precalculus

[hushed sphinx]

It's (5x+4y)^7.

You're being asked for the term in that expansion that looks like <some number>·x^2·y^5.

The task is to compute the <some number>.

[gusty pasture]

okay, i found the first one

not sure abt the second one

[hushed sphinx]

The second one is a bit of a trick question.

[gusty pasture]

would it be 0?

i tried DNE and it didnt work

[hushed sphinx]

Then I'd say 0.

[gusty pasture]

okay it worked

thanks so much!

@hushed sphinx would this be correct?

[hushed sphinx]

I don't have time to deal with that now.

[gusty pasture]

gotcha

[slender idol]

can anyone help me find the inverse of y = 3 + x + e^x?
I start by subtracting 3 from both sides but im not sure how to proceed from y - 3 = x + e^x

[summer ruin]

I guess it's beneficial to transform x + e^x into a logarithm of a product

then exponentiate both sides and apply lambert W function

I don't see any other way to express the inverse function more explicitly

[slender idol]

lambert W function is outside of my curriculum. book only explains log and natural log for this problem.

book gives the answer of 0.

[summer ruin]

well you don't seem to have any other choice

[slender idol]

specifically, this is the problem
if g(x)=3+x+e^x, find g^-1(4)

so first find the inverse, then evaluate for x=4

[summer ruin]

this does not require finding the inverse

as far as I'm aware

well just think about it what does it mean to evaluate the inverse function at x=4

given that the inverse is obtained by starting with y = 3+x+e^x and transforming it into the form x = f(y)

so it's a function of y, you just swap the x and y for convenience in the end

[slender idol]

right, y = 3 + x + e^x, but with the previous problems you can actually find the inverse function for g^-1(y)=x

[summer ruin]

well not this time

[slender idol]

just weird because the book doesnt go over lambert at all, and the whole section is about inverse functions and logs

[summer ruin]

you don't need lambert for this

[slender idol]

4 = 3 + x + e^x then?

[summer ruin]

yes

then the value of the inverse would be the solution of this equation in terms of x

which you can sort of guess, you can't solve this analytically

[slender idol]

1 = x + e^x
1 - x = e^x

ummmm then natural log?

[summer ruin]

that's an incorrect transformation

[slender idol]

omg im stupid

edited it

[summer ruin]

as I said you can't solve this on paper like you would any other equation

so there's only a guess you can make as to what x makes this true

[slender idol]

so this has nothing to do with this?

does e^x = y?

[summer ruin]

I'm not sure how this applies to the equation x + e^x = 1

[slender idol]

i mean you could infer that if x = 0 then 0 + e^0 = 1

but it bothers me i cant algebraically arrive at this answer.

[summer ruin]

yes that's just a bad exercise at this level because you can't prove that this is a unique solution

[slender idol]

because with previous problems i was able to cancel functions with their inverse and algebraically derive the answer, so im caught off guard that this one you cannot do that.

[slender idol]

thanks for the help

[mossy sierra]

someone pls help me verify this. i have been going in circles for an hour

[viscid thistle]

express tan(alpha) in terms of sin(alpha) and cos(alpha). you would get a fraction in the form of (sin + cos)/(sin - cos).
Multiply numerator and denominator with (sin + cos)
That should get you your answer.

[viscid thistle]

whats the answer for number 6? i got tanx but it doesn't seem to be right

[vocal parcel]

Wouldnt it be sinx over cosx

[mossy sierra]

yeah i think the answer is just tanx

[mossy sierra]

THANK YOU SO MUCH

[velvet peak]

for an upcoming project I have to use a series of polar and non polar graphs to recreate an image of sorts. What equations would help me recreate the image I have chosen, the Rolling Stones Hot Lips?

the image for reference

i get bonus points for animation but I’m stuck trying to create the base of the image first

[astral root]

$(\log(x))^2 \neq \log(x)^2$

[obsidian monolith]

Bobingstern

[astral root]

Is this true?

[astral root]

Also, what type of 2d time evolving function can represent a wave like ripple going inwards? Basically the reverse of the thing that happens when you drop a rock in a pond

[obsidian monolith]

stéphane

stéphane

[astral root]

So $\log(e^3)=\log(e)^3=3$ but $(\log(e))^3 = 1$

[obsidian monolith]

Bobingstern

[astral root]

Since I’ve faced some trouble saying this is true and some saying it’s not true

Very confusing

[uncut mulch]

saying those things not being equal is false,
those things although the notation on the right sucks, would be interpreted as being equal

[obsidian monolith]

stéphane

stéphane

[uncut mulch]

$\log(a^b)$ however is not the same as $\log(a)^b$ or $(\log(a))^b$

[obsidian monolith]

ℝamonov

[astral root]

Oh ok

Thank you

[obsidian monolith]

stéphane

[autumn wadi]

heya quick qn what's the diff between (log(a))^b and log(a)^b?

[uncut mulch]

they represent the same thing, but the latter notation is objectively bad

[autumn wadi]

ic

[stuck arch]

how do I find the derivative of this?

[hushed sphinx]

Derivatives are #calculus.

[stuck arch]

ah sorry

[viscid thistle]

Hey, here is your solution

It's probably correkt

[slender idol]

can anyone help me simplify $\ln[(x+2)(\frac{x}{(x^2+3x+2)^2})]$

[obsidian monolith]

b0ngl0rd

[opal tree]

Is there any context to this?

You can try using ln(ab) identity

[slender idol]

correction $\ln[(x+2)(\frac{x}{(x^2+3x+2)^2})]^\frac{1}{2}$

[obsidian monolith]

b0ngl0rd

[slender idol]

the goal was to create a single log expression from a compound expression, this is the correct result before simplification of the inner terms

[opal tree]

What's the original because now you're taking a square root of a natural log

And I feel like there's a bigger context to this

[slender idol]

im just needing help understanding how those two inner terms simplify to $\ln(\frac{\sqrt{x}}{x+1})$

[opal tree]

Are you raising ln(...) by 1/2 or is the argument being raised by 1/2

Like show me the full original problem

[slender idol]

ah yes sorry, its hard dealing with latex in discord.

$\ln[(x+2)(\frac{x}{(x^2+3x+2)^2})^\frac{1}{2}]$

[obsidian monolith]

b0ngl0rd

[opal tree]

Hm

[slender idol]

original problem is quite large. but if you want i can write it out here

[opal tree]

Send a picture

[slender idol]

41

i checked my work so far with symbolab and my intermediate simplification is accurate until it simplifies those inner terms

[opal tree]

Well for starters you can say that $\parens{\frac x{(x^2 + 3x + 2)^2}}^{0.5} = \frac{\sqrt{x}}{|x^2 + 3x + 2|}$

[obsidian monolith]

Umbraleviathan

[opal tree]

Not sure how picky they are with absolute value. Gonna keep it there for now

Oh absolute value doesn't matter because of the domain of sqrt(x) and x^2 + 3x + 2 goes negative outside of that domain

And then x^2 + 3x + 2 factors into (x+1)(x+2)

So you can cancel out (x+2)

And you're left with sqrt(x)/(x+1)

[slender idol]

i am following until you say cancel (x+2)

$\frac{\sqrt{x}}{(x+1)(x+2)}$ right?

[obsidian monolith]

b0ngl0rd

[opal tree]

Yeah

Well

[slender idol]

whats the reasoning for cancelling that term

[opal tree]

You forgot the (x+2) •

The other factor

$(x+2) \cdot \frac{\sqrt{x}}{(x+1)(x+2)}$

[obsidian monolith]

Umbraleviathan

[opal tree]

All I did was simplify (...)^(1/2)

[slender idol]

ohhhhhhh yeah sorry

[opal tree]

It boils down to that

Wait but ... 1/3 ln(x+2)^3 is not the same as 1/3 ln[ (x+2)^3 ]

@slender idol does your book treat that as equivalent?

[slender idol]

1/3 ln a is the same as log_e^(1/3) a i believe

errr wait

[opal tree]

log_e^3 (a)

,tex \logxprule

[obsidian monolith]

Umbraleviathan

[slender idol]

woah thats a cool definition. my book only explains that in two separate rules

but yeah i cancelled 1/3 and the ^3 in that first term

[opal tree]

But then ... by notation:

$$\frac 13 \ln(x+2)^3 ≠ \frac 13 \ln((x+2)^3)$$

Does your book treat it like they are equal?

[obsidian monolith]

Umbraleviathan

[slender idol]

i believe my book would denote the power belonging to the inside term with brackets if that were the case

i believe its raising the log to the 3rd

[opal tree]

Okay which is what it should be doing

Yeah but $\frac 13 \ln(x+2)^3 ≠ \ln(x+2)$

[obsidian monolith]

Umbraleviathan

[opal tree]

If 3 is raising the log

So I'm wondering if your book just has shit notation

[opal tree]

And treats this as equivalent (when in reality they aren't)

[slender idol]

i wanna say shit notation. theres some definitions that get really confusing because it switches variables around a lot

[opal tree]

In the case that it's just shit notation and it's actually just raising (x+2) and not the entire log, then yes it simplifies to ln(sqrt(x)/(x+1))

Just note that in general, $\log(a)^n = \log^n(a)$

[obsidian monolith]

Umbraleviathan

[slender idol]

thanks @opal tree you are a fkin master

[opal tree]

Np

[stuck arch]

Sorry but can you explain a bit on how you went from these steps into the next

[plucky totem]

I'm not too great with comp functions can anyone help me out RQ?

[viscid thistle]

Multiplied x to other variables

Then applied chain rule in differentiation

Differentiation of e is 0 as it is q constant so only x ones were differentiated

[stuck arch]

isnt d/dx e = e?

[viscid thistle]

Ddx of e^x is e^x

Ddx of e^1 is 0

That is why

[stuck arch]

ohh

I remembered wrong

[summer ruin]

d/dx 5 = 5

[stuck arch]

e as in eulers number or whatever its called

[viscid thistle]

Aaaaaghjhhhhhhh mene

Meme*

[viscid thistle]

Why did you do this

😂😂

[stuck arch]

Shouldnt green be multiplied to both red terms

[cold echo]

Question about limits: If I have a blackbox function which I don't know anything about. Except I give it input and receive output. Like some strange algorithm, or maybe physical phenomena. Are limits still valid here? Suppose I want to know limit at x=5. So I take the f(5-1) and (5+1) get 5.001. I squeeze it more f(5-0.1) f(5+0.1) get 99. What now? Are limits only valid when we know the common pattern/predicate all points have ?

[summer ruin]

that's numerically estimating the limit, nothing else

nobody of course said that this function is continuous and neither do limits have that as a requirement

[cold echo]

Find a b c such as their sum is below 15 and product is maximum.
Easy solution for that without enumeration?

[coral stream]

For a spiral of equation r(theta), what does r and theta represent

[summer ruin]

radius and angle

[coral stream]

yeah but what do i call the angle & radius? its very difficult to define

[primal quail]

use am gm?

(a+b+c)/3 >= (abc)^(1/3)

[summer ruin]

what's hard about radius and angle

it's taught in middle school

[primal quail]

I think you mean their sum if smaller of equal right, if thats the case use the equality case for am gm

also im explicitly assuming the numbers here are positive else, the answer is trivial

[coral stream]

like angle of what ? radius of what

[summer ruin]

you tell me, you didn't explain your problem fully and notation r, theta is often used to represent polar coordinates which has clear interpretation of radius and angle

[cold echo]

I don't understand the connection of division on left and cube on right. Would you mind quick expl?

[slender idol]

$\frac{x_{1}+x_{2}+\cdots+x_{n}}{n}\geq \sqrt[n]{x_{1}x_{2}\cdots x_{n}}$

[obsidian monolith]

b0ngl0rd

[haughty lance]

how did you get 4?

[subtle steppe]

wdym?

[haughty lance]

question 4

[subtle steppe]

rationalize twice and cancel x-2

[haughty lance]

ok

do you notice it's of the same form as ii?

[subtle steppe]

yea

but like theres a way u can do it by using q4part1 which i cant seem to get

[haughty lance]

i mean if you already solved part 1

you have ii for free almost

also think about if you can split the fraction...

[lime frost]

someone help I’m stuck

[summer ruin]

represent secant squared in terms of cosine

[lime frost]

1/sec^2x = 2 and then what

[summer ruin]

?

that's not what secant is in terms of cosine

[lime frost]

1/cos^2x = 2

right

[summer ruin]

now express cosine squared in the given equation and think for what values of x cosine squared achieves the right hand side

[lime frost]

ohhhh wait let me try to solve it

Thanks for leading me in the right direction, I got it

@summer ruin

[summer ruin]

and what was your answer

[lime frost]

Here

[summer ruin]

well that doesn't seem correct

[lime frost]

why

Where did I make a mistake

[summer ruin]

in figuring out what inputs make cosine equal 1/root(2) or -1/root(2)

the n is not in the right place in first series of solutions and second series doesn't even depend on n

[lime frost]

Ok I understood

I know that this is wrong but why I cant do this

@summer ruin

[summer ruin]

because the equation contains cosine in the denominator, which turns to 0 at pi/2 + pi * n

and you divided by sine there as well

what if sine is zero? you divided by zero

[lime frost]

man you are so smart

Thanks for help

[coral stream]

https://research-repository.griffith.edu.au/bitstream/handle/10072/58722/88799_1.pdf?sequence=1 here, at section 3.1, why does this represent an understatement? don't really get the approximation he is making and would appreciate some explanation

[coral stream]

<@&286206848099549185>

[mortal rampart]

Can someone explain how to do this for me

[fickle marsh]

You’re basically supposed to select the probability of the outcome given, eg. the answer to # 7 would be D, because the probability of picking a nickel or a dime is 7/10

[mortal rampart]

thanks i get that one now but the only one I dont get is number 5

[coral stream]

hi, can someone help please

[frank charm]

Well it is not really concentric annuli, it is more a spiral so here is the approximation

[lucid trench]

here are some cool precalc notes i took #10 (polar graphs!!

@worn geyser

[worn geyser]

TYSM!!

WOW I'M GONNA NEED THOSE AT THE END OF THE YEAR

[mortal rampart]

help with number 5 my mom is mad i cant do my homework she gonna spank me

[reef vigil]

You have to use P(A or B) = P(A) + P(B) - P(A and B)

[fringe sable]

how do i write this as an entire radical?

the answer is

[untold spindle]

we can rewrite 2/5 into cbrt(8/125). next we combine the cube roots. then finally we multiply the inside of the cube root.

it would look like this

[fringe sable]

thanks

[untold spindle]

np

[fringe sable]

how do i simplify this?

[cursive fiber]

simplify the fractions then common denominator

i think

so sqrt12 + sqrt24 /3x

i might be stupid

yea

its 2sqrt3 + 2sqrt6/3x

[fringe sable]

how did you get that?

[cursive fiber]

well

ill draw it

[fringe sable]

ok thanks

[untold spindle]

1.get rid of radical in denominator
2.get common denominator
3.add fractions
4.simplify radicals in numerator

[cursive fiber]

that

[fringe sable]

thanks

[untold spindle]

though, this only works assuming x is a positive integer

[fringe sable]

wait

where does 72 come from

[cursive fiber]

3 x radical 8 is radical 72

because you when you square 72 you take out the largest perfect square (9) and square root it then put it on the outside of the radical

[untold spindle]

i multiplied the top and bottom by 3 to get a common denominator of 3x

[fringe sable]

ohh you did 8x3x3

[untold spindle]

yep 🙂

[cursive fiber]

both greatest integer functions and rational functions are discontinous

correct?

[untold spindle]

on second thought i could have just kept the 3 on the outside of the radical lol

[untold spindle]

i think so, would a asymptote be counted as discontinuous?

[cursive fiber]

i think

but the answer key on my hw says that it is only one of them

it could just be an error

[untold spindle]

ah i searched it up

[cursive fiber]

the questions was something like which graph is discontinous

but there would be two answers

[untold spindle]

if the graph only existed on one side of the asymptote, its not discontinuous

for example, this is continuous

[cursive fiber]

no it looked like this

[untold spindle]

where as this is not

[untold spindle]

this would be discontinuous

because there is a point missing along the "journey"

[cursive fiber]

but this is also discontinous

[untold spindle]

yep, i believe so

[cursive fiber]

then my answer key is just messed up

[untold spindle]

you might have to consult someone else about this topic. im not too familiar with it so i could very well be wrong

[cursive fiber]

i asked one of my classmates and he said the same thing

[dry karma]

need some insight pls

[cursive fiber]

what is it

[lime frost]

no way bro who still takes notes like that

[opal tree]

This is considered continuous

Since 0 is not within its domain

It's continuous on its domain

That is, x in R \{0}

A step function is discontinuous because of the jumps in its domain

Although that's a more vigorous definition of continuity

If you assume a domain of R then yes, you could argue it's discontinuous

But ngl I wish this shit was taught in precalc

[untold spindle]

mhh ok i see

[opal tree]

It'll make more sense with multivariable shit starting to become jankier

[fringe sable]

how do i simplify this question?

[opal tree]

You really can't

Unless you wanna put the fraction back into the square root

[fringe sable]

the answer key says the answer is

[opal tree]

Multiply it by $\frac{\sqrt{8}}{\sqrt{8}}$

[obsidian monolith]

Umbraleviathan

[opal tree]

Then use exponent rules

[fringe sable]

i multipled and simplied the radical but i dont know where to go from here

[opal tree]

Remember that $\frac ab \cdot \frac cd = \frac {ac}{bd}$

[obsidian monolith]

Umbraleviathan

[fringe sable]

thanks i got it now

[fringe sable]

how do i simplify this?

[tranquil laurel]

Is this 2^3 or triple root (?

[wide vale]

You can bring 2 inside the cube root

Rewriting that into $\sqrt[3]{\frac{5}{2x}}$

[obsidian monolith]

A Lonely Bean

[snow ravine]

good morning. what does |n| mean in set theory?

[summer ruin]

what is n

[snow ravine]

i think its elements of the set

i cant write the symbol of is part of

[summer ruin]

if n is an element of a set then |n| is absolute value of n, whatever that might be

[snow ravine]

the fancy E

yeah makes sense

thank you

[cursive fiber]

what is the end behavior of a square root function

i know what it is but don't know why it is

also when is the union symbol used while describing the domain/range of functions?

[hushed sphinx]

When using a union symbol is the simplest or clearest way to describe the set you want to state is the domain or range.

[spark scroll]

not sure how to proceed

p^3 / q^3 / (pq^-2)

i cant move q^-2 up and turn it into q^2 right? because its in a bracket and id have to move the whole thing together dont i

[hushed sphinx]

Sure you can.

The exercise probably expects you to rephrase pq^-2 as a fraction and use the rule for division of fractions.

But you can also say p^3/q^3 = p^3·q^-3 and 1/(pq^2) = p^-1·q^2 and then multiply those.

With some experience you'll be able to see that those are really the same thing (or at least the difference between them doesn't matter in the big picture).

[lucid trench]

sitting with a 96

[zinc zenith]

Can someone throw me some ideas for my class's "Math Appreciation" project? It's where we present about things in real life related to maths (e.g. how would lightsabers work in real life, how do F1 racers turn fast, etc.)

[pseudo hamlet]

Maybe talk about the golden ratio and its use in art?

[vapid plaza]

Your examples sound more like physics than math

[sharp halo]

hello

[slim steppe]

You can't really talk about those without having an understanding of the physics and the fantasy behind

[viscid thistle]

Physics: applied math

Don't kill me

[zinc zenith]

He said you don't need to understand the formulas or the complicated maths behind it

You just need to be able to relate it to math is all

Thanks guys, I'll see what I can do

[lime frost]

@summer ruin

I love you

U saved my ass

[viscid thistle]

good job

[viscid thistle]

Hello, I was curious, but is there any algebraic method to derive the famous difference of squares formula of a^2 -b^2

the formula for a^3 -b^3, for example, can be derived using algebraic methods

I just don't see why that wouldn't be the case still for a^2 -b^2

[hushed sphinx]

Are you talking about (a+b)(a-b) = a^2 - b^2?
You need the entire identity before it makes sense.

[viscid thistle]

Yes

I do know of the typical geometric proof of it i suppose

[hushed sphinx]

Algebraically you just use the distributive law twice on the left-hand side and then let the ab and -ab terms that result cancel.

[viscid thistle]

Oh I was more talking about how to conclude what a^2 - b^2 = ? rather than what (a-b)(a+b) = ? if that makes sense

like assume we do not know that equality holds, and we want to figure out what a^2 - b^2 could be representing

[hushed sphinx]

The result says they are equal. That is symmetric: if one side equals the other, then the other equals the first.

[viscid thistle]

Alright. Thank you for the help

[vapid plaza]

one motivation is that the expression a^2 - b^2 is equal to 0 when a = b as well as when a = -b, so (a - b) and (a + b) are factors of a^2 - b^2 by something called the Factor Theorem.

[arctic obsidian]

for this equation, do i have to explain that i treat theta as circular (meaning theta does not equal theta+2pi) ?

explanation of variables:

[arctic obsidian]

<@&286206848099549185>

[tight vortex]

Idk how to solve these 2

[slender ice]

May not be strictly pre-calc related, but thats the class im in

Are these types of problems solvable algebraically?

I understand how to get the solution by rationalizing it graphically, but I was just curious if there is an algebraic approach

I may have spent an embarrassing amount of time trying to solve a similar problem algebraically lol before realizing how simple it was to just translate the values

[tight vortex]

Actually I got 25

and 24 so nevermind

[slender ice]

Nice, I've not made it to sin/cos yet x.x

[tight vortex]

Well i don’t know what your doing either so

[slender ice]

yeah I'm not really sure when the calculus starts in this course. So far it's just been reviewing Algebra but in bizarre ways I've never thought about before lol

[tight vortex]

I’m pretty sure there isn’t calculus its just a review of trig and algebra that’s useful for calc

🤷‍♂️

[slender ice]

Honestly I need it, I don't need it for my degree but im taking it anyways because I did so shit in Algebra for my AA

literally cheated through the course, never felt good about it. I want to understand lol

[tight vortex]

Lol I understand I’m in hs taking it for the first time

[slender ice]

it's definitely worth understanding, I've just turned 27, going back for a BA as an adult. Really wish I'd been able to wrap my head around it in hs

Already way better at it than I was, I work in IT and software and just the little bit of new understanding I've gained has helped a ton with my job

[pale marlin]

Why do we plot complex functions on a contour plot and not in a 3D plane? (or is it just easier to make a contour plot)

[hushed sphinx]

A full analogy with the graph of real functions would produce a surface in a 4D ambient space, which is hard to visualize. There are several different strategies for condensing the function down to something easier to visualize. Plotting contours is one of them, but one can also encounter 3D plots of, for example, the modulus of the function value, with the argument either being omitted or shown as colors.

[hazy terrace]

I've seen this being done with a sphere but f(x,y,z) represented their volumes and each sphere would be nested if smaller. Would that be considered a different type of plane? or dimension?

[swift trellis]

Should I start off the solution by finding f(x) using logarithm or is there any other simpler method for it?

Evaluation of functions^

Its just that sometimes I tend to struggle with logarithm

[timber thicket]

not sure if this is here or not but whats the name of a parabola which is y^2=2px (ik the name in my language not english)

[marsh cave]

help pls 🙂

[timber thicket]

tan(x) passes at 0,0 now it moved over to pi/4,0 so its a horizontal shift by pi/4 do you remember how you do that?

a wait

nvm

its not that simple

[ripe ibex]

can anyone help me with this mechanics question, no one from the other channels can do it

[fading crown]

Use Bernoulli's equation

[hushed sphinx]

(Sorry, ignore this post, I misread the problem).

[swift trellis]

All good

[viscid thistle]

Not for hw, purely wondering
Is there a way to algebraically find an extrema if there is only one and you are given the function?

[viscid thistle]

Try using vertex form

It has a horizontal shift and a horizontal stretch

So what variables are related to those? In Af(B(x-h)+k

[summer ruin]

yes, for example you can prove that the function is greater or equal to some lower or upper bound, then show the element that actually achieves this bound (this is actually the argument that the proof of Eckart-Young theorem uses)

$f(x) \geq g(x) $ (unique minimizer of $f(x)$) or $f(x) \leq g(x)$ (unique maximizer), then if I can find such $x^$ that makes the equality hold $f(x^) = g(x^*)$ then I'm done

[obsidian monolith]

Transparent_Elemental

[peak wing]

Tan(x-pi4)

The period is pi distance between tan functions

Pi/b = pi

B= 1

C/b be the distance between the origin for tan functions since the period is 1

Amplitude is 1 looks like a normal function

And no vertical shift

[fringe pulsar]

how to evaluate cos 160/sin 70 in exact form?

[stuck arch]

not sure if this should be here but

[hushed sphinx]

You could for example notice that cos(160°) = -cos(20°). And cos(20°) is the same as ...

[grizzled lodge]

Im stuck on this question

I acquire some assistance

[hushed sphinx]

There's a pretty good hint right there in the problem statement.

[grizzled lodge]

Hmmmm

[hushed sphinx]

But this is not "precalculus".

[grizzled lodge]

Oh what is it?

[hushed sphinx]

Calculus.

[grizzled lodge]

oh

[fringe pulsar]

oh my i didnt think to simplify cos 160

i was considering using half angle formula to reduce cos 160/cos 20

well thanks

<3

[viscid thistle]

can somebody explain 2 me what the statement on the side means?

[slender ice]

This question is insanely simple but I think I'm lacking important vocabular to understand it lol. The answer is 20 and 20, but whatever concept this is wasn't covered in the chapter at all

I just don't know what "a maximum" is in this context. a maximum of what?

[hushed sphinx]

The largest possible value you can get by multiplying any two numbers that sum to 40.

[slender ice]

ah okay that makes sense

Is there a way to solve for this, or is it just a guessing game? in this case it's really obvious but i'm assuming if this question exists there is a algebraic way to solve it

actually i think I understand. You could write a function to express the idea. f(x) = -x^2 + 40x

[hushed sphinx]

Right. It would be clearer what you're doing if you write it as f(x) = x(40-x) first, and then rewrite that into standard quadratic form as part of the process of finding the maximum.

[slender ice]

Questions like these ones always challenge me the most, they're along the same lines as word problems. Understanding the individual relationships of all these concepts is easy enough, but I find it pretty difficult to see those relationships in other situations

when I do though, the math is almost effortless. I nearly failed algebra but Stats was the most fun I ever had in a math class. Having every concept linked to measurable information and data made everything make more sense.

Wish I had to time to take each concept I'm learning and find a fun way to apply it. As it is, I spend so much time pushing abstract numbers and equations around, that my brain grinds to a halt when it sees a question written in plain English apparently lol

[slim steppe]

You're solving optimization problems

[pale marlin]

Point X is on a cone with vertex A, radius 1, and height 1, such that AX is 1/4 of the cones’s slant height. Y is diametrically opposite to X on the cone such that it XY is 3/4 of the cone’s slant height. What is the area of the cross section that goes through X and Y?

Is it pi*sqrt13/8?

[dim girder]

its ez

[dim girder]

60years

is it correct?

[opal tree]

My guy, don't give away answers

[willow bear]

!nosols

[tender quest]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[sly steppe]

i think it is 20

20+20=40

20*20=400

400 is the max number that x + y = 40

[willow bear]

!nosols

[tender quest]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[sly steppe]

what does it mean

[willow bear]

it is a command that makes the bot say the message you saw just now.

[sly steppe]

we must dont give answer?

i am new here and could you please explain what we must do here)

[willow bear]

you can read #❓how-to-get-help, #rules and #info

... this is a wild guess, but do you happen to be russian

[slim steppe]

It is

It's an optimization problem

[slender ice]

yeah the answer is pretty intuitive in this case, But im still not sure how to solve it in a more complicated setting, Like a question I'm working on right now I need to find the maximum for f(x) = 250x - 3x/4, where 3x + 4y = 1000

[sly steppe]

I think you need to find derivative

[storm lodge]

Completing the square

[slim steppe]

Can you write it out on a piece of paper

[slender ice]

sorry, was sucked into some assignments, It's actually a word problem

I solved A and B like this

[slender ice]

I've seen that method posted online when searching for this type of question, problem is I've not reached derivatives yet in this course

[sacred oriole]

Hey so, I’m in community college and the major I’m going for requires that I take precalc 1 and 2 + calculus. Last semester I took precalc 1, and I got a B. This semester is basically 1/4 of the way through and I’m basically failing. I am just struggling very hard with the material and I don’t entirely understand why the trig stuff for precalc is so much harder

All I ask is for some advice on how to get through precalc, my teacher isn’t very helpful because he’s from the Czech Republic and has a very heavy accent and his hand writing is sloppy

I’m struggling to learn off of YouTube videos but they seem to be my best bet? And like the stuff he’s publishing to canvas?

[viscid thistle]

learn trig identities.

[fringe sable]

are these two the same?

[viscid thistle]

no

[viscid thistle]

also organic chemistry tutor

[sacred oriole]

Thank you

[slim steppe]

Get a tutor

[sacred oriole]

I'm not sure where I can get one though

[storm lodge]

If you can buy it, get the aops precalc book (not class)

[crisp bane]

How do I check if my answers for law of sines is correct

[raw hill]

Google a triangle solver

[crisp bane]

So I use it and it seems I am right

[fringe sable]

how do i solve this question?

the answer is 9/4

my calculator doesnt let me use calculate for exponents other than 2 and 3, and i dont know how to simplify the radicals so that there are no more radicals

[storm lodge]

first divide by 2 on top and bottom

[fringe sable]

thanks

[willow bear]

what kind of calculator is that?

[ripe grove]

i wanna learn calculus

where to start?

[raven tendon]

yes

calculus is ez

start it from limits

[vapid plaza]

They probably never learnt about the ^ button

[viscid thistle]

Functions actually.

[viscid thistle]

Are you familiar with functions?

[glacial onyx]

can anyone teach me integration

just the basic level

[viscid thistle]

Some functions vary continuously while others jump erratically to understand such functions we need limits. When a function isn't defined at a particular value, say a, so what we'll do is explore the function in neighborhood of a and get as close as possible to a from the both sides (LHL AND RHL) - mathsmerizing's video

[viscid thistle]

Basic, as in, integrating the elementary functions?

[glacial onyx]

hmm

[viscid thistle]

sure!

[glacial onyx]

will you teach me?

[glacial onyx]

tell me in which thread u will

[viscid thistle]

i don't mind, is there any specific exercise you're dealing with solving integration problems?

[viscid thistle]

Idk how threads work 😭 i joined this server today

🥲

[glacial onyx]

but u dont have a new here batch

[glacial onyx]

teach me in dm them if u comfortable?

[viscid thistle]

Yes sure.

[lucid trench]

heres some cool precalc notes i took #11

[golden narwhal]

The frogg

[barren tulip]

loll the frog

[barren tulip]

precalc has determinants of matrices??

inverse matrices..

looks more like linear algebra bro what kind of precalc course r u taking 😭

[lucid trench]

I added this myself

my precalc course didn't have it

so i was like, screw it, i'll need it in the future anyway

[barren tulip]

ah

thats nice

[viscid thistle]

Anyone got any ideas?

Our precal teacher descively ambushed and destroyed the soilders of the B block precal class with a ICA that everyone forgot about.

The casualties were 80% and the results were that the teacher had successfully claimed most of the hopes and dreams of the class and destroyed them.

[viscid thistle]

go to khan academy and start with first video from there

[glacial onyx]

its too leangthy

[brave gust]

need help anyone?

[viscid thistle]

Yes me please

[brave gust]

ok now

[brave gust]

come on make ur channel

[viscid thistle]

I'm not sure how

[brave gust]

press help 0

[viscid thistle]

I cant see the help channels for some reason

[brave gust]

then wright sm

then u get it

[viscid thistle]

I dont see help0

[brave gust]

just preess help 10

[viscid thistle]

K I'm rhere

[raw swift]

can someone help me with these 3 questions?

[austere mulch]

is i++ part of math or is that just a programming language

[summer ruin]

neither

not all languages have this kind of increment nor does math

[austere mulch]

thanks

<#

❤️

[vital swan]

yo

how to convert large decimals to fractions?

like -1.154700538

but they ask for a fraction, which my TI-84 plus calculate can't make it to a fraction

[untold spindle]

im not sure if there is a proper way but if we take your example, and put it over 1000000000 it will be a whole fraction

like this

then just simplify the fraction if possible

[mossy sierra]

i need some help on this

[vapid plaza]

Take out common factor of the two terms on lhs and see if you can proceed from there

[chilly hazel]

how did they do this step

$x^2(x^2-5) = y^2(y^2-4) \$
$\text{find tangent line at (0.835, 1)}$

[obsidian monolith]

Price

[summer ruin]

just expanded and differentiated?

[chilly hazel]

(4y^3)' - (8y)'
is that equivalent to third line?

[summer ruin]

no

that's not what expanded expression looks like

it doesn't have y^3 anywhere

[chilly hazel]

how did y become x

[summer ruin]

it didn't

[summer ruin]

there's no x^3 in this expression either

[chilly hazel]

i mean in the image i sent

it became 4x^3-10x

[summer ruin]

it didn't

they just swapped the order in the equality

[chilly hazel]

i dont know what that means

[wanton robin]

Is this the right place to ask a question about the power of ten?

[summer ruin]

do you agree that if x = y then it's the same as y = x

[chilly hazel]

ah, yes

i understand the right hand side now

y^4 - 4y^2 became 4y^3 dy/dx?

[summer ruin]

that's only what first term became

you didn't differentiated 4y^2

[chilly hazel]

OHH, man i don't know why that confused me so much

now, how did it get into fraction form

dy = 4x^3-10x
dx = 4y^3-8y ?

[summer ruin]

no

dy and dx are not even separate objects, dy/dx is not a fraction

[chilly hazel]

oh

[summer ruin]

just express the dy/dx in terms of y and x by basic algebra techniques such as factoring

[solar olive]

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

d/dx x^4 - d/dx 5x^2 = d/dx y^4 - d/dx 4y^2

4x^3 - 10x = 4y^3 dy/dx - 8y dy/dx
4x^3 - 10x = dy/dx (4y^3 - 8y)
dy/dx = (4x^3 - 10x) /(4y^3 - 8y)

i think..

y - 1 = m(x - 0.835)
m = plugging the x and y in the dy/dx

[burnt hare]

can i ask when point slope form is used

[pseudo hamlet]

You use it when you're asked to find the equation of a line at a given point

[nimble urchin]

hi

[willow bear]

do you still need help with this

also might wanna go in #calculus given that this is literally a derivative problem

[solar olive]

i think its the y-y1 = m(x-x1)

[leaden willow]

Am I on the right path

[fringe sable]

how do i simplify this?

[thin elk]

-375 right? easy

[fringe sable]

no

the answer is 1 over 5^1 over 2

[thin elk]

sry just kidding root 5

√5 right?

[pseudo hamlet]

You just need to express everything in base 5 and then combine exponents

[thin elk]

so what is answer ? That’s all I need

[fringe sable]

this is the answer

[pseudo hamlet]

Wait no

Itd just be 5^(1/2)

[fringe sable]

oh youre right

how did you get that?

[pseudo hamlet]

Convert 25 and sqrt(5) into base 5 to get 5^2*(5^1/2)^-3

[fringe sable]

what does base 5 mean

[pseudo hamlet]

It's what is being raised by an exponent

Like in x^2 the base is x and it's being raised to the second power

[pseudo hamlet]

Using exponent laws, (5^1/2)^-3 = 5^((1/2)*(-3)) = 5^(-3/2)

[fringe sable]

i only got to here, where did the numbers from the exponents come from?

[pseudo hamlet]

Do you know about fractional powers?

[fringe sable]

i dont think so

[pseudo hamlet]

Ok well basically a fractional power is the same as taking the root of a number

For example, taking the square root is the same as raising it to the power of 1/2

[fringe sable]

yes

[pseudo hamlet]

Which is why I expressed it as (5^(1/2))^-3

[fringe sable]

but wouldnt sqrt 5 * 25 = 5

why has it become the exponent

[pseudo hamlet]

You can't combine the exponents of 25 and 5 until you deal with the -3 power due to PEMDAS

[solar olive]

25(sqrt(5))^(-3)
5^2 5^(-3/2)
5^(2-3/2)
5^(1/2)
sqrt(5)

[pseudo hamlet]

Ye that's what you're supposed to do

[fringe sable]

thanks @pseudo hamlet @solar olive i got it now

[north remnant]

If somebody could explain how to do this question that would be great!

I haven't been introduces to what "In" represents.

[uncut mulch]

ln is the natural log

i.e. log base e

[north remnant]

oh ok thank you!

[thin elk]

I can’t graph tho but lim x→＋∞f(x) and -∞f(x) are both 0

sry bad drawing

[ashen oyster]

How do i differentiate this

[thin elk]

f’(x) ＝2-x/√x＾2-243

[ashen oyster]

How did you get to that?

[thin elk]

You should differentiate 2x＋100and √x＾2-243separately

[ashen oyster]

Ok

[thin elk]

could you do former?

Latter is hard to do right?

[ashen oyster]

What’s former

√x＾2-243 is the part I don’t know how to differentiate

[thin elk]

ok just second

former is part of 2x＋100

[ashen oyster]

Ok

Wouldn’t 2x + 100 just become 2x ^-1?

[thin elk]

I guess you take calculus for differenciation

2x +100 turns into 2

[ashen oyster]

Oh

Now I see

But how would I do the part after it?

[thin elk]

can you see it?

hard to read lmao

[ashen oyster]

It’s not hard to read

[thin elk]

get it?

[ashen oyster]

Everything under the black line I don’t

[thin elk]

well second

[ashen oyster]

K

[thin elk]

how about this?

[ashen oyster]

Still got no clue

I think I’ll just leave the question with that

I haven’t learnt it yet (apparently it’s chain rule or something chain)

[thin elk]

ok just second

I’ll do my best

do you know what it means?

[ashen oyster]

Nope

Well I gtg now thx for helping

[thin elk]

Oh afraid not to make it clear

[raven tendon]

0/0 form

two h's cut

also is that s->0?

x->0?*

[carmine citrus]

hi can someone help me with an integration parametric question

need help with part b of this:

keep getting a negative and idk ????

[untold spindle]

I think this belongs in #calculus

[carmine citrus]

oops you'll have to forgive me in the uk we call it pure 👀

[untold spindle]

Ur good

[opal tree]

British moment

[spark quiver]

e=mc2

[misty pier]

?

[north remnant]

Learning the squeeze theorem, could somebody solve and show steps to the question? I’m not sure how you incorporate natural logs into the squeeze theorem

[north remnant]

Nvm.

[raven lily]

if I have something like $2 - \frac{x}{2}$ can I factor out a 2 from the fraction?

[obsidian monolith]

Unbearable Frequentist

[summer ruin]

of course

that'll be x/4

[raven lily]

would it be $2(1 - \frac{x}{4})$

[obsidian monolith]

Unbearable Frequentist

[summer ruin]

yes

[rich elbow]

can someone walk me through this

i’m so confused

[summer ruin]

why not just express tangent in terms of cosines and sines

it's far simpler than it looks

[rich elbow]

i broke it down and i don’t understand how u get it to the right side

[summer ruin]

"right side"?

[rich elbow]

like the right side of the equals sign

cuz it’s like a proof right ?

[summer ruin]

i'm suggesting starting from right side

[summer ruin]

and doing that

[rich elbow]

okay lemme try and i’ll send my work

[placid sandal]

does anyone know how to solve ??

[amber crater]

At every degree rotation on minute hand , hour hand is rotated by 1/12 degree. Now for a minute rotation minute hand should rotate 6 degree and therefore hour hand should rotate by 61/12 degree. Now initially the angle between the hands is 120 degree, after 1 min rotation the angle between the hands will be 120 - 6 + (61/12) .

Calculate the initial and final distance by pythagorean theorem and subtract them to find the distance increased. Divide this distance by 1 min .... you will get the speed

Note 61/12 = 6(1/12) (typo)

[hushed sphinx]

That should give a pretty good approximation, perhaps even good enough for three decimal places.

I wonder if the problem setter expected to get an exact answer without any calculus somehow.

[bronze summit]

the numerator can be expressed as sin(x+y)

and denominator as cos(x+y)

sin/cos=tan

Therefore, sin(x+y)/cos(x+y)=tan(x+y)

One more way is dividing each term by cosx*cosy

that way sinx*cosy/cosxcosy=tanx

and so on

in case u dont know what sin(x+y)is
its equal to sinxcosy+sinycosx

the derivation is huge so Just remember this

[summer ruin]

this requires knowing that the right hand side is tan(x+y), which, unless you remember the identity, also requires proof

[vapid plaza]

Divide numerator and denominator of lhs by (cos x cos y)

[bronze summit]

hmm just divide numerator by cosx cosy

[bronze summit]

Yep exactly

[edgy heron]

pre calculus and stuff befor is so hard

[spark quiver]

Guys seriously

Does e=mc2???

[hushed sphinx]

That's a matter of physics rather than mathematics.

E=mc² is a valid formula from the theory of special relativity, but it is useless (and meaningless, really) without a long explanation of how to use it and how the quantities in it relate to measurable physical phenomena.

[spark quiver]

I was trolling but thank you sir i greatly appreciate it.

[hushed sphinx]

Now go, and troll no more.

[spark quiver]

You forgot “your trolling has been forgiven thee”

[hushed sphinx]

A certain measure of forgiveness is implied by the fact that you're not banned. I wouldn't recommend pushing it, though; it might just have been because I was too lazy to check your posting history....

[willow bear]

A certain measure of forgiveness is implied by the fact that you're not banned.

[half bay]

is it possible to finish pre calculus in 2 months

I want to take calculus in 11nth grade but need to finish pre calc in the summer

[proud raven]

is precalc even necessary for calc

[untold spindle]

i would say so. precalc contains a lot of useful subjects for calc. for example, trigometery is a precalc subject and you will use that for calc. though, if you really wanna skip precal and go strait into calc you might have a hard time but its doable

[proud raven]

yea i did not take precalc

did take trig though

[untold spindle]

i figure precalc is just made to brush up on math skills necessary for calc

<@&268886789983436800>

[inland shuttle]

Also interested if it is possible to do in a similar timeframe to this, if anyone can shed some light on it

[spark quiver]

ik do appriciate and i do aim to learn math and gain assistance, ik what i was doing but made an unwise choice.

and i like math anyways

but yeah thx

[viscid thistle]

Hello, I am currently in Algebra 2

However, i have plans to take precalculus over the end of the school year to end of summer, so I can take calculus senior year

However, the online course for precalculus I am taking does not seem to be very good, does anyone know a pre calculus course?

[slim steppe]

Khan Academy

or buy a book

There are others like Albert.io (costs money)

You can try organic chemistry

or just get a tutor

[viscid thistle]

I noticed AP Precalculus has a sheet of material that they will cover, but I am not sure how to exactly get those units

[inland shuttle]

Ngl as Daniel has said khan academy

It’s pretty good tbh

I’ve used it numerous of times and have helped me massively in learning content

[viscid thistle]

is there a section for precalculus within khan academy?

[untold spindle]

yeah

https://www.khanacademy.org/math/precalculus

[viscid thistle]

ok then

i will use khan academy

wonderful, i will you guys once im in the big boy classes!

[slim steppe]

Well

Calculus, algebra, it's all taught around the world. There's nothing really special about it

[viscid thistle]

True but the image depends on the location

Taking calculus where i live makes you seem like a “big boy” and ahead of your peers and its true even though there are still many who take it

[bronze summit]

Can someone explain the derivative of xtan^-1x

[opal tree]

Product rule

[bronze summit]

Using first principle

[solar olive]

so the limit?

[bronze summit]

ya lim f(x+h)-f(x)/h

I dont get it

[solar olive]

do u know that uh , $\frac{dy}{dx} \arctan(x) = \frac{1}{1+x^2}$

[obsidian monolith]

Impractical

[willow bear]

d/dx not dy/dx

[solar olive]

oops

my bad

[bronze summit]

nope im kinda new to diffrentiation

I just know the first principle for now

[tidal prism]

U can derive almost everything from the basic principle

[old isle]

How to prove a)?

[solar olive]

$\log_{\frac{1}{2}}(a^{\frac{1}{2}}) = -\log_4(a)$

[obsidian monolith]

Impractical

[solar olive]

u can break the log as fraction logs

$\frac{\log(a^{\frac{1}{2}})}{\log(\frac{1}{2})}$

[obsidian monolith]

Impractical

[solar olive]

$\frac{\frac{1}{2} \log(a)}{-\log(2)}$

[obsidian monolith]

Impractical

[solar olive]

$\frac{\log(a)}{-2 \log(2)}$

[obsidian monolith]

Impractical

[solar olive]

which then turns into $\frac{\log(a)}{-\log(4)} = \frac{-\log(a)}{\log(4)} = \log_4{\frac{1}{a}}$

from there i think u know how

[obsidian monolith]

Impractical

[old isle]

Ohh I got it

Thankkss

[coarse kernel]

lim as h -> 0 of ((sqrt(3) + h)arctan(sqrt(3) + h) - sqrt(3)arctan(sqrt(3))) / h = lim as h -> 0 of (sqrt(3)arctan(sqrt(3) + h) + h * arctan(sqrt(3) + h) - sqrt(3) * pi/3)/h = pi/3 + sqrt(3) * lim as h -> 0 (arctan(sqrt(3) + h) - arctan(sqrt(3))) / h
what I've just done is basically the product rule
the thing we're left over is basically arctan'(sqrt(3)), and its value doesn't just go simply from the limit, as it in fact uses a hard-to-prove inverse function theorem, so you'd just differentiate it and find its value

well, maybe there is some simple solution for it as x = sqrt(3), but I don't think so

https://en.wikipedia.org/wiki/Inverse_function_theorem#Methods_of_proof the first proof is hard to grasp and is in fact very technical, whilst the latter one employs topology, which is something you definitely don't know yet

[bronze summit]

thanks for the help
ill learn the product rule and try this problem again

[viscid thistle]

Anyone else hate log rhythm ughh

[north remnant]

@solar olive could you enlighten me on where I would learn how to type to allow the bot to format the questions properly?

[hushed sphinx]

There's a pretty comprehensive tutorial at https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference
MSE uses MathJax which is technically different software than the LaTeX our bot uses here, but the input languages are deliberately very similar.

[north remnant]

Thank you!

[foggy frigate]

Hello, so theres this part on my hw assignment not covered on my book and tmr is the exam.
It’s
If f(x)=px+q find f(0) f(1) f(3) f(-3)
I have no idea where to even start

I mean i know i have to plug it in
But q in a function isn’t covered in the book

[summer ruin]

well if I gave you f(x)=3x+2, how would you solve the same problem

does it really matter what q is besides being some number

[foggy frigate]

Yeth, because
If that was the case it’d be that f(0) =q
F(1)= 1+q
F(3)= 9+q
And f(-3)=9+q
But i only got f(0)= q right

Do i have to write in the xs?

I get 2 more attempts

[summer ruin]

again review what you would do in the case of f(x) = 3x+2

is there any x left? no, why should there be one in the case of f(x) = px+q

p, q are just numbers

it wouldn't make sense if we used letters instead of these symbols that we call numbers and our math changed

[foggy frigate]

If f(1)
f(1)=3(1)+2

So if f(1) for f(x)=px+q
Would it be
f(1)=p(1)+q then?

[summer ruin]

yes but you can simplify this further and get rid of unnecessary brackets

[foggy frigate]

Ahh okay I see, yeah the p and q was tripping me up, thank you.

Idk why i was multiplying now that i look back at it there wasnt a value for p 🤕 i might actually just need a hw break but fr thank you

[sharp halo]

hi

[obsidian monolith]

Craig

[viscid thistle]

?

[amber heart]

Im currently looking to find the missing EAN number in astericks. However, im not too sure on how to find the check digit

[storm lodge]

Yep

[sharp halo]

well in this case we need to know the volume

[north remnant]

Could somebody explain why in part B. the discontinuities are actually removable?

I don’t quite know how limits work yet, Sorry if my limits are incorrect.

[summer ruin]

because at a point left and right limits are equal, yet the function is defined with a different value

[north remnant]

Which point are the left and right limits equal?

[summer ruin]

limits for x approaching 2

[north remnant]

Ohh ok I see it now, thank you so much!

I thought you needed to make the limit x approaches 0 every time

In these cases

[wispy shuttle]

hiiiiiii

I wanted to ask.... ik there's a property that is like... If a function f(X) is odd and strictly increasing at X>0, then it will me strictly increasing at X < 0

does anyone know the proof?

(ping me if u know something)

[viscid thistle]

i think this is true for any function that is rotationally symmetric around x=0, which you get for free from f(x) being odd.

[viscid thistle]

Thanks

[wispy shuttle]

oh, thats cool

b-b-but... do u know a proof?

[viscid thistle]

it's just a few lines and i think it's useful to derive yourself lol -- what does the definition of oddness -f(x) = f(-x) tell u about the rate of change?

[wispy shuttle]

oh, yes I see it, if f(x) is positive, f(-x) will be negative, if f(x) is more positive, f(-x) will be more negative

[viscid thistle]

ya youve got the intuition for it

[wispy shuttle]

:D

[onyx garden]

Quick question, I can cancel e out with ln but I can't cancel e out with e correct?

[hushed sphinx]

Can you give an example of what you want to do?

One kind of valid cancellation is that if you know e^a = e^b (and a, b are real numbers), then you can conclude a = b.

[fringe sable]

how do i solve number 2 and what type of problems are these called so i can search for how to do them?

[opal tree]

Domain and range of functions

If you're doing absolute values and restrictions you should've been taught an introduction to domain and range

[fringe sable]

can you reccomend me a video with similar problems?

i tried searching what you said but i only found function and algebra problems

[bronze summit]

What do you know about domain and range?

domain is the of values that u can input
Range is the output of those values

In the question
5x-2y=2

U should just find values that can be put to satisfy the condition

for example U can input
x as 2 and y as 4

[fringe sable]

i think its review for me but i havent done it in a year and i forgot everything about domain and range

[bronze summit]

its quite easy actually U just need to know what to input to satisfy a condition
and the range is just the set containing all the outputs

[fringe sable]

i dont know how to do that

[bronze summit]

like if u input a random x value in this question

U get a y value

x value is domain

y value is range

[fringe sable]

ok

so i have 2 for x

and isolate y

right

[bronze summit]

Ya u can do that

whats the answer for that

[fringe sable]

and x >= 2 means that x must be greater than 2

[bronze summit]

Yaa thats how u do it

[fringe sable]

thanks i got it

[bronze summit]

np :p

[chilly hazel]

$\text{is } x^2 \frac{dy}{dx} \text{ equivalent to } \frac{d}{dx} x^2 \text{ and } x^{2^{\prime}}$

[obsidian monolith]

Price

[uncut mulch]

no

[viscid thistle]

Is pre calculus fun

[pseudo hamlet]

Do you like math

[untold spindle]

depends on if you think algebra is fun lol

[viscid thistle]

Oh boy do i

[untold spindle]

then youll most likely find precal fun 🙂

[viscid thistle]

Will i use it in chem?

[untold spindle]

I have not taken much chemistry so I wouldnt know

[viscid thistle]

Oh

[pseudo hamlet]

I'm taking AP chem rn and I've only had to use basic algebra

[untold spindle]

same, though i wouldnt be surprised if precal or even cal shows up later on

[pseudo hamlet]

ye but that'd probably be if you major in chemistry

although they briefly bring up the concepts of derivatives and integration

[lucid trench]

chemistry at the high school level requires probably mostly arithmetic

[chilly hazel]

can someone explain what this part is asking me to do

i do not understand the notation

[untold spindle]

this is called the quotient rule for the derivitive

it can be read as v times the derivative of u minus u times the derivative of v

[chilly hazel]

ahh that is easier to understand

thank you

[untold spindle]

np 🙂

[slim owl]

Where does trig end and precalc begin?

[viscid thistle]

Hi, I have been given the question.

Find the electron configuration for Ar and Ar+

What is Ar+ ? I know Ar is Argon..

[untold spindle]

this is chemistry. you would prob have a better time puting it here. https://discord.gg/eexdsFw

[viscid thistle]

There are no channels even in there

[slim steppe]

Basically it’s asking you for the number of electrons in each “shell”

[opal tree]

Argon is a noble gas

Ar+ means it got oxidized

Aka lost an electron

[slim steppe]

Cation

[viscid thistle]

How to do it

[lofty juniper]

the order of electron levels goes 2,8,8,18,18, etc. Since argon is in the 3rd period on the table, it is going to have three levels in the electron arrangementand since it is in the final group, that means it will have a filled valence level meaning the electron arrangement will be 2, 8, 8

and if it is Ar plus 1, that means it has lost one electron (since electrons are negative and 0- (-1)= +1) which means it would have an electron arrangement of 2, 8, 7

hope that helps though its not precalculus lol

[tepid narwhal]

guys how do i find arctan(-sqrt3/2)

[fringe sable]

how do i get the answer for these questions?

the answer for 1 should be D {x|xER} and R {y|yER}

answer for 2 should be D{x|x=2, xER} and R{y|y >= 4, yER}

and can someone reccomend me a video with questions and answers similar to these so i can study them?

[visual torrent]

Ar+ means it got charged(it lost an electron) +1 mean it lost one electron +2 means it lost 2 and so on,
since argon is a noble gas it normally has 8 valence but since Ar+ lost an electron it has 7 valence electrons.
So, the configuration for Ar is 2,8,8 and Ar+ is 2,8,7

this Isnt math related but yea

[inland shuttle]

So the electron configuration for Argon: Argon has 18 electrons thus 1s^2 2s^2 2p^6 3s^2 3p^6 , or you can put it in a short hand as [Ne] 3s^2 3p^6 as the neon will represent the electrons from the 1s orbital to the 2p orbital. Ar+ will just be 1s^2 2s^2 2p^6 3s^2 3p^5 with one less electron in the 3p orbital. Meaning the short hand will also be [Ne] 3d^2 3p^5. To remember how to do this next time, it is useful to remember how many electrons each orbital can hold.

[hushed sphinx]

Let's stick to math here.

[viscid thistle]

Thats great use to me as well thanks

[ripe grove]

any youtube channel which teaches precal

in easy manner

i know organic chemistry tutor, for one

but its only one

[slim owl]

What is usually the cutoff subject of where trig ends and precalc begins?

[slim steppe]

There's math in everything but this isn't pre calculus or anything just basic algebraic manipulation

[slim owl]

Was that towards me or

[slim steppe]

Tropo

[slim owl]

Ah

[viscid thistle]

Hi guys. As far as I know limit of |x| when x approaches 0 is undefined. Why?

[quartz inlet]

How?

Uh u might be somehow thinking of the derivative?

[slim steppe]

Its 0

[viscid thistle]

I've heard an explanation which I did not understand. When we approach 0 from the positive numbers we get the positive zero (+0) and when we go from the negative ones we get the negative zero (-0). -0 ≠ +0

[quartz inlet]

There is no negative or positive zero.

[slim steppe]

There's no such thing as positive and negative zero

[quartz inlet]

They’re the same zero

[viscid thistle]

Then, there is no way for the lim |x| when x->0 to be undefined, right?

[quartz inlet]

Well I guess it depends on the context if you want to be formal, but yeah

Like in almost all cases this is taken to be zero

[patent breach]

ik this is the wrong channel but can someone help me with pre algebra

[viscid thistle]

Cheers I figured it out

[inland shuttle]

No worries

[viscid thistle]

Can you help with this? I created the volume function for the first part, would the domain be all R because it is a polynomial function? The reason why I am hesitant on that is because x can only go to 40cm until no more cupboard is left..

[inland shuttle]

I am afraid my skills end at mathematics. I’m just a biomed major trying to relearn and learn mathematics and CS from the ground up so I can go into systems biology/computational biology one day

[woven roost]

hello can anyone help me with a calc question

[viscid thistle]

Actually I figured it out now!

[viscid thistle]

What question?

[inland shuttle]

I’m glad

[woven roost]

they are true or false

i think a is false

[viscid thistle]

c is true

[woven roost]

where is that spot

[viscid thistle]

d is false

[viscid thistle]

0,2

[woven roost]

ah I see

[woven roost]

e is false right?

[viscid thistle]

e is false

yeah

a is true

[opal tree]

!nosols

[tender quest]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[north remnant]

Could somebody please explain what I did wrong? The tangents slope is suppose to be -1/4… I got that there is no tangent in the curve.

[north remnant]

<@&286206848099549185>

[viscid thistle]

what?

[opal tree]

Read this @viscid thistle

[viscid thistle]

Omg i am so sorry

Oops

[north remnant]

Finally found my mistake, geez it’s the simple things..

[turbid scroll]

<@&286206848099549185> How do I solve this problem?

[chilly hazel]

why isn't d/dx [y^3] = 3y^2

it is 3y^2 dy/dx

[turbid scroll]

for which problem?

[chilly hazel]

sorry, was my problem

i do not understand it

[wheat flame]

its kinda like chain rule.

ur not given that y has a relationship with x or somethin

looks like chain rule tho

ye its not dy/dx (y^3)

so it wouldnt be 3y^2 by itself

[chilly hazel]

all the different notations for derivatives confuse me

[wheat flame]

ye its mad weird

[eternal cargo]

Yawn*

[snow flare]

What would this mean to you? It's not some different notation.

[snow flare]

What notations have you learned?

[viscid thistle]

What if you have a disconnected function or a piecewise function