginning, I want to master it so I can understand basic calculus calculus and etc. (idk if thats the order)

any book suggestions or others

[proper pilot]

pls help, what did I do wrong, is the question wrong or am I missing somthing, my tan is negative idkk

sorry for the bad hand writing

[pliant locust]

Know your algebra and polynomials really well, complete the square, polynomial division etc.
Understand definition of derivatives with limits
Graph polynomials and asymptoptes, integration and derivation with simple rules, no limits.
Get good at trigonometry
Get confident using e(x) and it’s inverse the natural logarithm.

Then the only thing left is understanding inverses and solving some nasty inequality equations used for epsilon-deltas and proving functions are bijective in calc1.

I might have missed something but the prerequisites for calc1 aren’t that many really.

[proper pilot]

yo thankssss

[storm spoke]

hii

does anyone know how to do the

r = 2sin(theta)-3cos(theta)

convert to rectangular form

OH NVM I GOT IT

LOVE U MUAH

[mild swan]

😐

[novel cargo]

There is a book "Precalculus by Ron Larson". It's pretty good.

[tough hemlock]

Can someone please help me with this

[velvet granite]

it has a hole

if it was solid then the value would be defined

[sweet sundial]

(This is my first message every lol) solve for x: sec^2(x) - 1 + 2tan(x) = 6/tan(x) + 5 -- write a general solution -- could someone show me how they would solve this

[sick steppe]

write everything in tan, then solve

[jagged sun]

This place aint that active 😦

[sweet sundial]

@sick steppe you were able to work through it/

?

[tender galleon]

Can I have some help understanding a function/domain question? I'm unsure of what I'm doing wrong when attempting to create a function that has a certain domain. The domain is: (-∞, -5) U (-5, 2] I believe that the function should be the attached image, yes?

[sick steppe]

,w domain of (x+5)/cbrt(x-2)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by moshill1#9771

[uncut mulch]

you should use cbrt instead of ^(1/3)

otherwise it takes the principle cube root in complex

,w domain of (x+5)/cbrt((x-2))

[sick steppe]

,w domain of (x+5)/cbrt(x-2)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by ramonov#0921

[uncut mulch]

firstly, why did you exclude -5?

[tender galleon]

This is the first problem that I've ever done that requires me to create a function from an existing domain

Honestly, I'm kind of lost as to where to go, but I thought I was right with the above answer. I'll make some revisions really quick

[uncut mulch]

also I misread your goal

[tender galleon]

That's fine. I did type a large blurb

[uncut mulch]

utlise square roots instead of cube roots

give it another go, and then if you're still struggling I can walk you through it

[tender galleon]

I have a few domains here, but I feel like I'm so close to actually having the solution, but I still feel lost? I know that I'm close though. Thank you, I really appreciate this!

[uncut mulch]

(-∞, -5) U (-5, 2]

so you want to exclude -5 and values greater than 2 from your domain.

to exclude -5, you'd want the denominator of your expression to be 0 when evaluated at -5.

i.e. the (x+5) should be in the denominator of your fraction

does that make sense so far.

[tender galleon]

Let me try something really quick

This may be the hint I need!

This is the answer! This excludes values great than 2!

[uncut mulch]

not quite

[scarlet saffron]

Hey, I am having trouble understanding what to do for this problem. I am unsure if this is the right section, so don't mind me if I post it in the wrong section. If anyone can solve this, would you mind giving me step by step instructions? I would appreciate any help. <@&286206848099549185>

[uncut mulch]

that excludes values less than -2

[tender galleon]

WHOOPS! Sorry 2-x sorry

[pliant locust]

Now it makes sense 🙂

[tender galleon]

I think I understand a little bit better! Thank you!

For anyone that cares, the answer is the attached image. Thank you, Ramonov!

[worthy seal]

why is the answer not DNE?

wouldnt x -> 6 be undefined?

[uncut mulch]

no

the expression may be undefined at x=6
but when taking the limit you don't really care about that

you're considering what's happening around it, value being approached etc,

[pliant locust]

It means that the function is 4x- 3 if and only if x is greater than 4 else function evaluates to value 6. in first question, x=-5 which is less than 4 meaning that the function evaluates to 6.

[umbral oar]

Hello guys can you help me with this?

[surreal finch]

could someone help me real fsat

fast

[scarlet saffron]

Can someone explain what I have to do in terms of steps in order to solve this? <@&286206848099549185>

[shadow zodiac]

I'm trying to figure out the equation for a curved line and its been a minute since I've done this,

plots are (1,6), (5,8), (10,10), (15,12)

[clever pecan]

f(a) = 2a/(a - 5)

f(a + h) = (a + h) plugged into each x in f(x)

when you do more in calculus you'll learn $\lim_{h\to 0}\frac{f(a + h)-f(a)}{h} = f'(a)$

[obsidian monolith]

Modular Code

[clever pecan]

but the difference quotient itself is just another way to compute the slope of the secant line of function, which can approximate the derivative based on the mean value theorem

the derivative is the way to compute infinitesimally small slopes

anyways

I'm sure based on how you find f(a + h) and f(a), you can find the 3rd option @scarlet saffron

[scarlet saffron]

Thank you so much.

[clever pecan]

np 👍

would you mind if I showed you?

how you compute the slope of a linear function with the difference quotient

[icy raft]

bruh im tryna do some verify identities

real hard for some reason

like it makes sense why its true or false but I have to show work and thats whats messing with me

[scarlet saffron]

@clever pecan I would appreciate that.

[clever pecan]

so let's say you have this function:

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

and you're given the points (10, 20) and (5, 10)

when you use the difference quotient 20 - 10 = h

you can pick an x value from one of the given points

let's say 10

and we can plug everything into the difference formula: $\frac{f(x+h)-f(x)}{h}$

[obsidian monolith]

Modular Code

[clever pecan]

so it should be: $\frac{f(10 + 10)-f(10)}{10}$

[obsidian monolith]

Modular Code

[clever pecan]

which is f(20) - f(10) over 10

f(20) = 40, and f(10) = 20

40 - 20 = 20

and 20/10 = 2

so the slope is 2

you must've learned (f(b)-f(a))/(b - a)

that's way easier than this process in order to compute the slope of a function

it also works for derivatives

$\lim_{x\to a}\frac{f(x)-f(a)}{x-a} = f'(a)$

[obsidian monolith]

Modular Code

[clever pecan]

I replaced b with x

it's just this is for given points

let me give you an image

[scarlet saffron]

Thank you for showing me. I appreciate it.

[clever pecan]

np

[shadow zodiac]

Was this in response to mine? How did you get to this answer?

[clever pecan]

@shadow zodiac I was replying to wookienipple

[proper pilot]

is there any excellent books that would help a mindblock like me improve at Pre Calculus?, i'm jealous that one of my school mate is getting 45/45 easily when i'm struggling so hard, I know a book wouldn't make me good ''brrrttt u r smart now'', I know it takes a lot of dedication, time and patience

is there any materials like book, youtube channel to follow to improve at Pre Calculus?

materials that can help even a mindblock like me

because my teacher is not helping me, and I'm going so down right now, I'm passing simply by having a formulae next to me, it makes me feel guilty. if something helped you improved with a book, I'd thank you forever

[steel venture]

what exactly is holding you back though?

you can always look up yt videos on topics you don't completely get

[proper pilot]

if I know myself very well, it's because im blindly memorizing stuffs, I really don't know what am I doing, I'm just passing like a piece of shit

[steel venture]

there's also khan academy, and organic chemistry tutor is a great resource on yt

[proper pilot]

YT videos just makes me memorize it, I really don't understand

it's like, I know what 1+1 cause I memorized it but if I get asked what is 1+2 I would get frozen

cause I don't know what to do

[steel venture]

well i wouldn't blame it on a mind block then, because your classmate clearly is also memorizing and doing just fine

unless you are being taught different things

[proper pilot]

yeah, it's not im failing, i'm just passing and writing stuffs that I don't know what the fuck im writing

[steel venture]

then it's probably best to ask questions, or google "why does the quadratic formula work"

[proper pilot]

is there any materials that will break me down these stuffs

[proper pilot]

the problem is that I really don't get a relliable answer

I do that all the time

[steel venture]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/v/proof-of-quadratic-formula

[proper pilot]

for example in getting coterminal angles, our test today is to get the coterminal angles of stuffs

but what I was taught is that there are infinitely

many

coterminal angle

so I got really confused

[steel venture]

yes

[proper pilot]

and I had to resort into googling stuffs

[steel venture]

why wouldn't there be infinitely many coterminal angles?

[proper pilot]

yeah, I know there are infinitely many, I understand that, next is like soh cah toa, I don't know how it is useful

I know how I apply stuffs

like

I know sin is opp/hyp

etc etc

but I really don't know

it's hard to explain XD

Imma study at Khanacademy again

[steel venture]

well i can explain to you sohcahtoa if you'd like, the issue is that you probably haven't gone far enough to truly prove it

or understand a proof of it

[proper pilot]

I got jealous of this guy who got 45/45 in a test, while i'm struggling af he is just swiftly doing stuffs

[steel venture]

well he is memorizing just like you, so the memorization doesn't seem like the issue

[proper pilot]

yeah, is there any materials that goes in detail, and explains what is and what does it do in simple words

my teacher is stating big words in English

and English is not my first language

[steel venture]

then ask what they mean, it can only help

if not they'll never know you don't understand

and just mindlessly move on

[proper pilot]

I do ask, but I have a feeling that i'm holding back

everything

do you have any

book suggestions

or any authors

[steel venture]

no

[proper pilot]

oh that's unfortunate then

[steel venture]

im sure you could find some but it would seem as if these more basic topics would have less literature written on them

do you have a textbook by any chance?

to go along with your class?

[proper pilot]

the funny thing is that we don't, they print out modules by Math Teachers in our country

then

my Teacher is telling us to ''don't trust this''

and the modules are incomplete, they are only there for activities

hence I want a textbook to follow on

[steel venture]

i don't recall much about my prealgebra textbook, i mostly remember lectures more than readings, so i can't comment much on it

but you could just find textbooks online and read reviews on them

see their contents

see if they are just formulas or explanations as well

and figure out something from there

[proper pilot]

yeah, my plan is to follow a textbook and a youtuber/lecturer at the same time

If I don't improve my understanding with maths then i'm switching to other course

[steel venture]

i honestly find that asking here is your best bet. its free and answers are relatively quick

plus you can ask follow up questions if something is confusing

but a textbook is a great solution too

[proper pilot]

oh yeah, I've asked questions here before and I got big help

all this time I didnt know sqrt of x^2 is just absolute value

so yeah, I wish I can improve my mathematics

I love maths

[steel venture]

what do you mean

[proper pilot]

I was told that sqrt of x^2 = |x|

is it true

I haven't got a chance to ask anyone

[steel venture]

in a sense it could be

[proper pilot]

but I was told its like that

[steel venture]

usually square roots are associated with +-

so

$\pm\sqrt{x^2}$

[proper pilot]

yeah

[obsidian monolith]

maximo

[steel venture]

which could be $x, -x$

[proper pilot]

yeah, that made a lot of sense

[obsidian monolith]

maximo

[proper pilot]

I bet the guy who got 45/45 is not listening to our lecturer at all

I could be wrong

but I could also be right

it's not that I want to get 45/45 too so I can flex

I want to understand mathematics because i'm going to take a course that is going to be related on maths

so yeah

thanks for replying

[steel venture]

then don't bother with the score

[proper pilot]

if anyone can suggest a textbook, youtube channel or some website for precalculus, pls pls @ me

[steel venture]

you're putting too much focus on that 45, when the content seems more important

[proper pilot]

my mindset is that if I don't score 45 then I didnt understand it

[steel venture]

that's a poor mindset

if you make a silly mistake and no longer get a 45, does it mean you didn't understand the content?

[proper pilot]

I want to understand the contents

[steel venture]

and if you get a 45 by just memorizing, is it really understanding?

a score is a score, don't confuse it for intelligence

[proper pilot]

yeah, thats why I'm here asking, I don't want to score on something that I just memorized

I want to understand it

because if I don't I would fail in Basic Calculus

and also, I like maths so I want to understand it

[steel venture]

and that's great, but lose the interest in the 45. good grades are important, but they're not the determining factor between understanding and not understanding

[proper pilot]

thanks for the enlightenment I will keep that in mind

i'd try to re-follow Khan Academy again

[pliant locust]

Actually nvm, this just served to confuse you more

[lilac storm]

can anyone help me with this question.

[somber yew]

@lilac storm What have you thought so far?

[lilac storm]

so i am confused, so i know that it is approaching 5 from the negative

and it =3

so that curve stops at 3 and then starts at x=2

i think it is false

if we are talking like about the function at x=2 to x=5, then it looks true

so i am confused

so how do you figure out this question?

by reading this, to me it looks like it is true but I am not a 100% sure.

are you there?

are you there?

can anyone please help me out.

[stable yacht]

I’m not really sure where to go from here, or if my work up to this point is even correct.

[sick steppe]

only issue is the conjugate in the denominator turned into a minus instead of the plus you originally had

[stable yacht]

Oh, that explain a lot. I just made a random sign change for no reason. Thanks for catching that!

[lilac storm]

can anyone please help me with this question.

[somber yew]

Oops, sorry for leaving on a cliffhanger back then.

[lilac storm]

yeah, no worries.

[somber yew]

You see, as you get closer and closer to 5 from the left, the value of the function does remain 3 consistently. What does this tell you about the left hanf limit of f(x) at x=5?

[lilac storm]

that as x approaches 5 from the negative, f(x)=3

[somber yew]

Yes.

So should the given statement be true?

[lilac storm]

but when it goes down and you can see the point (2,2), there is a break so this part confuses me?

[somber yew]

What happens at near x=2 is not relevant for the behaviour of the function near x=5.

[lilac storm]

and what about the hole in between the line (2,3) and (5,3)

[somber yew]

Again, not relevant.

[lilac storm]

oh, ok

so that means, this is true.

right?

[somber yew]

When talking about limits, you would like to see that the points in the immediate neighbourhood are approaching a certain value.

Yes.

The basic idea is this: as you get closer to the point, the function values should get closer to the limit, if it exists.

[lilac storm]

oh, ok.

ok, thank you so much.

[somber yew]

No worries; goodluck!

[lilac storm]

can anyone help me with this question.

so i know and i was able to do the first and last step for which the answers are, so the answer for the first step that i got is

and the answer for the last step i got is

can anyone please help me with step 2 and 3

anyone there that can help me.

[lilac storm]

is anyone there to help?

[viscid thistle]

Can't u just send 1 picture containing everything @lilac storm

[lilac storm]

oops, yeah, soory about that?

sorry*

can you help me with step 2 and 3

[viscid thistle]

Just take the derivative

then y-f(x)=f`(x).(x-f(x)

[lilac storm]

so i take the derivative of what?

[viscid thistle]

Function

6-3x

[lilac storm]

yeah so that is just -3

[viscid thistle]

Seems slope would just be y=f(x)

So

-3

Is the slope

[lilac storm]

so is it f(x) = -3(x+6)-(-3)

[viscid thistle]

What

No the slope is just - 3

Your answer

[lilac storm]

yes, i know that, what i need help in is writing step, how would you write step 2, i know that the slope is -3 as i have already mentioned above in my answer.

[viscid thistle]

Dunno differentialquotient was long times ago

[lilac storm]

sorry, what do you mean?

[viscid thistle]

That's differential quotient without the limit

[lilac storm]

yeah, i still don't understand what you mean.

[faint sun]

can someone help out with this problem: $\sqrt[i]{1 \frac{1}{2}} \cdot i \sqrt{\frac{4}{3}}$

[obsidian monolith]

Yolobro117

[steel venture]

what are you meant to do

evaluate it?

if so use the fact that $x=e^{\ln{x}}$

[obsidian monolith]

maximo

[steel venture]

and $\ln{a\cdot b} = \ln{a} + \ln{b}$

[obsidian monolith]

maximo

[calm frigate]

Alright honestly no idea what im doing wrong with this, so A Ferris wheel is 10 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. How many minutes of the ride are spent higher than 12 meters above the ground?

This is a homework question and a failed attempted one so its a good example

I get that you need both T values but I subtract them from each other its a few points off from the actual answer

[bright grail]

im confused on what to do beyond this point

do i log both sides? natural log?

this is what i have in mind

[viscid thistle]

What's the question?

Find the inverse?

[bright grail]

yes

im p sure i did everything right

im just unsure about taking the log of both sides

[viscid thistle]

Then what you did is totally correct

[bright grail]

how about this

its asking for the domain

and im unsure if i did this one correct

i found what e^x is

but i got ln(-3) which i think is not possible

and ln(1) which is 0

meaning x = 0

so would the domain be 0, infinite

[viscid thistle]

yes, that's correct. Preferribly (0,+∞)

Though unsure of what you did

To find the domain of f, you can notice that the argument of the log must be >0, ie solving the inequality: argument>0, but you somehow reach that without being clear on what you are doing

[pliant locust]

He recognized the input as a polynomial, factorized the polynomial and solved x for polynomial =0

[bright grail]

i mightve not written it properly x)

[viscid thistle]

I know what they did. I suggested writing it explicitely.

[bright grail]

i did a similar question

pretty sure this is correct

it said to solve for x though

5^x = 5

x = 1

5^x = 1/2

ln both sides i think

x = ln(1/2)

[viscid thistle]

5^x=1/2's solution isn't correct

[viscid thistle]

e isn't the base on the left hand side, so you can't just "cancel" the e's with the ln as you did with the previous one

ie saying ln(5)=1 is incorrect, which looks like it is what you showed

[bright grail]

so how would i do it

do i take the log

[viscid thistle]

you'd get $x\ln(5)=\ln\left(\frac12\right)$, you can just finish by dividing both sides by $\ln(5)$

[obsidian monolith]

Al𝟛dium

[bright grail]

i see

couldnt u also do it with log though

[viscid thistle]

You can as well yeah

Alternatively, you can also log with base 5 on both sides, and use the fact that log_5(5)=1 to then get x=log_5(1/2)

[bright grail]

i like that

sorry for all these questions homie

i rly appreciate it 🙏

im rly stuck here

[viscid thistle]

Note that when you divide both sides by -5 you want already to indicate the flip of the inequality sign

Now in order to solve $\log_{\color{blue}{2}}(x)<-\frac95$, you can consider what do you do when you are solving for $x$ on an example like: $\log_3(x)=4$. Though you'll have to consider something else as we are solving an inequality.

[obsidian monolith]

Al𝟛dium

[bright grail]

unsure of how to do that to be honest

wanna give me a hint 😓

[viscid thistle]

Sure

Consider: ${\color{blue}{a}}^{\log_{\color{blue}{a}}( {\color{green}{x}} )}={\color{green}{x}}$

[obsidian monolith]

Al𝟛dium

[bright grail]

so raise it by 2

😓

[viscid thistle]

excluding values where log_a(x) is undefined

[viscid thistle]

correct

But you have to consider something else as we are in an inequality and not in an eqn.

[bright grail]

fuck

u cant just raise both sides

[viscid thistle]

There's something subtle to consider

You can if you think about it.

When do we have to flip the sign of an inequality? ie in which cases do we have to?

[bright grail]

negative

when u multiply/div

[viscid thistle]

Alright. Now we can be sure to apply this, as for $a>1$, \$\log_a(x)>b\implies x>a^b$ is true. Due to the behaviour of the log/exponential graph. And as our $a$ is indeed greater than 1, we can safely do: $$\log_2(x)<-\frac95$$ $$x<2^{-\frac95}$$

[bright grail]

oooo i did that

but how does that differ from an equality

[obsidian monolith]

Al𝟛dium

[viscid thistle]

Because we have to take into consideration the behaviour of log/exp functions, while in an eqn you can just simply not worry about flipping the sign. And also consider later where log(x) is undefined, etc.

[bright grail]

makes sense

here its log4(x) < 3/2

so im guessing u cant just simply raise it here? 🤔

[viscid thistle]

Did you just dropped the absolute sign bars?

[bright grail]

yeah i was planning on doing < 1

and then > -1

because i remember that being possible

[viscid thistle]

Oh okay

Okay, be careful, from line 3 to 4, log(a-b)≠log(a)-log(b)

But instead, log(a/b)=log(a)-log(b)

[bright grail]

😓 i knew i did that wrong

i had a feeling loool

im so used to sigma notation or whatever

[viscid thistle]

Don't worry

Surely you can apply what you know from previous exercises at the line log_4(x²-4)<2, same way you did before

This time you just have x²-4 instead of x, which you'll take care of later

[bright grail]

wait so u can just raise it to the 4 here

[viscid thistle]

correct, and consider again what i said about the behaviour, as 4>1, you can safely apply it here

[bright grail]

makes sense 😄

[viscid thistle]

After doing so you get a simpler inequality to solve, i'm afraid i have to be afk rn, so good luck with the rest.

[bright grail]

appreciate it homie

😗

[fathom root]

Hey for a right triangle, does the hypotenuse side stay the same for all 3 angles but the adjacent and opposite sides vary for each of the 3 angles?

[weak needle]

This is more suited for #geometry-and-trigonometry

[viscid thistle]

Need recommendation for a video to learn how to draw polar equations

[neon walrus]

<@&286206848099549185>

[steel venture]

170=c + T - t

130 = T + t - c

if you add both equations up you get that 2T = 300

so the table is 150cm

[round quest]

how would i find the vertical asymptote for y=3cot pi x

[sick steppe]

3cot(pi*x) = 3/tan(pi*x)

[serene heath]

are you trying to isolate P_2

[atomic urchin]

How would One set this up and solve this?

[sick steppe]

write out the proportionality statement, then convert it to an equation w/ the prop. constant

[lilac storm]

can anyone please help me with step 2 and 3 of this question.

is anyone there to help?

[uncut mulch]

do the algebra

[lilac storm]

yes i did it but i don't know why it told me it is the wrong answer again and again

like i got the first step right

can you help me out?

so what i have for step 2 is (-3x-3h+6)-(6-3x)

are you there?

[uncut mulch]

simplify comepletely

[lilac storm]

yes so i got 3x+3h

i have tried this before and it said it is wrong.

[uncut mulch]

how are you getting 3x+3h

show your steps

[lilac storm]

oh i think i got my mistake, thank you for pointing out

i thunk this was the mistake which was messing up my answer

think*

so -3h is the answer for step 2 then what will be the answer for step 3?

oh is it -3h/h

[uncut mulch]

simplify completely

[lilac storm]

i just typed in -3h/h and it was wrong

-3 is the answer for the last one

[uncut mulch]

how is that relevant?

[lilac storm]

oh, ok

ok, thank you so much for your time and help.

[robust nest]

I dont know how to start

im completely lost

[uncut mulch]

start with a circle centred at (0,0)

[robust nest]

ok @uncut mulch

where do I go from there

[uncut mulch]

identify your quadrant from the given interval

[restive bone]

Anyone know how to factor e)?

The a+b and b-a are confusing me

[crisp citrus]

FIND VALUE OF X OR GAY

[full pagoda]

what do you know about those two angles

[restive bone]

Solve 2x + 23 = 5x -112

Any love for my factoring question??

[full pagoda]

you seem to be on the right track

you just need to write in the last thing, you factored a six out of six

or are you looking to completely expand it and then factor it?

[restive bone]

Ya forget my pencil stuff

I need to get to 6(a-b-1)''

'' means squared

Appearently thats the answer

[full pagoda]

i've expanded both the answer and the problem 5 times now

i'm 90% sure the answer you're given is incorrect

[restive bone]

hmmmmm

its possible

thats from the answer key

its been wrong before but rarely

dont worry about it too much ill skip it

i appreciate your help tho 🙂

[full pagoda]

👍

i just keep getting sign differences with that answer

[strong ermine]

[crisp citrus]

lol

[dark sky]

can someone pls double check my work for these problems

[zealous cosmos]

Looks good

[zealous cosmos]

It's also probably fine to leave it as $$\left(\frac{1}{x-a}\right)^{2}+3$$

[obsidian monolith]

jolimath

[zealous cosmos]

I personally would try to simplify this more ... into a single fraction bar rather than 3.

[dark sky]

Ok kewl thx

[limpid rampart]

fellas

i been stuck on this for like 20 minutes

$|x+1| -|x|+3|x-1|-2|x-2| =x+2$

[obsidian monolith]

Someone

[uncut mulch]

identify the x values where the insides or your abs vals are 0
and consider what happens before, between and after those values

[limpid rampart]

thanks 😄

[faint nest]

how do i go about solving 5-10??

[sick steppe]

when is x/(x-16) not defined?

[faint nest]

Uhhh

x =/= 16

or -16

idkk

[sick steppe]

which one?

[faint nest]

16 i think

[sick steppe]

since division by 0 is undefined @faint nest

[faint nest]

@sick steppe it says support ur answer graphically

so how do i do that?

[sick steppe]

draw it I guess?

[opal cosmos]

why is (1,b) point of exponential graph only one above the horizontal asymptote (when there is no stretch or compression)?

[sick steppe]

your question makes no sense

since the y value isnt 1...?

[opal cosmos]

in exponential isnt base to power of x just equal to b so thats y value tho

[sick steppe]

yes, but what do you mean by "only 1 above the horizontal asymptote" when b=1 means b^x is just y=1

[opal cosmos]

like the point (1,b) that is transformed after applying all the transformations

[sick steppe]

You said no transformations

[opal cosmos]

my teacher told me that that point will usually be one above HA when there is no stretch/compression

[sick steppe]

Can you, maybe, crazy idea, post the explicit question instead of quoting

[opal cosmos]

if there is stretch or comp it will be more than one above HA or something but idk the reason

she gave us this graph and wanted to write what the function would b

[sick steppe]

yeah, so what f(x) did you get?

[opal cosmos]

1/5^x-1 -4 I think

i didnt get it right the first time so i had to go ask her

x-1 is the exponent of 1/5 btw and -4 was just vertical shift

my bad i meant x+1 as exponent

[hidden willow]

this is on my pre calc warm up

the circular blade on a saw rotates at 4200 revolution in a minute
whats its angular speed

[reef spade]

how do I find out if the function is Surjective and Injective?

[pliant locust]

Let a != b (not equal b)
If you find a solution to equation
f(a)=f(b) then it means the function isn’t injective and thus not bijective. When it comes to surjectivity I know only how to prove surjectivity when the codomain is the functions range. So if you know how to prove that the range of the function is R then you know.

I have two ways of proving bijection on its own range. Either prove it is strictly increasing or decreasing or just solve f(a)=f(b) (a != b).

A general approach:

Let upper function of the piecewise function be called g(x) and the lower called p(x).
You can start with showing that the upper g(x) is bijective on its own range either by proving it is strictly increasing for x>2 or showing that g(a) =/= g(b) when a > b (implies a =/= b). Then do the same for p(x). Now the last step is to show that p(x1) does never equal g(x2) in other words
f(x1) =/f(x2) where x1 =/=x2.

This is just proving that it is bijective when the codomain is its own range. The function isn’t injective btw.

You can also instead of just solving inequalities use derivatives and knowledge of polynomials but I dunno exactly what they expect of you.

[halcyon granite]

would the limit as x approaches one just be 4?

[sick steppe]

graph it and find out

[halcyon granite]

i did, its a horizontal line

so can a horizontal line have a limit

id say no, but calc has proven me wrong a few times already

[ornate lintel]

guys whats intergration?

[lilac pier]

@halcyon granite yes the limit is 4

[halcyon granite]

@lilac pier can you explain why its 4? i feel it should just not exist

[lilac pier]

limit doesn't exist when left hand limit and right hand limits aren't equal

[halcyon granite]

because they arent approaching 4 ever, its just always f

4

[lilac pier]

g(x) is always 4 no matter what x is(except x can't be 1), so when u approach x from the left and the right

g(x) is 4

so the left hand and right hand limits are same

[halcyon granite]

so they dont need to be approaching 4, if they are equal to four, then that can be seen as a limit too?

[lilac pier]

yeah

[halcyon granite]

@lilac pier one last thing, for a limit to exist, the function must approach a finite value, the limits must be equal on both sides, x must approach a from both sides but what else? I have those 3 on my notes but the practice sheet i got asks for 4

[lilac pier]

maybe the 4th one is the requirement for continuity?

[halcyon granite]

doesnt continuity also require all that i just said?

[lilac pier]

yes but one more condition that the value of the function at a point and limits at that point must be equal

[halcyon granite]

but you can have a hole and there still be a limit right?

so how can continuity be mandatory for there to be a limit

[lilac pier]

we can have a hole and the limit can exist, but for continuity, the hole shouldnt be there

[halcyon granite]

ok well then that means that continuity is not necessary for there to be a limit correct?

[lilac pier]

Yes

[halcyon granite]

i need a last reason why there cant be a limit

[lilac pier]

continuity implies that the limit exists

converse isn't always true

[halcyon granite]

i agree

but i need something that is never true if that condition is met

like there can be no limit if the function has this

[reef spade]

@pliant locust thanks

[halcyon granite]

so why does sin(1/x) not have a limit as x approaches 0

[sick steppe]

$\lim_{x \to 0} \sin{x^{-1}} = \sin{\left(\lim_{x \to 0} x^{-1}\right)}$ since sine is continuous

[obsidian monolith]

moshill1

[sick steppe]

which is equivalent to $\lim_{a \to \infty} \sin{a}$

[obsidian monolith]

moshill1

[halcyon granite]

how does it being continuous mean it doesnt have a limit? y=x is continuous and has a limit as x approaches 0 am i wrong?

[lilac pier]

when did he say that

[sick steppe]

"since sine is continuous" was for why I could bring the limit inside the sin

[halcyon granite]

huh

[pliant locust]

Just one counter example is enough to show it isn’t injective like

f(-2+p) = f(-2-p) for -4 <p<2

[lilac pier]

@halcyon granite What moshill is saying that because the sin function is continuous, we can say that lim x--> 0 sin(1/x) = sin[ lim x---> 0 (1/x)]

[halcyon granite]

yeah i can agree with that

oh and because 1/x has no limit as x approaches 0?

[sick steppe]

That, and the limit of sinx as x goes to infinity is undefined. Since as x gets bigger and bigger, sinx continues to just oscillate on [-1,1]

[halcyon granite]

so in a function with infinite oscillations, there is no limit?

[sick steppe]

yes, if the value keeps changing and doesnt approach a value, it's undefined

[halcyon granite]

ok thank you

[robust nest]

I got pi/2 for this but the key says that's wrong

Used half angle identites

[uncut mulch]

show work

[robust nest]

Kk

[uncut mulch]

by cancelling the (1-cos(theta)) like that, you're missing soluions

[robust nest]

really?

@uncut mulch how so

[uncut mulch]

you're dividing both sides by something that could potentially be 0

hence losing the solutions from (1-cos(theta))=0

using a simpler case:
x = x^2

x = 0 is a trivial solution to that

but if you divided both sides by x,
→ 1 = x

that information is lost

instead you should consider factorisation

[robust nest]

ahhh

so instead what identity should I begin with

you said to use factorization correct

[uncut mulch]

the first step was alright
just rearrange to stuff = 0
and factorise

[robust nest]

ok so starting from the second step of the pic I sent

subtract 1 and add cos

right?

[uncut mulch]

from both sides, yes

[vale eagle]

nice precalc

[wanton wedge]

Hi ummm I was wondering if could get some help, I’m not quite sure on how to do this

[mighty fiber]

Instead of using a matrix, why not just do elimination and get rid of c then b?

are u required to use a matrix?

[proper pilot]

What should I always remember when dealing with sin, cos, tan graphs?

and transformation graphs

[viscid thistle]

wow, that's very general

uh

As in how to graph them?

[proper pilot]

like, the properties and how to determine transformation of graph

like, I'm given points, and I need to determine what is the value of theta (like sec theta and other stuffs)

what should be my guide

thanks

[viscid thistle]

your question is worded very vaguely, and it is still not clear at all what you're asking. May i ask you to either reword it or give an example of those type of exercises?

[proper pilot]

I was given a point earlier, and I need to determine what are the values of the six trigo functions, i'm sorry I really don't get the topic myself

our topic is about graphing sin,cosine and tan

oh nevermind, I think I get it now, but thanks for replying

I just realized that I can just do the soh, cah, toa formulas to determine what I need to find, so yeah

the graph have formulas which I found in Brian McLogan youtube, in case anyone is wondering

have a nice day people

[sick steppe]

ok then..?

[hearty bronze]

can someone help with this question?

[sick steppe]

plug in the given point and solve for a

[hearty bronze]

so if i use desmos

i would set a equal to the options listed

?

and if f(pi/4) = -4

what would the amplitude be

[sick steppe]

plug that in and isolate for a

$-4 = a \cos{\left(2(\frac{\pi}{4})-\frac{\pi}{6}\right)} + 6$

[obsidian monolith]

moshill1

[hearty bronze]

ok

thanks

[lunar mirage]

Hi can anyone help me with intervals?

[sick steppe]

what have you tried?

and dont spam your question everywhere

[lunar mirage]

Oh sorry lol I'm just not sure if it's i (- infinity, 0) and for decreasing (0,- infinity)

I just don't know of its increasing or just decreasing

[sick steppe]

decreasing = tangent w/ negative slope

[lunar mirage]

Oh okay, does that apply with that graph?

[sick steppe]

well is the tangent slope every positive..?

[lunar mirage]

No?

[sick steppe]

Yep, so it's always decreasing

except for 1 place

[lunar mirage]

Ooh okay I see

[pine kindle]

would anyone mind helping me with some exponents rq?

[astral mantle]

[pine kindle]

i understand for the equation you're going to have to convert the negative exponent into a fraction

do you apply the exponent outside the parentheses after that?

[astral mantle]

yeah

you can turn the inside into 6w^2/z^2

[pine kindle]

oh shoot i didn't think of doing that

i assumed it'd turn into 1/z^2 lol

[astral mantle]

it does

6w^2 * 1/z^2 = 6w^2/z^2

[pine kindle]

when applying the exponent outside the parentheses does it go to both the top and bottom then?

so, i'd get 12w^4/z^4?

[astral mantle]

yes

Its just 6w^2/z^2 * 6w^2/z^2

you just multiply across, adding the exponents

it would be 36w^4/z^4 though

[pine kindle]

oops

i forgot applying ^2 to 6 would be 36

[astral mantle]

its ok

[pine kindle]

alright, it looks like it makes sense now

i'll be back w more in a bit

thanks haha

if the negative exponent came first, does the same rule apply?

whereas if i had an (8m^-5 n^4)

would it end up as (n^4/8m^5)?

[astral mantle]

the 8 doesnt go to the denominator

it would be 8n^4/m^5

but yeah order does not matter

multiplication is commutative

[hazy furnace]

https://gyazo.com/2994e805c065450c0efd509849aab721 wouldnt this be horizontal shrink by 4 but that isnt an option

horizontal compress is probably the right answer but a horizontal compress of 1/4 would actually be a stretch by 4
like the second and last answer choice are the same thing

[round quest]

how do i find this graphs equation

[zealous cosmos]

It's ... a secant ... for starters

[sick steppe]

why.... the dots...

[dusky thunder]

yup

[zealous cosmos]

Because they're not part of the graph. They're just guiding information.

I would say it's sec(x) + 1. Final answer.

[sick steppe]

I meant in your typing

[dull ginkgo]

Urgent <@&286206848099549185>, does anyone know what l_1, -1 is?

[lilac pier]

you should show the full question

[zealous cosmos]

I don't know, actually ...

I want people to hear the pauses in my voice when I physically pause to think about something.

Sometimes I use it it indicate that I'm not finished with a sentence.

And sometimes I use it to make a statement that expects a response ... even if the statement is not a question.

[unique cypress]

hi

[viscid thistle]

roughly worded, but yeah seems like so.

i mean all i've guessed you've told me is that f(x)=cos(x), then a new function g is transformed by those characteristics you've said, so uh yeah, i would definitely specify the new function g defined as g(x)=2cos(x)+1

[viscid thistle]

"A rectangle has a length of 12 inches and a width of 9 inches. Squares of length 3x by 3x are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x. "

Is this solvable?

I think my teacher may have messed up

[sick steppe]

yes it's solvable

draw a diagram and go from there

[small tree]

how to write this in radical form: -5x^3/5 y^3/5

[clever pecan]

$\sqrt[b]{x^a} = x^{\frac{a}{b}}$

[obsidian monolith]

Modular Code

[clever pecan]

so you want to write $-5x^{\frac{3}{5}} y^{\frac{3}{5}}$ into radical form right?

[obsidian monolith]

Modular Code

[clever pecan]

@small tree

dang nobody helped you for 3 hours?

[viscid thistle]

Lol

[viscid thistle]

lol

[lilac storm]

so i have factored the eqs and i am getting (x+3)(x-1)/(x-2)(x+1)

so i can't cancel anything so what do i do?

can anyone help?

[uncut mulch]

your factorisation is incorrect

[elder charm]

the numerator turns to zero when x=2, so clearly it must have (x-2) in its factorization

[lilac storm]

i checked multiple times but i can't see any mistake in my factorization?

[uncut mulch]

how are you checking?

[lilac storm]

so i simple did sum and product to factor both the top and bottom eqs.

simply*

[uncut mulch]

can you show your work/how you're doing it for the numerator?

[lilac storm]

yes of course

so for x^2-3x+2, the sum is -3 and product is 2 so the numbers are 3 and -1 so the factors are (x+3)(x-1) on the top

yeah i found my mistake, it was a really huge silly mistake that i was making, thanks a lot for your time and help.

[lilac storm]

so i have started off this question by multiplying the top and bottom by the conjugate which is (sqrt of x+5 + 3)

so on the top i have (x+5)-(3) but i am confused on the bottom on how to multiply it out

so in the denominator you have (x-4) multiplied by (sqrt of x+5 with a 3 added to it)

so how would you multiply that out?

so would you have like (x times sqrt of x+5) - 12

anyone there to help?

anyone there to help?

[viscid thistle]

(x-4)(sqrt(x+5)+3)

Just foil

[sick steppe]

dont foil

[sick steppe]

you didnt expand the difference of squares correctly

[lilac storm]

it doesn't work with foil.

[viscid thistle]

Wot

[sick steppe]

$(\sqrt{x+5} -3)(\sqrt{x+5}+3) \neq x+5 - 3$

[obsidian monolith]

moshill1

[viscid thistle]

Oh ye ig you dont foil

[lilac storm]

sorry is it (x+5) - 9

[viscid thistle]

Mhmm

[sick steppe]

yes, which simplifies to?

[lilac storm]

but what about the denomiantor, that is what is confusing?

[sick steppe]

answer this

[lilac storm]

x-4

oh i got it now

[sick steppe]

right, so you have $\frac{x-4}{(x-4)(\sqrt{x+5}+3)}$

[obsidian monolith]

moshill1

[lilac storm]

thank you so much

so now i just cancel the x-4s out

[sick steppe]

yes

[lilac storm]

that makes much more sense

[sick steppe]

that's the reason you rationalize the numerator in the first place.. since the x-4 in the denom is the problem

[lilac storm]

right.

[sick steppe]

(And usually if the answer is rationalize it'll work out)

[lilac storm]

okay.

[crystal osprey]

How are you supposed to make regression models without technology...

[full breach]

Scalar product
Given there are two unknown vectors a and b where |a| = 2 and |b| = 3.
The angle between the vectors is 60°.
How can I find out if two vectors u and v are perpendicular when
u = 7a - 12b and v = a + b?

[lilac storm]

can anyone just help me in how to write this using interval notation.

[sick steppe]

u . v = (7a-12b).(a+b), then expand the dot product

[full breach]

And just see if the product equals to 0?

Where does the angle information come handy in all of this?

[sick steppe]

to find out the value of a.b

since you'll have a a.a term, a.b term, and b.b term

so you need a.b =

[full breach]

I'm confused... what does the scalar product of a and b do?

a.a etc.

[sick steppe]

well the dot product is just a way to multiply cartesian vectors

[lilac storm]

is it [1,3) U (3, infinity)

[sick steppe]

$\vec{a} \cdot \vec{b} \in \mathbb{R}$

[obsidian monolith]

moshill1

[full breach]

We're just learning about finding the dot product of a single vector, but I've yet to understand what it's used for

[sick steppe]

you cant find the dot of a single vector

[viscid thistle]

@lilac storm yes that seems fine, but next time avoid posting questions on a channel that is occupied. Read #❓how-to-get-help

[lilac storm]

ok, sorry and can you explain why do we not include -4 since that is also a factor?

[sick steppe]

I mean.. it's a way of multiplying vectors, but in physics dot product is usually associated with Work

[viscid thistle]

@lilac storm let's move to #help-9

[sleek socket]

Hey I need help

[pliant locust]

The dot product is a function that Maps a pair of vectors to a real valued number.
A vector that is its own argument( input = (v,v) ) in the dot product function grants you the squared length of the vector .

In other words, let v be a vector:
v dot v = |v|^2 it grants you the squared length of the vector in R^n, a dot product in euclidean space grants you the length aswell.

Its use is pretty neat because with it you can find the orthogonal projections of vectors which is useful in finding orthonormal bases in at least euclidean vector spaces. You can use it to determine wether two vectors are orthogonal aswell etc etc.

[viscid thistle]

I have a question regarding that. Why didn't you include the case when if we multiply 2 different vectors we get uv^T which is also as a vector that we got though the dot product

I know that you will say it is given like that by definition but in fact, why can't we just store the xy x1y1 .... in a matrix?

[pliant locust]

I am not really sure what you are asking. I am still doing linear algebra. Yes, if u and v are given in orthonormal bases then the dot product can be written as the matrix mutliplication u^T*v.

I dont see why you wouldnt be able to just store it in a matrix but why? It is just a matrix with one element, it can lead to confusion since every row represents a linear combination, your coefficients are still there.

Maybe you are asking why a distinction is made between the dot product and a matrix multiplication of the form 1xn * nx1. Well one reason I can think of right now is that the dot product isn’t the matrix multiplication if the coordinates aren’t given using ON-basis. The dot product is the matrix multiplcation if and only if the basis is orthonormal.

[proper pilot]

Yo, How do I determine the amplitude, period, phase shift at y = cos x, maximum value, minimum value and zeroes?, in questions like involving graphing the sin, cosine and tan

[viscid thistle]

I see and yeah, that is what I was trying to understand and that is why I was confused, by the way. Matrix multiplication sometimes is also called a "dot product" because you get a scalar value from multiplying rows and columns. So in some way, it is a sequence of dot products. Sorry, I thought that 1xn and nx1 multiplication can be interpreted as a one iteration operation which made things confusing when I thought of the dot product that ouputs scalar

[pliant locust]

The standard dot product in R^n is like that since well you are always assumed to be in ON-basis. You can also redefine the scalar product on a vector space such that it fulfills certain conditions, if it fulfills them they are then called euclidean vector spaces.

[fresh ledge]

mathamatics

[vague stump]

anyone know how to work around dis problem

[potent creek]

hey guys. How would I go about this? From my understanding, I need to have 2 cases for if n is initially + or -, right? The - part is easy as all terms become postive but when its instially positive idk what to do. Calculating in my head ik that if n <= 4 the 5 saves the day but how would I prove that. Thanks

[pliant locust]

You have the right approach

Determine for what n 4n > n^2

[potent creek]

div both sides by n so just 4 > n?

[pliant locust]

Yes and now determine if n^2 -4n is less than 5 when n< 4

[potent creek]

ok thanks for the help. We just started learning about numerical proofs so are we allowed to like write words in order to explain? Lol if that sounds dumb

[pliant locust]

It is ok, I am not really the guy to ask about formality of proofs

[uncut mulch]

completing the square would be the most efficient

[pliant locust]

Yup

[potent creek]

Ok thanks for all the help mateys

[uncut mulch]

are you supposed to do induction or allowed to do anything you want

[potent creek]

wait doesnt any int include the negative ones?

[uncut mulch]

whoops misread it

read an extra positive in there

[potent creek]

np. As for the methodology, it doesnt really say

[uncut mulch]

then yeh, complete the square / vertex form

[potent creek]

ok so @uncut mulch if I just complete the sqaure from the start then it doesnt matter if I do a - or + test case cuz it always get squared to a + number, right?

for refrence it becomes (x-2)^2 + 1

[pliant locust]

Yup

[potent creek]

Thansk @uncut mulch and @pliant locust

[rugged wigeon]

hello! i was wondering why x^2 becomes (limx)^2 and also why does 9 become lim9? What property did they use?

[viscid thistle]

properties of limits