precalculus

[bleak lance]

Does anyone know vedic maths?

[fiery wren]

how do you solve this

[tardy ridge]

you know g(2)

now you just have to hope g(2) is in the domain of f(x), which it 100% is because this is a question that is answerable.

(fog)(x) is just f(g(x)), and fog(2)=f(g(2))

[obsidian monolith]

Yes:

[terse ravine]

hmm

Is the answer 2pi/7?

[terse ravine]

<@&286206848099549185>

[opaque olive]

Is the answer 2pi/7?
@terse ravine yes

[copper kindle]

who else here is first year engg watup yallll

[dusk mulch]

How would I solve questions like these by hand?

[uncut mulch]

pythagoras

[dusk mulch]

2nd pic is part of 1st

I did some wacky shit on my calculator. Cos(2(cos^-1(-7/8))

[uncut mulch]

and/or compound/half angle identites

note that you don't actually have to find the value of t

[dusk mulch]

nani

explain

[uncut mulch]

e.g.
cos(2t) = 2cos^2(t) - 1

sin(2t) = 2sin(t)cos(t)
and sin(t) can be determined from pythagoras, accounting for the sign from the location of t

etc

[upper mirage]

in a case where there are two stationary points with coordinates given, one local maximum and one local minimum, how would one go to determine which coordinates are which (max/min)? is the stationary point with the higher y value always the local maximum of the graph?

[somber yew]

I suppose that's true, or you could use the second derivative test.

[stoic stratus]

Can someone help guide me on finding the linear approach to this function in the point (1,f(1))? 🙂

[uncut mulch]

wdym by linear approach

@stoic stratus

[somber yew]

I guess first order approximation using differentials

[unborn mist]

the taylor expansion?

[uncut mulch]

equation of tangent line?

[somber yew]

No, just a linear approximation. The sort of $$\frac{dy}{dx}\approx\frac{\Delta y}{\Delta x}$$

[obsidian monolith]

TedNotKaczynski:

[somber yew]

I don't remember exactly, but the basic idea was to create an approximation this way

[blissful kayak]

Consider an initial point, and another point close nearby

Then draw a secant line through the two points and look at its slope

And then from here, try bringing the nearby point closer and closer to the initial point

Also see what happens to that secant line's slope

[gritty axle]

can someone help me with part c?

@everyone can someone help me with derivatives?

[obsidian monolith]

The Godfather:

[blissful ridge]

$f'(c)= \lim_{h \to 0} \frac{f(c+h)-f(c)}{h}$

[obsidian monolith]

The Godfather:

[blissful ridge]

Do you understand this?

[proven marten]

Pretty sure this is calculus

[gritty axle]

@blissful ridge how do you use that formula

oh ya, sorry i didnt realize that this was the pre-calc one

ill take it to the calc one

[jolly spoke]

hey can someone help me understand this problem

I know how to get a domain from a function but not the other way around

And ik how to do if it its all parentheses and -inf, inf at the ends but this is confusing bc of the brackets

[dim jungle]

o you know where it is bad

x=-1,x=1,x=4

and you know x≥-3

[jolly spoke]

Yea cause thats the restriction?

[dim jungle]

yea

so lets first look at x≠-1,x≠1,x≠4

what should you do to make sure these conditions hold

[jolly spoke]

Uh would you multiply (x-1)(x+1)(x-4)?

[dim jungle]

you would multiply where

so right now lets say u have f(x) = 1

where would u put (x-1)(x+1)(x-4) so that those points are not reachable

[jolly spoke]

wdym where

Sorry, i dont know what you mean by that

[dim jungle]

im bad at explaining lol

so basically if you dont want a point to be in the domain

you can mutiply by 1/(x-that point)

so like f(x) = 1/(x-1) means the point x=1 is excluded from the domain

[jolly spoke]

ohhh

OHHHH wait

so would -3 be in the numerator bc its a restriction..?

And the equation i get from (x-1)(x+1)(x-4) goes in the denominator bc of that?

[dim jungle]

so first we focus on x≠-1,x≠1,x≠4

so yea that would be denom

so rn u have f(x) = 1/(x-1)(x+1)(x-4) . NOw, think what function thing can restrict a whole part of the graph from like -infinity to some value

[jolly spoke]

A radical?

[dim jungle]

yea a square root works

so you should have the asnwer now

[jolly spoke]

Ohh

Okay, but what about -3? Do i not have to worry about it?

[dim jungle]

u do

put a square root in

[jolly spoke]

I figured i would have to do an extra step for it or something

Thats all?

[dim jungle]

you know that sqrt(x-k) leads to a domain of x≥k

so in this case you want x≥-3

what should you do?

[jolly spoke]

i have no idea

Im sorry i genuinely dont understand that part

[dim jungle]

do you understand this
sqrt(x-k) leads to a domain of x≥k

[jolly spoke]

Kind of

[dim jungle]

just imagine it

if you have a number x<k, then the inside square root is nonreal

its like, if you have x=k-1, then sqrt(x-k) = sqrt(-1)

[jolly spoke]

ohh

Okay that makes more sense

[dim jungle]

ok so then

you want x≥-3, so k=-3

[viscid thistle]

how do you do this

Im so confused

[unborn mist]

write out what (n+1)! is using the definition of a factorial

and see if you can find some similarities

[viscid thistle]

i did

(n+1)!/n! (1-(n+1))

[unborn mist]

cool

so do the same with the top

and simplify

you know that (n+1)!=n!(n+1)

[viscid thistle]

so that would give me

(n+1) / 1 - (n+1) right

[unborn mist]

right

and 1-(n+1)=-n

or -(1+1/n)

[viscid thistle]

how did you get an equal sign

if its an expression

[unborn mist]

well you are changing the expression into something that it is equal with

by simplifying the expression right

the expression equals this simplifed version of the same thing

[viscid thistle]

could you explain how you got from (n+1)/1 - (n+1) to the final answer?

[elfin crescent]

cos(x-90) is a type of complementary angle identity right?

[unborn mist]

@elfin crescent yes

uhh sure

so you factor out the n! on the numerator and denominator

and you can ccnel the top and bottom

[elfin crescent]

k

[viscid thistle]

doesnt the n! cancel out

[unborn mist]

yeah they do so you are left with

(n+1)/(1-(n+1))

but the bottom is -n

so (n+1)/(-n)

is your final answer

[viscid thistle]

omg

im dumb

thank you :))

[lunar citrus]

hi can someone help me with my problem?

[viscid thistle]

I need help

Our teacher is bad

How tf am I supposed to sketch tangent line

[eager scroll]

anyone active?

[strong ermine]

yeah

[eager scroll]

ok cool

[strong ermine]

need help?

[eager scroll]

i'll let u know fs i'm struggling a bit but ur

[ember crane]

Hi, Idk how to do this problem, can someone help me?

[patent beacon]

Are you looking to use ε-δ?

[ember crane]

I think that I use limit. but I never use the sign "ε-δ"

[patent beacon]

Then yeah you just want to show that the limit exists everywhere, and that the function is equal to its limit everywhere

[ember crane]

even though I read the example of the similar one,

but I don't understand this particular question

[stuck lark]

use everything you know on limits to show for all c in [4,infty), lim x->c f(x)=f(c)

[ember crane]

is this the right way?

[terse ravine]

How do I rationalize the denominator?

cube root 3 9(x+10)/3 ?

[terse ravine]

I'm not sure what I did wrong with the part c

[uncut mulch]

sign error

[terse ravine]

yeah

[blissful kayak]

How do I rationalize the denominator?
@terse ravine You multiply the numerator and denominator TWICE

In general, to rationalize the denominator of index $n$, here's what you'd get at the end:
\par
$\frac{\sqrt[n]{x^{n-1}}}{x}$

[obsidian monolith]

Coleculus:

[digital spruce]

hey guys need help with these

[viscid thistle]

I need some help

[ember crane]

@mossy escarp rate of change is basically find the slope of the two points

[mossy escarp]

So how do I do it?@ember crane

[ember crane]

tell me the slope function formula

@mossy escarp

[mossy escarp]

Y2-y1 over x2-x1

[ember crane]

yeah, u know the x value?

[terse ravine]

x=8+sqrt4y-5 ?

[mossy escarp]

Yeah so what is y value?

[ember crane]

see it in the graph, you will find the y value

[mossy escarp]

My brain is still in summer mode, I don't know why they giving this rn

[ember crane]

when x=6, y=? and when x2= -8, y2=?

when u find that, plug it into the equation and that is ur answer

@terse ravine u got the first step, now solve for y

[terse ravine]

That's the part I don't know what do next. What I did was remove the sqrt 8+4y-5. Then I kicked the 4y to the left and rewrote it as 4y+(8-5). Then, I got 4y+3 and subtracted -4 on both sides and I got y+ (3-4), then I got y-(-3+4). I got the ans of y-1. I know this isn't right.

[ember crane]

no u mixed up that part. u need to move the 8 over, then the sqrt, then the 5, then the 4

[old flame]

Can anyone help me with some guidance on a problem

Just the final part of a problem, simultaneous equations

[ember crane]

yo @old flame hold up, the previous question is not done yet~

[old flame]

Sure no worries

[ember crane]

@terse ravine get it?

[terse ravine]

sqrt4y-5 +8, then 4y-5+8?

[ember crane]

no, when u substitute the y for x and the x for y in the main function. Don't move the sqrt over to x part yet.

woah wait

THEN the sqrt over

[terse ravine]

weird x=8+ to x-8 =

[ember crane]

cuz it a positive 8 when x=8..........so when u move it over, it becomes negative

[terse ravine]

Yeah

So now I put sqrt over x-8 and remove sqrt over 4y-5?

[ember crane]

yeah

[terse ravine]

now +5 to both sides?

[old flame]

can I add my 2 cents to that

Oh actually nevermind

maybe I didn't read all the question

Oh this is a reflection

[terse ravine]

sqrt x-8/5 = 4y

[ember crane]

...

[old flame]

The inverse of a fucntion is a reflection

[terse ravine]

darn

[old flame]

function

[ember crane]

it supposes to be [(x-8)^2 + 5]/4

[terse ravine]

can you show me those steps

on the paper

[ember crane]

k wait

[old flame]

oh

I know what you have to do

for this

Hey Vanish do you understand what it is you are actually doing

when you do this?

Like conceptually

[terse ravine]

The inverse is set up its the algebra that I need to get right.

The inverse is the reflection of the original.

[old flame]

Okay

sorry

[ember crane]

this is the step.

[old flame]

Neat

[ember crane]

yeet

[old flame]

Yeet

I fear I may fall asleep before anyone gets to me

[ember crane]

WAIT! its plus 5

[terse ravine]

Oh when you remove the sqrt on 4y-5 you put the ^2 on the other side.

[ember crane]

this is the correct one

[terse ravine]

Ok going over these steps

So at (x-8)^2+5 = 4y you divide both sides by 4

The 4 cancels on on the right and isolates the y.

Which gives (x-8)^2+5/4 = y

[old flame]

Hello?

Just wondering if anyone is around

[unkempt magnet]

why is the codomain positive real numbers when it can also map to 0

0 is in the domain of both g and f and sqrt(0) = 0

[somber yew]

You're right, it should've been $\bR^+\cup{0}$

[obsidian monolith]

TedNotKaczynski:

[unkempt magnet]

would [0, infinity) work? @somber yew

[somber yew]

Sure.

[unkempt magnet]

thanks

[old flame]

Hello could someone help me with this question?

I have the equations, and structure, there are just some conceptual things that are preventing me from being sure of my answer

??

[crude light]

What do you have so far

[old flame]

So ... I have the two equations for protein and carbohydrate

respectively

0.27x + 0.73y = 45

and 0.73x + 0.27y = 55

I solved for x,y using substitution

with x = 1400/23 and y =900/23

So ... I guess I am very confused and can't for the life of me figure out is how i then work out the Food X and Food Y ...

So eqn 1 and eqn 2 are the proportion of protein and proportion of carbohydrate ...

I then thought I could work it out by then manually calculating Food X (for instance) 27 per cent of x(1400/23), and adding that to 73 per cent of y(900/23) but that just g ives 45

[crude light]

Think about what else they give you in the question. You know that the total amount of X eaten + Y eaten = 100

[old flame]

and I'm not sure that it's right

Yes

Okay yes

oh

Oh it's that easy

Food X = 100 - y?

Food Y = 100-x

(Sorry it's 4am)

[terse ravine]

@ember crane Ok I tried this on my own, this should be correct.

[old flame]

Yeah I'm not understanding still

I'm not seeing it

[crude light]

So your answers make sense if you add them and they equal 100 in total

900+1400/23

[terse ravine]

Darn, I got the inverse wrong hmm.

Domain is correct tho.

[ember crane]

lol, where is the minus sign in front of the (x-4)^2 ?

[terse ravine]

where does the minus come from though?

[ember crane]

wait, but how the domain f^-1 (x) is [4,infinity)...... and it is right?

I thought it is supposed to be (-infinity, infinity) cuz it is a quadratic formula

[ember crane]

yeah, that is the part I dont understand, can u explain?

[terse ravine]

I entered the (x-4)^2+5 into desmos and observed the graph.

the domain shows [4, infinity)

x is pos in quadrant 4

[ember crane]

are there any condition for this problem? and did u add the minus sign?

[terse ravine]

So if I entered -(x-4)^2+5 it still is the same Domain.

No condition.

Let me check,.

Ok so x-4 = sqrt5-y

[bleak lance]

Why do we need to test points in precalculus?

[terse ravine]

Then you remove sqrt from left and added square to right side

(x-4)^2= 5-y

[ember crane]

yes,

[terse ravine]

after this part I'm wondering what you did next.

[ember crane]

then -5

[terse ravine]

you subtracr -5 from both side

[ember crane]

yes

u still have the minus sign in the y part

[terse ravine]

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

[ember crane]

that minus sign apply to the whole equation in the (x-4)^2 - 5

which is how u get to the last part

[terse ravine]

I see that.

how did the 5 turn positive?

That is the part that is messing with me.

[ember crane]

kay, wait, Imma elaborate this on the paper so u can see it

this is the best explanation that I can do

[terse ravine]

I see. ty : )

[bleak lance]

How do ik if I should set x < -4 or x > -4?

[crude light]

Did you write out the positive/negative for each test interval?

[bleak lance]

Wdym?

I didn’t test anything yet

I’m wondering if I set x < -4 or x > -4?

[crude light]

okay so you’ve found the zeros of the function, and now you want to determine where it’s positive?

[terse ravine]

@ember crane Ok, I think this is correct. What I did was work from the outside to inside. I basically ^9 both sides, then performed algebra.

Yay! I determined the inverse.

[limpid rampart]

hell

o

i have a question

how would i sketch y = (x+1)(x-p) where p>0

[fiery wren]

hi

can someone check me if i'm right

for these two questions

[unkempt magnet]

for f(x)=x^2 where f:R→R, is this even a function if you count the codomain of all (positive and negative) real numbers?

[viscid thistle]

is finding the constant term of this binomial expression the same thing as finding the coefficient to x6?

[patent beacon]

The constant term is the x^0 term

They want you to get the x^6 term

[viscid thistle]

yeah i got the answer

so instead of setting the exponents to equal 0, I set it to equal 6 instead

[swift sequoia]

, rotate

[swift sequoia]

Sorry for resposting, I get something like

$\sum i^2\left(\frac{1}{i+1}-\frac{1}{n}}\right)$

[obsidian monolith]

Hastte:
Compile Error! Click the reaction for details. (You may edit your message)

[swift sequoia]

And stuck at this point ( I found this by some telescoping)

No one ?

<@&286206848099549185> sorry for ping

[unkempt magnet]

why is this an even function?

[daring eagle]

it's a function

just not a continous f

wait

[patent beacon]

To check even/odd-ness
You want to find f(-x)

[unkempt magnet]

the answer says its even with a period of 1

yh idk how to do that in this case

ngl

i get confused with the x and n

[patent beacon]

f(-x) is just f(x) but you replace x with -x

[unkempt magnet]

ik but this function

do i do -(x-n) or something

[patent beacon]

"do"?

Anyway nuu fam

Same process. n is just there to be part of the definition

[daring eagle]

when x is in the -ve

you connsider -ve n

[unkempt magnet]

so

[daring eagle]

e.gg 0 to -1

[unkempt magnet]

say for example when x=1 right

[daring eagle]

-1 to -2

[unkempt magnet]

1 is odd so it would be x-1?

[daring eagle]

yes

[unkempt magnet]

but x=1

and 1-1=0

[daring eagle]

yes

wait

wrong

odd is 2nd line

[unkempt magnet]

oh shi

so when x=1

its 1-x

but x=1

so 1-1

which is still 0

[daring eagle]

1-x+n

sry, my "n" key has prob

[unkempt magnet]

huh

oh

[daring eagle]

which will give you 1

and it will go to 0

[unkempt magnet]

wait so

1-x+n

x is 1

whats n?

also 1?

[daring eagle]

yes in thios case

[unkempt magnet]

oh

so 1-1+1 which is 1

[daring eagle]

yes

[unkempt magnet]

now for x = 2

x-n

[daring eagle]

but this is not a constant fn

[unkempt magnet]

so

2-2 which is 0

[daring eagle]

yes

so it zigzags between 1 and 0

[unkempt magnet]

wait

when x=1

nah nvm

oh i see why its periodic

[daring eagle]

ya

i misread your qn... i thought you were askin inn frustration "why is this even a fn" vs "why is this an even fn"

[unkempt magnet]

i just drew it out

they connect by straight lines right

or is it like a curve

[daring eagle]

i think its straight

[unkempt magnet]

what happens when x=0

wait nvm

its just 0 then

[daring eagle]

so you can see that the pattern is the same for f(-x)

[unkempt magnet]

how do you even draw graphs like these

@daring eagle

[daring eagle]

you shrink it i believe

[unkempt magnet]

i was thinking about that

but i find it hard to conceptualise how and where n actually varies

for the previous one we went through ok n is the same value as x

but i just dont understand how this n works

[daring eagle]

okay..simple

what is sin pi?

[unkempt magnet]

0

[daring eagle]

what is sin pi/2

[unkempt magnet]

1

[daring eagle]

yup

[unkempt magnet]

the period shrinks by n

[daring eagle]

so sin(nx), let nx = k x pi and (k +.5)x pi respectively

[unkempt magnet]

2pi/n?

[daring eagle]

would be part of it yeah

i just chose this pts since

[unkempt magnet]

ah that period was correct

[daring eagle]

sin(k pi) = 0

[unkempt magnet]

ah

[daring eagle]

so k pi = nx, so let n = 2, x = ppi/2

n=3, x = pi/3

etc etc

[unkempt magnet]

hld on

so x=pi/n?

[daring eagle]

when sin(nx) = 0

yes

[unkempt magnet]

oh

[daring eagle]

of course, this exteds to all values of sin

so squeeze/shrink it is what i meant

[unkempt magnet]

n cant be 0

[plain root]

could someone help me with

[daring eagle]

well, n=0 is pretty pointless right?

sin(0x) = sin(0)

[unkempt magnet]

sin(0) is 0

yh

im still confused

[daring eagle]

which part?

[plain root]

zyzt could u help me w my problem

it shoud be simple i thought i got it right but it market it wrong

[daring eagle]

@unkempt magnet

@plain root idk...maybe you left it blank?

[plain root]

nah lol

i deleted it

[daring eagle]

oh

[plain root]

before i screen shotted

[daring eagle]

what did you input?

[plain root]

8 - 3sqrt8-x

[daring eagle]

for the 1st one?

[plain root]

yea

[daring eagle]

yeah, that's not correct

[plain root]

oops

[daring eagle]

since, you are supposed to input the stuff in the bracket

not after applying the composite fn

[plain root]

so how would i solve it

[daring eagle]

for the 1st one, try inputting g(x)(pls expand of course)

3rd blank is just 8 - x^3

[plain root]

how did u get that

[daring eagle]

how did u get that
@plain root by quoting the question

[plain root]

ok

[daring eagle]

i think all you have to do is literally input what you see into the brackets lmao

the qn is tryig to make you overthink

[plain root]

ya lol u just put what it gives u

[unkempt magnet]

@daring eagle i see those graphs

wait so

the fact that f(x) = sin(x) is odd

does that mean f(x) = sin(nx) is also odd

i think that just gave me the answer i was looking for lmao

theres a harder question though that ill check out tomorrow

@daring eagle thanks, those graphs you sent somehow made me realise that after everything lol

[crude light]

the base? Or am I being dumb

[terse ravine]

Unless they want: log_8n=r

[crude light]

lol yeah perhaps

[sudden bay]

Is f(g(x)) the same thing as fg(x)

generally speaking

[ebon fiber]

true or false? how can i approach it?

[tropic bison]

For the first one, the RHS is small, and so u can just keep trying numbers for (x,y) until u run out of possible x and y values

For the second one, think Pythagoras

Actually the answer for the first one depends on if 0 is a natural or not

[ebon fiber]

hm why Pythagoras for second ?

Assuming 0 is natural then (5,0) or (0,5) are possible solutions right

[tropic bison]

Yes, that’s if 0 is natural, but I think that assumption makes these 2 questions way too easy

hm why Pythagoras for second ?
Note that 25=5^2, so the eqn is x^2 + y^2 = 5^2

There is a relevant Pythagorean triple for this

[earnest coral]

Can someone check tthese for me??

I feel like I got something wrong

[tropic bison]

Ur green and yellow curves r correct

What do you understand by ‘bounded’?

[earnest coral]

Ummmm

Something about a real number, I’m not sure tbh

[tropic bison]

To be plain, a function is bounded if it doesn’t shoot off to infinity

Clearly, the red curve doesn’t shoot to infinity

So it would be bounded

[earnest coral]

Ohh

[tropic bison]

Can u see why the blue curve is not bounded then?

[earnest coral]

Yeah, that makes more sense

I can see the difference now

Thank you

[tropic bison]

[uncut mulch]

the first image is ambiguous though

[earnest coral]

Uhh another question.. so in this graph, would ‘B’ the absolute max or local max

[uncut mulch]

local

[earnest coral]

Oh okay. So A is the local min and C is the absolute min, am I correct?

[uncut mulch]

C would be local and absolute

[earnest coral]

Ohh okay

[hard mulch]

Why is the domain 0

Im confused

[tropic bison]

The domain isn’t 0

Is there a question this comes from?

[hard mulch]

To find the domain

Or this equation

Of*

When I plug it into a domain calculator

U get (-infinity,0) u(0,infinity)

But, i would think it would be x is equal or not equal to -2

Not 0

[uncut mulch]

division by zero results in something undefined

hence 0 would be excluded from your domain

the domain is the set of reals excluding 0

[hard mulch]

How would I know its a division by 0?

[uncut mulch]

solve denominator = 0 to determine values of x that would result in division by 0

[hard mulch]

So like this?

And if u divide it

U get 0

So ur right!

[uncut mulch]

that chicken scratch is very unclear

[hard mulch]

Hahaha

Wait

Ill re do it

[uncut mulch]

still very bad

don't attach a bunch of operations to your expression like that

write it in a separate line

regardless, its still unclear in justifying that 0 should be excluded from the domain

[uncut mulch]

NO

[hard mulch]

Ahh

Ok

[uncut mulch]

expression is undefined when denominator is 0
that happens when 2x = 0
and solving that equation should get you x = 0

[hard mulch]

Ahhh

Ok

Same thing tho

I solved for it and got 0

[uncut mulch]

you didn't solve anything

[hard mulch]

Which makes sense in my head that way

The way i did it

[uncut mulch]

what's happening between
$2x = 0$ and $\frac{0}{-2} = 0$

[obsidian monolith]

ramonov:

[hard mulch]

Exactly, thats what I wrote out

[uncut mulch]

you wrote -2x on both sides but doesn't really make much sense in context

[hard mulch]

Ahh

I see what you mean

[uncut mulch]

are you subtracting? dividing?

[hard mulch]

Dividing

[uncut mulch]

neither gets that result and tells you nothing about the value of x when that happens

[hard mulch]

Hmm

But in some cases it can be equal or not equal to -2

[uncut mulch]

0/(-2) = 0 is just a true statement

wdym

what can be equal or not equal to -2

[hard mulch]

Like sometimes when I try to solve domain. Ill have an answer like x cant be equal or not equal -2

And the problem would look similar

For example

1/2x+4

[uncut mulch]

1/(2x+4)

same idea, determine when the denominator is 0 to determine what to exclude

solving 2x + 4 = 0
gets you x = -2

[hard mulch]

oooo

ur right!!!

dude I love you

you made it click in my head!

[tame fractal]

hi can anyone help me out with this question?

[viscid thistle]

How do you apply the infinite into the x?

[viscid thistle]

Does my math here look ok?

[elfin crescent]

would an exponential graph be an example of a steep line?

a line that has a greater m

[viscid thistle]

an exponential curve is not a line

[fresh ruin]

https://gyazo.com/ee8fdcad0e763faae57e0d6fe7189b48

c. Estimate the minimum rate of fuel consumption and the specific time at which it occurs.

I have no clue how to start this one, any suggestions

[spark veldt]

Can someone tell me how to solve sin3x=1 for all real solutions

[quick mirage]

sin3x = 1
3x = sin^-1(1) = pi/2
x = pi/2 *(1/3)
x = pi/6

If you dont use radians think of pi/2 as 90°

And theres only one solution

[ancient geyser]

uh

(0,0) is not a relative minimum, right?

It's not a minimum at all

The graph has end behavior of positive infinity, it never goes down again

[terse ravine]

I'm stuck after adding both sides by 12 and divided both sides by 7.

I'm at e^x = 15/7

lne^x=ln 15/7

then I bring the x to the front

xlne=ln15/7

Then?

[plain root]

any know how to solve this

[quick mirage]

@terse ravine x = log(15/7) / log(e)

[terse ravine]

there is no log

[quick mirage]

log anything works here

ln is not needed

[terse ravine]

I'm at step xlne=ln 15/7

divide both sides by lne?

[quick mirage]

x = ln(15/7)/ln(e)

ln e is just 1

[plain root]

i put in -1,-1 for my answer and it was wrong

[hexed otter]

i have some issues

about this problem

conic section: hyperbola

i couldnt find center

given the focus, and vertices

[quick mirage]

Yeah, but log b (b) is always = 1

So u can simplify ln(e) into 1

[terse ravine]

in this case x times lne is always x**

[quick mirage]

Is always x*

Yes

[terse ravine]

ty for clearing that.

[quick mirage]

Np my pleasure

[plain root]

https://cdn.discordapp.com/attachments/363224154469826562/755957528172691536/Screen_Shot_2020-09-16_at_7.05.12_PM.png

Anyone know why this is not (-1,-1)

[quick mirage]

It says to create a relationship, which im assuming is an algebraic equation

Not too sure what they mean exactly :/

Maybe x = y?

[hexed bolt]

Hey, I need help finding g'(5) and f'(5) can anyone help plz

[quick mirage]

Any constants derivative is always 0

if f(x) = constant, f'(x) = 0

q(5) = f(5)/g(5) = 6/3 = 2
q'(5) = 0

@hexed bolt

[hexed bolt]

Thank you

[somber yew]

Solve the inequality: $$\vert x^2+3x \vert\geq 2-x^2$$I solved it for the case where $x\geq 0$ and found the solution interval $[1/2,\infty)$. I'm a bit confused about the case for $x<0$ and would like to get some help with that.

[obsidian monolith]

TedNotKaczynski:

[somber yew]

Ping me when anyone's around to help. 😅

[blissful ridge]

The intervals you should be concerned about are

$x<-3$\
$-3<x<0$\
$x≥0$

[obsidian monolith]

The Godfather:

[somber yew]

Umm it's the -3<x<0 bit which is bothering me to be specific.

How do I evaluate the inequality in this interval?

Ah nvm

The solution interval here is (-3, -2/3], and then for x<=-3, it's (-inf, -3], thus the union gives (-inf, -2/3]. Checks out with the solution.

Thanks!

[blissful ridge]

To solve the inequality you need to remove absolute value function

To remove absolute value function you should know which value(positive or negative) it takes in that interval

[somber yew]

I understood that, but the quadratic function inside the abs confused me a lil bit.

[blissful ridge]

You just have to check where quadratic is positive and negative

[somber yew]

👍

[hexed otter]

pls help me in this equation it confused me, hyperbola conic section

so i have to find the standard eq given the focus and vertices

the focus is at coordinate (9,3)

vertices is at (9,1) (9-5)

help ;-;

[gritty canyon]

did you try drawing what the hyperbola may look like

[echo wagon]

Where are you stuck?

Every point on the y axis has x coordinate 0, and every point on the x axis has y coordinate 0. Use this.

[celest phoenix]

nvm

i got now my bad

It was prettty simple

one is zero

and u do equation

and sub 0 into equation

and figure out the other axis

[hexed otter]

did you try drawing what the hyperbola may look like
@gritty canyon yes

o wait i think i get it now

i will try to solve it

[small basin]

im a bit confused on interval notation, if i had something like the image below are the points bordering the union hard or soft brackets?

because they're included in the line and filled circles?

the only soft brackets would be for the very ends to -infinity and infinity respectively, right

[willow bear]

are the points bordering the union hard or soft brackets?
not sure what youre asking

the domain of this function as shown is all real numbers

[small basin]

@willow bear yeah but we had to write it like interval notatit

So like (-inf, -5]U[-5,3] etc

[willow bear]

(-∞, +∞)

that's it lol

$[a,b] \cup [b,c]$ is literally the same as $[a,c]$

[small basin]

I was just confused because would it be hard brackets

[obsidian monolith]

Ann:

[small basin]

Let me look at the question I guess

Oh

I had to do it like that because like

Oh I'm so dumb what the fuck

We had to list like increasing decreasing and constant intervals of the function

But it would be soft brackets cuz they're not connected

Even though they're included?

Or would it be hard brackets because those points are included even tho they're on the border

Sorry I guess I wasn't clear what the question asked so like if it was "what intervals is this function increasing" would it be
[-5,-3]U[-1,1]U[4,5]

[shut fractal]

how would you describe end behavior of a function by using limit notation?
for example lets take 4x^3 + 2x - 7/ 9x^3 + 2

[small basin]

I rly have no idea what that ends up being but I guess you'd just do if it's infinity or excluded you'd use soft brackets and if if was a hard end point or included you'd use hard brackets

Also sorry I can ask someone else but I'm gonna be afk for a while so I don't want anyone to waste time responding but thank u all for your help

[wintry cedar]

how can i find the domain of this ? 🤔

[viscid thistle]

Are there any undefined x values?

[wintry cedar]

ye its a log ( im trying to find the domain), it should be greater than 0 (if that answers ur question im not sure .. ) @viscid thistle

[viscid thistle]

well for what values does the equation ≠

[wintry cedar]

its all defined , but the result shouldn't be less than 0 , as u see

[viscid thistle]

How would I do this?

With e^sqrt5

[uncut mulch]

sqrt(5) is just a number

what's wrong with doing the same thing you did for all the others

[viscid thistle]

Idk is it just e^sqrt of 5?

[left fable]

Yes

[viscid thistle]

Or do I do something else

[uncut mulch]

yes...

[viscid thistle]

Like e^sqrt of -3 is the reciprocal

[uncut mulch]

if x = sqrt(5), e^x = e^(sqrt(5))

[viscid thistle]

Ah I see thank you

[uncut mulch]

you don't even need to bother with reciprocals

[left fable]

Plug and chug 👍🏽

[uncut mulch]

calculators are quite capable of evaluating e^(-3) directly

no need to convert it to 1/e^3

[left fable]

Like ti-84

[viscid thistle]

Why is this wrong?

It’s just

Never mind

I was using the wrong numbers

[daring yarrow]

why did you write log again when its already there

[quick mirage]

@terse ravine just write the coefficients

is what piece means

[terse ravine]

Thanks for clearing that.

[daring yarrow]

if what i said wasnt clear you could've just said so

[viscid thistle]

I'm not sure what the question is asking for, can anyone clarify? Thanks.

[tardy ridge]

it's asking domainand range

domain doesn't include -2

and range doesn't include 1

[dire bridge]

Not sure where this goes but can sqrt(u-1) be written as sqrt(u) - sqrt(1)?

[past meadow]

nope

just substite numbges for example

if u=2

sqrt(u-1)=1

and sqrt(u)-sqrt(1)=sqrt(2)-1

clearly different

[terse ravine]

hmm

I need to get rid of that x

[viscid thistle]

That is also (10x(log(2))/log(8)) -7)/8

[terse ravine]

Going to work on another problem since I'm stuck on that one.

[quick mirage]

@terse ravine you dont even need to use log

Shadow was my phone D;

Since if a^bx = c^dx and a^n = c then just expand c as a^n and solve

[fiery wren]

how do you read this graph

i know that i got the answer right but

[old flame]

Urgh anyone avails?

[quick mirage]

Perhaps

[old flame]

I need some advice solving a chemistry equation using gaussian elimination

and I am getting myself confused

So the specific equation is oxidation of Iron as follows:

[quick mirage]

Chemistry? As in balanced equations?

[old flame]

Fe + O2 ==> Fe2O3

Yes

[quick mirage]

Ok

[old flame]

So I thought it would be simple but I plugged it into a gaussian elimination calculator and I Have no idea how to interpret the answeer

So I have an augmented matrix ... not sure where to go from there

[quick mirage]

What do you need to find exactly?

[old flame]

Any advice would be great

the coefficients

so it's easy to solve normally ...

it balances to : 4Fe + 3O2 ==> 2Fe2O3

(pretty sure)

but my mathematical answer doesn't match this

[quick mirage]

Whats your mathematical answer ?

[old flame]

So I reduced it row echelon form of ...

well it's not really an answer ... I just dont know what to do with it or understand where I'm at

I reduced it to ... [1 0 -2 | 0]

[0 1 -3/2| 0]

[0 0 0 | 0]

And I don't understand why there is no 4 in it

or what to do with the fractions

I think I might be doing something dumb

[quick mirage]

How did you arrive to that matrix?

[old flame]

using row operations??

[quick mirage]

Wouldnt it be

[old flame]

??

[quick mirage]

[1 2 | 0]
[2 3 | 0]

[old flame]

Yeah not if you include z as a plane so that it is in row echelon form

And not if you have already performed row operations

[severe bison]

any1 know how to do the above?

that for me @terse ravine?

[terse ravine]

no

[severe bison]

ok lmao

[terse ravine]

Can you rotate it correctly and repost because its sideways?

[severe bison]

sure

[viscid thistle]

There's a multichoice question on my hw and it is really confusing

I understand what it is asking, but I have no idea how to go about this

[viscid thistle]

well what’s getting you stuck

[scenic heart]

Noobie question: What is it called when you have something like "f(x) + 3"

nvm

[earnest coral]

How do I find the domain of a function? We're doing inverse functions and compositions right now but I have no idea how to find the domain...

[willow bear]

it should be either explicitly given or able to be inferred from context

[scarlet birch]

Someone can help me?

I'm trying to prove this inequality

[viscid thistle]

Why isn’t this right?

[fleet yew]

@viscid thistle why would that be correct

there's no x in the original equation

[finite valve]

Someone can help me?
@scarlet birch use binomial and we get (x + y ) ^4 > 0

[scarlet birch]

The terms have no coefficient @finite valve

I can't use the binomial theorem

[finite valve]

I can't use the binomial theorem
@scarlet birch actually u r right

Please check if writing x^3y in form 3x^3y - 2 x^3y will help? And doing same with other terms and then Taking negative to rhs

[scarlet birch]

Ok I'll try with this way

[finite valve]

👍🏻

[gilded brook]

So to convert degrees to radians you just do Degree x pi/180

How do you convert radians to degrees tho? Radina x 180/pi?

[scarlet birch]

How do you convert radians to degrees tho? Radina x 180/pi?
@gilded brook Yes

[finite valve]

How do you convert radians to degrees tho? Radina x 180/pi?
@gilded brook yup this is correct

[gilded brook]

ight ty

So example would be like 2pi/3 x 180/pi

[scarlet birch]

Yes, that's equal to 120°, you can verify

[gilded brook]

ight ty

I couldn't find anything online only calculators that did it for you

[violet granite]

dm me if you could help me with pre calc questions anytime?

[copper kindle]

hey would this be 5?

<@&286206848099549185>

[viscid thistle]

@copper kindle that does not suit here

That is calc

[copper kindle]

oh sorry

can i pls get help in a room?

[hallow thunder]

@copper kindle i do believe that it is 5

[copper kindle]

so DNE times 0 is 0 right?

[hallow thunder]

think so

[mossy tiger]

So this first one I have no idea what I am doing wrong. With the second screenshot I did a tutorial and just put the same answer but how is it $(-\infty , \infty )$

[viscid thistle]

Okay

Both problems are basically identical procedure

From $$\abs{5x+7}+9<7$$ you need to substract both sided by something, so that you have the abs value on one side and a constant on the other

@mossy tiger

[obsidian monolith]

Al𝟛dium:

[mossy tiger]

I understand that I have to move the 9 to the right side

so then the right has a value of -2

I put no solution

because the right is a negative number

the answer is no solution

but how come the top it isnt

[viscid thistle]

What? You have abs(5x+7)>-2

And remember that the absolute function is always positive

For all reals

And remember that any positive>-2 is true always

So the solution is $(-\infty, \infty)$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

As x can take whatever value, and the absolute function will be always positive, so it is always true no matter what

[mossy tiger]

how come it's 5x+7>-2

i just moved the 9 to the right

wouldn't it stay as 5x+7<-2

[viscid thistle]

Why?

You flip the sign if you multiply or divide by a negative number

[mossy tiger]

but i didn't divide or multiply

[viscid thistle]

Hold up

[mossy tiger]

and the answer is NO SOLUTION

i plugged it in

and it says NO SOLUTION is the answer

[viscid thistle]

Okay

I misscopied the problem

Yeah the same logic

As x can take whatever value, and the absolute function will be always positive, so it is always false no matter what

Bc you have abs(something)<negative number, and as the abs function will be always positive, you'll end up with positive<negative which is not true

@mossy tiger

[mossy tiger]

thank u

[terse ravine]

Hmm log_b n=a <->b^a=n

hmm

5^13=12x+6 ?

[viscid thistle]

Almost, as the bases of the logs are the same, we can do 12x+6=13 as simple as it sounds

[terse ravine]

Ok, x = 7/12

[half star]

If (x-2) is a factor that means f(x)=p(x)(x-2) for some polynomial p, so plugging in x=2 should return f(2)=0; work from that. This is known as the Factor Theorem in some books.

[gilded brook]

to get a central angle do I just arc length/r?

Also I feel like I messed up somewhere, could someone confirm if this is the right answer to this question

Calculate the area of a sector of a circle with radius 7 kilometers given the arc length of the sector is
28 kilometers.

A=98km^2

[viscid thistle]

@gilded brook that seems correct.

[gilded brook]

ight ty

[terse ravine]

5700(1+0.16/2)^9 = 11394.3263

5700x2 = 11400

years = 9 ?

I think I did this is wrong.

I'll use F= PE^(rt)

11396=5700e^0.16x4.33

ok ln(2)/.16 = 4.332 years

[terse ravine]

Ok time to read.

[viscid thistle]

Will this be an odd or even or neither function?

[ivory echo]

@viscid thistle Neither.
Odd functions have the property f(-x)=-f(x), so they appear reflected across both the x-axis and the y-axis.
Even functions have the property f(-x)=f(x), so they appear only reflected across the y-axis.
Everything else is neither.

[willow bear]

Odd functions have the property f(-x)=-f(x),
they don't just HAVE this property they're DEFINED by it

[ivory echo]

A good example of odd is sin(x), f(x)=x, f(x)=x^3, (notice the odd powers) while an even function would be something like cos(x), f(x)=x^2. (Notice the even powers)

[willow bear]

btw you can combine piecewise function defns in a single graph in desmos

[ivory echo]

^ also true, but ngl I hate their syntax.

[willow bear]

f(x) = {x ≤ 0: x^2, 0 < x < 5: x, 5 ≤ x: sin(x)}

sth like that

[ivory echo]

yee

[viscid thistle]

Guys im confused on this make homework, my teacher gave me 3 pieces of a function (Exponential (left), linear (middle), and absolute value on the right, but my teacher also told me to make it odd, im confused because absolute is positive and linear is odd so how do i graph this and make it odd?

[willow bear]

any more details?

[viscid thistle]

nah

i dont get this question at all

ik how to make the piecewise function

but how do i make it odd when it contains absolute (even function) and exponential (niether function)

[willow bear]

please don't bro me

[viscid thistle]

I made something like this, i thought it would be odd cause both end behaviours are going in oppoiste directions

[willow bear]

the black lines
can you show the black lines?

there are no black lines in your desmos graph so i don't know what you're matching with

[viscid thistle]

yea i removed those lines cause why would i need them?

[willow bear]

also, i will reiterate: please edit the bro out of your previous message

[viscid thistle]

Ok sorry

[willow bear]

why would i need them?
because without them nobody else but you has any idea what parts of the graph you're given???

[viscid thistle]

im given these restrictions

those black lines on desmos is just a example tho

[willow bear]

you're being hella unhelpful right now

can you share the entire problem the way it was stated originally

[viscid thistle]

yea

This was the original question

and those were the 3 functions i was given

i get how to make the piecewise function but im confused on the odd part

[willow bear]

hrghrghrhrhrghrhrggrh

is it really all that hard to give the ENTIRE thing and not share it piece by piece

[viscid thistle]

that is the entire question tho

[willow bear]

you've shared three images which all appear to be parts of the same assignment

so no it's not the entire question

[viscid thistle]

cause my teacher gave us information in different folders

so i ss them

[willow bear]

[viscid thistle]

but the question is- Teacher given me 3 pieces of a function {absolute, linear and exponential} and i have to make a piecewise function, i get that part but i dont get about the odd restriction

its ok ill ask another time, thanks for ur help

[proud sequoia]

how hard is calculus should i take it next year?

i wanna be rich

[lime bolt]

it is easy

[viscid thistle]

rich of knowledge I suppose

[left fable]

Calculus is easy bro. It’s really just notation for heavy algebra

[reef jasper]

not sure if this is pre calc but heres my question: Assume a machine during its initial testing phase produces 10 widgets a day. After 10 days of testing (starting on day 11), it begins to run at full speed, producing 40 widgets a day. After 50 days at full speed (days 11-60), it gradually starts becoming less productive, and produces 1 fewer widget per day, (ie. 39 widgets on day 61, etc.) until on day 100 it no longer produces any widgets. Write the functions for these statements.

idk how to get the formual after 60 days

[viscid thistle]

but the question is- Teacher given me 3 pieces of a function {absolute, linear and exponential} and i have to make a piecewise function, i get that part but i dont get about the odd restriction
@Harsh#7731
I don't see any necessity to make it odd or even function. There's an option for neither as well

[reef jasper]

yeah sorry ur supppose to make piecewise function from this

i tried to shorten it mb

oh sorry thought u were talking to me

[gritty meteor]

who here is cracked at math

[floral tide]

x^e=0
i cant use logs here right?
what other methods do i have available?
apart from seeing that 0^e=0?

[viscid thistle]

Nothing else

[floral tide]

for real?

[viscid thistle]

Im not sure about complex

for real?
Yes

[floral tide]

ok ty

to use logs the base has to be Z+ ?

positive integers

[viscid thistle]

More like R+

[floral tide]

ok t

ty*

[viscid thistle]

Domain of logs is R+

Better said

[floral tide]

yeah i could not remember the english word for domain xD

[viscid thistle]

Don't worry

[reef jasper]

could someone help me find piecewise functions

[viscid thistle]

@reef jasper just post your q

[fossil crown]

From

#❓how-to-get-help

Rule 1

The help channels are solely for help with math, so feel free to post your question. Asking whether you can ask a question or if anyone knows about some specific topic is unnecessary, so please try to avoid questions of that nature.

[reef jasper]

ok mb

not sure if this is pre calc but heres my question: Assume a machine during its initial testing phase produces 10 widgets a day. After 10 days of testing (starting on day 11), it begins to run at full speed, producing 40 widgets a day. After 50 days at full speed (days 11-60), it gradually starts becoming less productive, and produces 1 fewer widget per day, (ie. 39 widgets on day 61, etc.) until on day 100 it no longer produces any widgets. Write the piecewise functions for these statements.

[viscid thistle]

@reef jasper what have you tried so far?

[reef jasper]

i got the first two equations

cant figure out how to write it after 60 days

[viscid thistle]

Can i see them?

[reef jasper]

days <= 10 : 10(days),........... 10< days <= 60 : 100+40(days-10)

[viscid thistle]

Hold up

So you are saying $\ f(d)=\begin{cases} 10d& 0≤d≤10\ 100+40(d-10)& 10<d≤60\end{cases}$

[obsidian monolith]

Al𝟛dium:

[viscid thistle]

Where f(d) is just the widgets made per day

And d the number of days

[reef jasper]

yes sir

now i need help to find when 60<d<=100

[viscid thistle]

@reef jasper okay but, why d***-10***?

Where does the -10 come from

[reef jasper]

because thats the total of the first 10 days which is 100 so i won't caluclate and extra 10 days

[viscid thistle]

Yeah okay

So for the last part

Hold up

Hmm

The way this is phrased and what the parenthesis mean, kinda confuses me and i don't have a paper at hand rn

[fiery wren]

is there anything else im missing