precalculus

[uncut mulch]

yes exactly

[silver musk]

but by removing the factor

it works

[uncut mulch]

hence 1 isn't part of the domain

[silver musk]

but it is

tho

[uncut mulch]

no its not

[uncut mulch]

desmos doesn't explicitly show holes at a glance

[silver musk]

sheesh

[uncut mulch]

hover your mouse over where x=1

and an undefined circle should popup

[silver musk]

oh wait how

do i enable that

[uncut mulch]

manually do it

drag your mouse along the curve

[silver musk]

damnn so

in that case it doesnt contribute to an asymptote

[uncut mulch]

(x-1)/(x^2-4x+3) behaves pretty much exactly like 1/(x-3) except at x=1 where it is undefined

[silver musk]

damn thanks man so now how do i know wether its a hole or asymptote

if its 0/0

?

[uncut mulch]

consider what the expression would simplify to (if you were to disregard domain issues)

[silver musk]

but if its a/0

then it an asymptote?

if it 0/0 it a hole?

[uncut mulch]

ugh...

too vague

[silver musk]

true

but for the case

of rational functions

would it be true?

[uncut mulch]

for this case:
(x-1)/(x^2-4x+3) = 1/(x-3) for x \neq 1.
there would be a hole at x=1
and you should see that x=3 would be a vertical asymptote from 1/(x-3)

[silver musk]

i see but what would be the key discriminant

between a hole and asymptote

wether its 0/0 or a/0

?

[uncut mulch]

wdym by 0/0 or a/0

[silver musk]

like when i put x=1 i get 0 for both numerator and denominator but when i put x=3 i just get 0 for bottom

[uncut mulch]

like i said earlier that's too vague

and won't be applicable to something like
x/x^2

[silver musk]

but considering the case for raitonal functions

oh

i see

[uncut mulch]

which is why you should simplify and state the restrictions being applied

[silver musk]

thanks man

much appreciated

idk i feel like these ideas are neglected in my highschool math system

[dapper chasm]

How do i find the point in time where there only where 25000

Should i put 25000 in x?

[pulsar raven]

Maybe you plot the function f2(x)=25000
Are you using the Ti Nspire CAS?

@dapper chasm

[dapper chasm]

Yes

Is it did it differently and got 6.37531 but i guess they just rounded up the number

if you plot it

[pulsar raven]

yeah they round it

you did it with solve right

[dapper chasm]

Yes

[pulsar raven]

👍

[dapper chasm]

Is there a easy way in TI to chose the growth rate

@pulsar raven

[pulsar raven]

What do you mean by the choice of growth rate?

[dapper chasm]

I worded it wrong

If i wanna use choose the growth rate to the time 15

If it makes sense

[pulsar raven]

there is section called analyse the graph

And in this section there is

And then you can enter number where you want to have the growth rate

[dapper chasm]

I can only click on the graph

How do you get choose them?

[pulsar raven]

click on menu in graph menu

[dapper chasm]

yea

[pulsar raven]

on the calculator

[dapper chasm]

I dont understand

[pulsar raven]

are you on the handheld or on computer?

[dapper chasm]

Computer

[dapper chasm]

ok

I clicked on menu

[pulsar raven]

Then you find:

@dapper chasm did you find it?

[dapper chasm]

YEah

[pulsar raven]

nice

[viscid thistle]

Can someone help me with some calculus homework?

dm me

[nimble storm]

is the endpoint of a given interval considered an exrema?

[pulsar raven]

not everytime only when it is the greatest or smallest point

[nimble storm]

ok ty

[fallow storm]

Can anyone walk me through this proof? I changed both the csc and cot to their reciprocals I just don't know the next step

[fallow storm]

<@&286206848099549185>

[silver musk]

can someone help me solve this i can utilise logs laws but i get an equation set to zero with irrational exponents

whats the method to solve functions like this with such expoenents

[uncut mulch]

did you type the question correctly?

that's ugly af

you can use calculus and/or graphing to get an approximate solution

[silver musk]

i know

is there some way of doing it algebraically

like some function

[proper pilot]

how do I approach these type of problems?

[paper zenith]

ya need to do the thingy with arclengths n stuff

Note down the information you know:
length = something
Diameter = 22 (radius = 11)
want to find angle

$$\theta \times r = arclength $$

[obsidian monolith]

Doodaide

[paper zenith]

but theta must be in radiams

[placid ledge]

good old $s = \theta r$

[obsidian monolith]

keto11

[upper frost]

Change of base rule?

[silver musk]

yeh i tried that and got a polynomial with an irrational exponent (a log)

idk how to solve

[spark lance]

I'm trying to find the inverse, and not sure how to determine what x should equal once I square both sides

also the correct answer is different, here it is

[hushed heart]

those two statements are equivalent

negate the numerator and the denominator of either expression and you get the other one

[spark lance]

oh I see it now, thank you!
how do I get the -1 < x <= 1 though? @hushed heart

[hushed heart]

the domain of an inverse is the range of the original, and vice versa

[sterile wedge]

Can someone please help me with question 23? I got A= 1.221 * 9 in but the answer key says its wrong

[uncut mulch]

you have rounding issues probably.

[sick steppe]

what's the dot of 2 orthogonal vectors?

no

$\vec{a}\cdot \vec{b} = \sum_{i}a_ib_i$

[obsidian monolith]

moshill1

[sick steppe]

$\vec{F}\cdot\vec{d} = Fd\cos{\theta}$

[obsidian monolith]

moshill1

[vale urchin]

sorry I dont know F or d

[sick steppe]

F is the force, d is the displacement/distance, theta is the angle between those vectors

[vale urchin]

54 newtons is force

and d I dont know

[sick steppe]

d is what you're trying to find

[vale urchin]

so start with joules

1430.4/54?
for d?

[sick steppe]

$W=Fd\cos{\theta}$ you have W, F, and theta

[obsidian monolith]

moshill1

[vale urchin]

ohhh wait so isolate d

[sick steppe]

yes

[vale urchin]

so would it make sense to have W on top of Fcos(theta)

[sick steppe]

yep

$d=\frac{W}{F\cos{\theta}}$

[obsidian monolith]

moshill1

[vale urchin]

so 1430.4/54*cos(28)

[sick steppe]

but yes

[vale urchin]

in degree form

[sick steppe]

yep

[vale urchin]

I get 30.00052223

[sick steppe]

yeah, so 30 (units)

[vale urchin]

that would be in m?

[sick steppe]

yep, cause d is a distance

[vale urchin]

Nm is not a thing?

[sick steppe]

and SI units of distance is m

Nm is units of W

[vale urchin]

oh

[sick steppe]

N*m since F has units N and d has units m

we just define N*m to be called a Joule

[vale urchin]

is this the same thing?

finding joules?

[sick steppe]

same formula, yes

[vale urchin]

why did they do 52 pounds?

[sick steppe]

Read the stuff before the question again

[vale urchin]

units for work is foot-pounds

[sick steppe]

yes

[vale urchin]

so its just 60 * 52 /cos(47)

[sick steppe]

[W]=feet-pounds if d is in feet and F is in lbs

why are you dividing by cos(47)?

[vale urchin]

because isolate

oh

isolate F?

no because we need work

[sick steppe]

What are you looking for in the question?

[vale urchin]

work

[sick steppe]

Yeah, what's the formula for work?

[vale urchin]

work = f*d

[sick steppe]

$W=Fd\cos{\theta}$

[obsidian monolith]

moshill1

[vale urchin]

oh and cos

so 60*52 is F?

[sick steppe]

52 is F

60 is d

52 pounds 60 feet

[vale urchin]

why did I get confused like that?

[sick steppe]

[vale urchin]

the foot-pounds should be 2127.834883

[sick steppe]

yep

[vale urchin]

ty

🙂

[crystal osprey]

I'm kinda confused on how there's 2 types of inverses

1 type of inverse function is the actual inverse of a function.
f(x) = x^2-5
f^-1(x) = +-sqrt(x+5)

And the other type of inverse is just... isolating the other variable

[hushed heart]

i'm not sure i follow

[crystal osprey]

in this case they both are the same

But the normal way to get an inverse is to swap the independent variable with the dependent variable, then isolating the dependent variable.

[hushed heart]

that's what happens in the example you gave

[crystal osprey]

yes

But the other type of inverse that I'm seeing getting thrown around is just... flat out isolating the independent variable to turn it into the dependent variable

Wait a second both of them should yield the same equation regardless, just with different variables representing them, now I'm really confused

Because I'm getting different results with other equations

[hushed heart]

you mean they isolate for x and then swap at the end?

it yields the same result

[crystal osprey]

I'm really not sure how to explain it

[hushed heart]

can you show me an example of where you are getting different results?

[crystal osprey]

I can't find the question now but it was a exponential equation

maybe I just... did it wrong

[hushed heart]

regardless of what method you choose, it should give you the same answer

[obsidian monolith]

Dr

[crystal osprey]

Hm, if I notate f(x) as y, then x=+-sqrt(y+5)

seems to be the same

[hushed heart]

yes

[crystal osprey]

Ig I just did that question before wrong then, damn

Thanks for helping with the trouble

[hushed heart]

[remote storm]

how do we know that we have to check for left and right limits for this function? / in general?

[remote storm]

alright! thanks

[silver musk]

is that one a DNE?

[crystal osprey]

Yes

The 6 is irrelevant because 1/x^3 will always give a different side of infinity depending on the direction it approaches 0

[tough hemlock]

Can someone help?

Dark blue right?

[dark sky]

how to find t intersept without graphing

[magic mantle]

Yes

[magic mantle]

Ok so t^3 -4t^2 + 2t + 4 = 0

You can try some numbers for t that seem to work.
I found t = 2.

For example

So you know that (t - 2) is a solution.

Then you can factorize. So,
(t - 2)(t²-2t-2) = 0

And I think you are able to solve it now.

[glass dagger]

if a sine graph looks like an oscillation like an orbit or something what does an absolute value graph look like what does the V graph shape an example of?

[worn anvil]

I got this wrong, and I am unsure of the correct answer. The only thing I know for sure is that the Amplitude is 2 and the sinusoidal axis is prolly 2 as well

So could anyone help me out? Thanks!

[lilac storm]

can anyone please help me with this question?

[elder charm]

What are the derivatives you got?

[lilac storm]

so the velocity eq would be s=32t

right?

[elder charm]

yeah

well, no

velocity isn't s, after all 😛

[lilac storm]

oh?

isn't it the derivative of the eq?

[elder charm]

your right side is right, yes, but the derivative of distance is velocity, not distance again 🙂

[lilac storm]

so v=32t?

[elder charm]

yup

[lilac storm]

so how do i calculate the velocity after getting the derivative?

is it setting 32t equal to 1296, meaning 1296=32t?

which gives me 40.5

is this correct what i just said, or no?

[elder charm]

to calculate the impact velocity, you need to substitute the impact time into the velocity equation

and the time you can get from the distance equation, setting it to the right distance

is it setting 32t equal to 1296, meaning 1296=32t?
No. This is why I don't like formulas without units - if there were actual dimensions here, you'd immediately see it is wrong, because you're trying to make a velocity equal to a distance.

[lilac storm]

so your saying finding the time, so do i solve for time by doing 1296=16t^2 and just rearranging it and finding the answer?

which gives me 9

[elder charm]

yup

and that time you can plug into the velocity formula

(and the acceleration formula, but the acceleration here happens to be constant all the time)

[lilac storm]

so the acceleration would be 32, right?

[elder charm]

yup

[lilac storm]

ok, thank you so much for your help, i really appreciate it.

[knotty echo]

does anyone know the formula to calculate vector projection for 3d vectors

[sick steppe]

$proj_u(v) = \frac{v\cdot u}{u\cdot u}u$

[obsidian monolith]

moshill1

[sick steppe]

@knotty echo

[solemn oxide]

need help putting this into factored form

[vale urchin]

<@&286206848099549185>

[quartz lance]

Given y = 25 - x^2 how would I find the points at which it crosses the X axis and the turning point of the line

Nvm got it

[cedar eagle]

can anyone help out?

[worn anvil]

Need help finding this

[lilac storm]

so i have started off this question by first taking the derivative of the eq

then i set the derivative eq equal to 0 and solved for the x's

i want to ask that have i done this question correct so far and what do i do next, i'm a little confused?

i think i got it but i just want to make sure, so the x-ints that i get of the derivative are 9 and -5/3

so i ignore -5/3 and take 9 and substitute it into the original eq which gives me 582

and here i have double checked by using desmos

and you can see the point (9,582) is the max

so i want to ask that have i done everything correct?

[hallow thunder]

@lilac storm if this involves working out you need to find the second derivative and use that to prove that x=9 is a maximum point (2nd derivative < 0)

[elder charm]

alternatively, you specifically need to know that the point you found is where the derivative goes from positive to negative. You know that automatically, though, because the derivative is a parabola with negative main coefficient, so first root of the derivative is a local minimum and the second is a local maximum.

[tall basin]

any clue how to do this?

particularly b

[elder charm]

find the time when they are in the same position, substitute into the formula for velocity

[lilac storm]

can anyone please help me with this question?

[elder charm]

Write down the formulas for the total surface area and volume of a cylinder based on its radius and heigth. Minimize the area while keeping volume constant.

[lilac storm]

yeah so how do i do that?

so like how do i minimize the area?

so i have the formulas for the surface area and volume so how do i use them?

are you there?

[fallow slate]

volume for a cylinder is (pi)(r^2)(h) and you know that the volume is 36 cubic inches

therefore you can set them equal to each other

the second thing you should do is rewrite the equation for surface area in terms of height

you should get "h = " and so on, then you plug that into the volume equation

you should graph that to find the local minimum

[lilac storm]

yes so the first thing that you just told me so i get 36=(pi)(r^2)(h)

so my question is do i take the derivative or anything like that or do i just keep it like that?

and i'm still confused about the second thing.

how do i..?

[fallow slate]

hold on let me try to solve it

ill get back to you really quick

[lilac storm]

yes absolutely.

[fallow slate]

wait do you have an answer key?

[lilac storm]

yes

[fallow slate]

so for the radius I got 1.789

if thats the right answer i can show you how i got it

[lilac storm]

yes, that is correct.

[fallow slate]

alright, my first step was to find an expression for h, or height

i used "36=(pi)(r^2)(h)" and converted it into "h = 36/(pi)(r^2)"

the equation for surface area (which is what we're trying to find) is "y = 2(pi)(r)(h) + 2(pi)(r^2)"

you can now substitute "h" into the surface area equation so that you only have one variable on the left side, which is "r" or radius

eventually you'll get "y = 72/r + 2(pi)(r^2)"

i think the only way to find the minimum is to graph it

using the value for r you can then find the height

[lilac storm]

so sorry, what is the value for r?

[fallow slate]

it is 1.789

[lilac storm]

oh

[fallow slate]

or the x-value for the coordinate point shown above

[lilac storm]

and then i sub it into which eq?

[fallow slate]

oh... good question actually

oh i know

you plug it into "h = 36/r^2"

[lilac storm]

do you mean h = 36/(pi)(r^2)?

[fallow slate]

yes of course, my bad

[lilac storm]

ok, thank you so much for your help.

[fallow slate]

yup, no problem

[tall basin]

anyone know how i can solve for this

i tried to take derivative of the are but it did not meet the >100 requirement

[sterile wedge]

can someone please help me with a section of my math homework. I've been trying to figure it all out and watch youtube videos but I still don't understand it. I have a quiz on it tomorrow and I am stressing because I haven't been able to figure out after 3 hours of trying. I am willing to voice chat and screen share or we can do it over text. Examples of what I have to do are - find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse, to evaluate each trigonometric function of angle A, exercises, solve for the unknown sides of the given triangle, exercises, use a calculator to find the length of each side to four decimal places, Finding x of a triangle, and then real world applications of it. We can do a problem for each one so I can figure it out and do the rest myself so it doesn't take long for us to do.

[uncut mulch]

can you post a specific question you're struggling with here

[odd rivet]

@sterile wedge use the sin rule

[uncut mulch]

start with drawing a generic right triangle right angled at C

[zinc plank]

yo

so

why is logarithm and root different? i dont see a difference, but they are different for sum reason

[viscid thistle]

..what?

are you asking why in other words, log(x) and sqrt(x) are different?

[zinc plank]

yea

[pliant locust]

We need to explain to him what a function is

Obv, for some inputs x they aren’t mapped to the same output

That is what makes them different

[pliant locust]

https://youtu.be/52tpYl2tTqk

[viscid thistle]

yeah, which can also be seen graphically:

,w plot sqrt(x) & log(x)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by Al𝟛dium#4084

[zinc plank]

oh what

[viscid thistle]

(you are only interested in the first graph on your case)

[pliant locust]

,w plot log_2(x) & sqrt(x)

[viscid thistle]

,w

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by rts#2928

[zinc plank]

what does "," mean?

[viscid thistle]

just so that the bot renders the graph

nothing math related.

[zinc plank]

oh

[viscid thistle]

did you read what was being said?

[zinc plank]

yea

alr so u said like they have different outputs? but those functions are even different

oh wait

[pliant locust]

For some x they the y values are pretty close but they aren’t the same at all

[zinc plank]

interesting

so

in which scenarios should i use each

oh wait i think i know

so root is like x^b

or not

[viscid thistle]

that's an incredibly vague question and you aren't probably going to be answered what you want to be answered, may you rephrase the question?

[pliant locust]

log_2(y) is like asking the function for what x should I raise 2 with to get y?
2^x = y
Is the same as
log_2(y) -> x

If I have 2^3
Log_2(2^3) outputs 3

Log_2 will output the exponent of 2 that is the solution to
2^x = some number

[zinc plank]

so root is like getting the original num and log is getting the power to raise to?

oh wia

tn

[viscid thistle]

that's a big missconception about functions in general

[pliant locust]

Root is asking the function “what two number to multiply with each other to get y”

[zinc plank]

hmm

[zinc plank]

isnt that sqrt?

[pliant locust]

Yeah root

Squareroot

[zinc plank]

ah

[viscid thistle]

there are more numbers other than 4 or 9 which the sqrt maps a nice value as in 2 and 3.

[zinc plank]

wait so like root is getting the x in x^b right?

and log is the b

[pliant locust]

Yeah!

[zinc plank]

yooooo

[zinc plank]

wait wot

[pliant locust]

That is true aswell what aledium is saying

[viscid thistle]

what?

[zinc plank]

idk

[viscid thistle]

that's a big no if i'm understanding your question correctly

[pliant locust]

If b is two then squareroot will give you the x

[viscid thistle]

by any means, at all, it is said that for x^b, the sqrt(x^b) will give you just x everytime, that's a huge missconception again.

[zinc plank]

welp

so

what is the

thing

[pliant locust]

Aledium is highlighting something important

For example, squareroot of 4 when sqrt is an operator

[zinc plank]

i still need to process that

[pliant locust]

What is it equal to?

2 right?

[zinc plank]

e

*ye

[pliant locust]

But

-2 is a solution aswell

[zinc plank]

oh yea

i think i kinda get the difference nao

[viscid thistle]

what?

[zinc plank]

me?

[viscid thistle]

sqrt(4)=2 and not -2 nor any negative number.

[pliant locust]

Only if we are talking about it as function

If we have sqrt as operator

Sqrt(4) is -2 and 2

[zinc plank]

wait but why is that invalid for a func?

[viscid thistle]

this is only going to confuse lyc even more, and that's pretty irrelevant to what they are learning.

[zinc plank]

cant u pass in -2 as well?

[pliant locust]

I will raise my hands, I assume I misunderstood you aledium

[zinc plank]

btw what do u learn in precalc?

i think my school call it stats or smth

[viscid thistle]

don't know about the us curriculum since i'm not us, so..

[zinc plank]

ah

[pliant locust]

Either way to sum up,
For positive x:
$$\sqrt{x^2} = x$$
$$\log_{2}{2^x} = x$$

[obsidian monolith]

rts

[zinc plank]

yea thx goys

ye

[obsidian monolith]

lyc

[lilac storm]

can anyone please help me with this question?

[sick steppe]

what do you need help with?

[lilac storm]

yeah so basically i don't understand this question at all, like how do i start this question and how do i solve this question?

[sick steppe]

do you know how to do optimization questions?

[lilac storm]

yes

[sick steppe]

ok, so what's the constraint? (ie what has to remain constant?)

[lilac storm]

it says that the capacity is 36 and it has to be constructed with the least amount of material.

are you there?

[sick steppe]

yeah I was waiting for what had to remain constant

not restating the question

[lilac storm]

oh, ok

is it the radius and height?

are you there?

are you there?

[jolly raven]

moshill headed out

lol

[lilac storm]

can you help me with this question?

anyone there that can please help me with this question that i have posted above a little while ago?

[copper musk]

what has to be minimized?

[lilac storm]

this is the question i need help with PROnoob

[copper musk]

yes i know im asking you

what will u minimize

[lilac storm]

oh

is it the radius and height?

[copper musk]

both?

their sum?

[lilac storm]

i'm not sure?

[copper musk]

their product?

you see they have said you need the least amount of metal

[lilac storm]

right.

[copper musk]

so what should be minimized?

[lilac storm]

the metal?

[copper musk]

and what does that mean

how will you minimize that?

[lilac storm]

uh, i'm not sure?

[copper musk]

what do you think?

[lilac storm]

can you please explain to me like how do i start off the question, maybe that can help me because i'm not understanding based on the words, if we can start off the question so then maybe i get it then?

like how do i start mathematically*?

[copper musk]

you need to know what needs to be minimized and what remains fixed

[lilac storm]

oh

[copper musk]

this is given in the problem

but you need to read the question carefully to figure that out

[lilac storm]

so fixed is the capacity which is 36

and i think the amount of metal is the thing that needs to be minimized.

am i right?

[copper musk]

yes this is correct

[copper musk]

yes but what do you mean by 'amount of metal'?

[lilac storm]

the radius and height?

[copper musk]

?

what does 'radius and height' mean?

the sum of radius and height?

[lilac storm]

radius times the height?

[copper musk]

hmm

this is correct

[copper musk]

but why did you say this?

[lilac storm]

because the formula of a cylinder whether the volume or surface area, the radius and height are being multiplied.

[copper musk]

ya right

but in volume its radius squared times height

[lilac storm]

yes

[copper musk]

so are we minimizing volume or surface area?

[lilac storm]

hmm

[copper musk]

what is 'capacity' here?

[lilac storm]

the amount that can be taken

[copper musk]

and how is it measured?

[lilac storm]

surface area?

[copper musk]

nopee

its the volume

[lilac storm]

oh, ok

[copper musk]

so what are we minimizing?

[lilac storm]

the volume

[copper musk]

think again

[lilac storm]

the surface area?

[copper musk]

yess

ok so you know how to differentiate and stuff right?

[lilac storm]

yeah but if you can help me start off?

[copper musk]

ok so what is fixed here?

[lilac storm]

36, which is the capacity

[copper musk]

and capacity is the...?

[lilac storm]

volume

[copper musk]

yes

so you know that volume is fixed at 36

[lilac storm]

so to start off, do i write 36=(pi)(r^2)(h)

[copper musk]

yep

and you need to minimize the surface area

[lilac storm]

then do i isolate h which gives me 36/(pi)(r^2)=h

are you there?

[copper musk]

yes you can do that

[lilac storm]

so then i take the surface area formula and plug in what h equals which is above.

[copper musk]

yes

then you will get surface area as a function of r alone

[lilac storm]

yeah so i have y=72/r + 2(pi)(r^2)

[copper musk]

where did the + come from

[lilac storm]

so the SA formula is 2(pi)(r)(h)+2(pi)(r^2)

the + in the middle

[copper musk]

oh okk

right

[copper musk]

okay so what do you do next?

[lilac storm]

yeah, now i am stuck again

i'm not sure what to do next?

[copper musk]

you need to minimize y

what will you do?

[lilac storm]

i'm not sure?

can you tell me the next step, then i might know from there?

[copper musk]

differentiate y

[lilac storm]

oh

so is it this y' = -72/r^2 + 4(pi)(r)dr/dx

[copper musk]

dr/dx?

you differentiate y wrt r

so dr/dx is not needed

[lilac storm]

so is it just y' = -72/r^2 + 4(pi)(r)?

[copper musk]

yes

so if you are at the minima of y what is y'?

[lilac storm]

the minimum?

[copper musk]

y is minimum

so what is y' at that point?

[lilac storm]

0?

[copper musk]

yes

[lilac storm]

so now do i set the derivative eq equal to 0?

[copper musk]

yes

[lilac storm]

so how will i be isolating this eq, if you can help me out a little bit?

do i isolate r?

are you there?

are you there?

[copper musk]

you need to find the value of r

this gives r where the SA is minimum

[lilac storm]

yeah so i started off by doing 72/r^2 = 4(pi)(r)

[copper musk]

find r from this equation

[lilac storm]

so i basically brought the -72/r^2 to the left side which makes it positive

[copper musk]

?

[lilac storm]

sorry, find r from which eq?

[copper musk]

this one

[lilac storm]

yeah so i am now left with 72/4(pi) all of it under a cube root = r

is this correct?

[copper musk]

ya

[copper musk]

.

[lilac storm]

so i have 1.79 =r

is this correct?

[copper musk]

idk the exact values

[lilac storm]

ok anyways so now do i plug in the value of r into 36 = (pi)(r^2)(h)?

are you there?

[lilac storm]

are you there?

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

I really appreciate it

[round quest]

how do i prove sin^2t/tan^2t=cos^2t

[pliant locust]

Recall that
$$ \tan(x) = \frac{\sin(x)}{\cos(x)}$$
$$ \tan^2(x) = \left( \frac{\sin(x)}{\cos(x)} \right)^2 $$

basically rewrite tan as a fraction of sin and cos and start from there

[obsidian monolith]

rts

[pure creek]

@here can I have help with this?

[proud raven]

theres a great formula for this

it involves the mins and maxes of the exponents

and is super worth memorizing

but i dont have it memorized so gimme 1s

does that make sense

[pure creek]

@proud raven gotcha I'll try to use that

[warm lintel]

Am I right in assuming that the Latus Rectum of a parabola is the points at which the parabola intersects the line symmetrical to the vertex relative to (0,0)?

[pure creek]

I'm not exactly sure how to use this

[proud raven]

you have two numbers in prime factored form

say like uhh

look at easier numbers

say $20=2^2 \cdot 3^0 \cdot 5^1$ and $90=2^1 \cdot 3^2 \cdot 5^1$

[obsidian monolith]

jan Niku

[proud raven]

see if you can figure out gcd by thinkin

but check out the 2's

we have one to a power of 1, and one to a power of 2

so our gcd will have 2^1

we can do the same for each prime factor, and get $2^1 \cdot 3^0 \cdot 5^1 = 10$

[obsidian monolith]

jan Niku

[proud raven]

see, we just took each prime factor, compared to see which is lower, and used that

make sense?

[proud raven]

.

[pure creek]

Ok I just don't know how to apply it in the context of the problem

@proud raven

[proud raven]

? use it in the way i described

compare exponents

[pure creek]

ok

So I simplified the exponents and got 3^2 5^1 and 13^1

[faint nest]

Please someone just

Help

[bold lintel]

Is there an easier way of digesting this besides creating a table like my "help me" tab gave me? Plugging in these variables gives me decimals

[viscid thistle]

@bold lintel do you still need help?

[bold lintel]

sure @viscid thistle

[jolly gust]

Yo can someone help me with this

[viscid thistle]

@bold lintel ok you there?

I need help with some problems anyone here to help?

[stable yacht]

You know can solve for the hypotenuse (using Pythagorean Theorem) and write the functions from there.

I think that is what the question is asking.

[viscid thistle]

@vale urchin don't multipost. please read #❓how-to-get-help

[lilac storm]

can anyone please help me with this question?

[lilac storm]

is anyone there that can please help me with this question that i posted a little while ago?

anyone there to help...?

[viscid thistle]

i would try to but my brain aint big enough

[lilac storm]

no it's all good, if you could help me with the the question posted above?

[lilac storm]

Amaxx, is it possible if you could help me with the question that is posted above?

[viscid thistle]

this one?

[lilac storm]

yes, exactly

[viscid thistle]

wouldnt u just multiply 10,000 by 5?

[lilac storm]

uhm, how did you get that?

[viscid thistle]

since every bottle is $5 and u sold 10,000 bottles

[astral mantle]

you produced at least 10,000

you need to create a function for profit with what you are given

and maximize said function

[lilac storm]

Star, if you can please help me on how to create a function then maybe i get it and it becomes more clear?

[lilac storm]

like if you can help me on how to start off the question, what do i do to start off the question?

[astral mantle]

Make a function P(x) to express profit in terms of wine bottles sold

you have P(x) = (amount of bottles)(price at x bottles)

[lilac storm]

would this be correct, P(x) = (10000)(5x)

[astral mantle]

no

you need to consider reducing cost

every bottle past 10,000 decreases price per bottle by 0.0002

[lilac storm]

uh, is this ok now, P(x) = (10000+5x)(10000-0.0002x)?

[astral mantle]

closer but still wrong

whats the total number of bottles?

starts at 10,000 and increases by x bottles

[lilac storm]

i'm a little confused?

[astral mantle]

you are starting with 10,000 bottles and adding x bottles

[lilac storm]

so is it, P(x) = (10000+x)(10000-0.0002x)?

[astral mantle]

closer

now you need to work on price per bottle at x bottles

the starting price is 5 per bottle

and decreases at 0.0002 per additional bottle

[lilac storm]

can you give any other hints or information because i'm still confused and stuck?

[astral mantle]

P(x) = (10000+x)(function to express price per bottle after 10,000 bottles)

[lilac storm]

so, P(x) = (10000+x)(5-0.0002x)?

[astral mantle]

yes thats correct

Now just distribute and maximimze

[lilac storm]

so i don't have to take any derivative or do anything like that?

[astral mantle]

maximize by taking the derivative lol

[lilac storm]

oops, sorry

[astral mantle]

take the derivative set it equal to zero find the maximum with second derivative test

substitute back into the original

[lilac storm]

yeah yeah, sorry about that

[lilac storm]

thank you so much for your time and help.

[pastel carbon]

Can I get help with this?

(x-6)/(x^2-4) ≥ 0

I have to solve it algebraically

But I’m kinda confused because my answer is in interval notation

[quick mirage]

@pastel carbon Try making an interval chart then

And determine intervals where the resultant rational function would be >= 0, respecting any restrictions given.

[pastel carbon]

I ended up being able to solve it on my own (: I appreciate it

[valid estuary]

could someone help me out with this problem? I keep getting 0 but apparently it's 1/2

[uncut mulch]

how are you getting 0

[valid estuary]

Let me write out my work neatly hold on

[uncut mulch]

how are you leaping from the 2nd last line to 0

[valid estuary]

identity that 1 - cos(theta) / (theta) = 0

[uncut mulch]

limit and parentheses.
but what about the thing on the right?

[valid estuary]

It's neglible because it's multiplied by 0

[uncut mulch]

what does that approach when theta→0

no its not negligible

It's neglible because it's multiplied by 0
by saying that you're implying that it doesn't matter what the denominator is when evaluating limits (which is clearly false)

[valid estuary]

but if I'm trying to simplify this down, and I have successfully arrived to a place where I have 0 * something, is it not just 0?

[uncut mulch]

no

take $$\lim_{x\to 0} \frac xx$$
as a counter example. the limit of that should clearly be 1.
you could manipulate that to:
$$\lim_{x\to 0} \br{x \cdot \frac 1x}$$
which by your logic would be 0 since $\lim_{x\to0} x$ is 0 \ (since you're disregarding everything else present)

[obsidian monolith]

ℝamonov

[valid estuary]

but in the beginning with the (theta) / (sin(theta)) s am I not disregarding everything else in simplifying those to 1? What I see is that I'm doing the same thing

[uncut mulch]

you can apply the limit product properties if the limits exist.

however here, the limit as t → 0 of sin(t)/(t * cos(t)) does not

and you would have an indeterminate form

,w lim as x to 0 tan(x)/x^2

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by ramonov#0921

[valid estuary]

hm

[uncut mulch]

you should instead consider factorisation / conjugates /pythagorean trig identities

[valid estuary]

so when do you actually use (1 - cos(theta)) / (theta) = 0 then

[uncut mulch]

that doesn't work that well here

you could apply it if the limits of each part exists

[valid estuary]

how exactly are you determining if the limit exists

[uncut mulch]

algebra, conjugates, common limits, consider left right limits as needed.

[valid estuary]

ok I think I'm going to watch some YT videos or something just so I can understand exactly what I'm doing with these trig limit problems

Thanks for your help

Oh you know what I think I see what you're getting at now

Looking at the other problems I did

It's like you can't take out the 0 identity just to kill everything to 0, the other part needs to actually be, as you said, a limit, or something you can simplify

That's when you can take out a 0 -- when you're multiplying it with a solved limit

Makes sense

[obsidian monolith]

smb3dx

[smoky pagoda]

That's exactly what ramonov was saying...

[grand barn]

are there any solutions to -3 = sqrt(2x-5)

couldnt find any real solutions but idk if there are any complex solutions

[viscid thistle]

there are none

[lilac storm]

can anyone please help me with this question?

[lilac storm]

is anyone there that can please help me with this question that i posted above a little while ago?

anyone there to help?

anyone there...?

[viscid thistle]

which part is giving you troubles?

[lilac storm]

yeah i just needed help starting off part a

so for a, do you sub in 100 for D?

[lilac storm]

are you there?

[viscid thistle]

i mean you can

but i'd really recommend not to

[lilac storm]

oh

[viscid thistle]

and instead isolate I first

[lilac storm]

ok

[viscid thistle]

and after plug the numbers in.

[lilac storm]

so how would i isolate I?

[viscid thistle]

can you try yourself first to see where you are able to get up to?

[lilac storm]

yeah, i'm not sure what to do?

if i try the other way by subbing in 100 for D, i'm left with this, 23.03 = ln I/Io

is this correct or no?

[viscid thistle]

i mean, approximately yes, but i do not recommend that way.

[lilac storm]

ok

[viscid thistle]

assuming you didn't mess up the "typing into the calculator" part

[lilac storm]

ok i am now trying the way you told me to isolate I first

[viscid thistle]

well you want to isolate I, what's really the first instinct that comes to your mind?

[lilac storm]

so far i have, D times (ln10/10) = ln I/Io

[viscid thistle]

great.

now a little review on exp equations.

if you have ln(x)=2 what can you do to isolate x?

[lilac storm]

um, i'm trying to remember

but i know

[viscid thistle]

sure!

take your time.

[lilac storm]

x = e^2

[viscid thistle]

right.

and what did you do to get there?

[lilac storm]

so you write your base as e on the other side which removes ln

does this sound correct?

[viscid thistle]

you raise e to both sides

[lilac storm]

yes

[viscid thistle]

and due to the defn, e^(ln(x))=x which ends up as x=e^2.

can you try with this logic onto our problem?

[lilac storm]

e^(ln10/10) = I/Io

[viscid thistle]

where's D?

[lilac storm]

like i don't know what to do with D?

actually, e^D(ln10/10) = I/Io

is this ok now?

[viscid thistle]

what is that?

is it $e^{D(\frac{\ln(10)}{10})}$?

[obsidian monolith]

Al𝟛dium

[lilac storm]

yes

[viscid thistle]

ok then put the appropiate parenthesis.

e^(D(ln(10)/10))

now you are pretty much one step behind

[lilac storm]

or actually e^(ln10D/10)=I/Io

now i can sub in 100 for D, right?

[viscid thistle]

don't know what that's supposed to be

$e^{\frac{D\ln(10)}{10}}$?

[lilac storm]

oops, that's my bad

[obsidian monolith]

Al𝟛dium

[lilac storm]

you are right

[viscid thistle]

if you wish to have it like this, then sure

and yeah, you can plug the numbers in now.

[lilac storm]

so the answer that i am getting is 10000000000, is this correct?

[viscid thistle]

do you want me to check if you plugged numbers into your calculator correctly?

i mean fine, wait a second.

[lilac storm]

yes, if you don't mind

[viscid thistle]

wait but did you take into account that
e^(ln(10)D/10)=I/I_0 and NOT just I right?

or did you completely ignored that?

[lilac storm]

how does that change anything?

[viscid thistle]

because you are solving for I and not for I/I_0

[lilac storm]

yes, yes

i just read the question again, your right again

[viscid thistle]

..yeah.

so are you able to finally isolate I?

[lilac storm]

yes now i get 0.01, is this finally correct now?

[viscid thistle]

seems correct now.

[lilac storm]

and if you can please help me start off b as well?

how would i start part b?

are you there?

[viscid thistle]

..yeah, do you ever realise that one can't just sometimes answer within less than 2 minutes because they are doing maybe something else or just reading part b?

because it is not the first time you say this.

[lilac storm]

sorry about that.

[viscid thistle]

something from the wording really puts me off

but anyways, do you have any ideas on what can we extract from "4 times more intense than I_0"?

[lilac storm]

4 times Io?

[viscid thistle]

yes.

and what would be 4*I_0?

ie what are they talking about that it is equal to 4*I_0?

[lilac storm]

is it (10^-12) times 4?

[viscid thistle]

and this is where the bad wording of b comes in

but looks like no.

D isn't just 4(10^(-12))

the key word is intense

what are they talking about that it is equal to 4*I_0 once again?

[lilac storm]

so i can't just do 10^-12 times 4 for Io, then solve it like the previous part?

[viscid thistle]

for I_0? not following you

[lilac storm]

so how do i start off the question, like how do i set it up to start off, then maybe i can take it from there?

[viscid thistle]

you'd once again know how to start off, if you considered reading my now 3 times attempt to asked question:

what are they talking about that it is equal to 4*I_0 once again?

[lilac storm]

so i don't get what does that mean and what do i do with it?

[viscid thistle]

"what do i do with it"? i mean, try to think of what the question is talking about when saying "...of a sound that is 4 times more INTENSE than I_0"

what does that small phrase give us as info?

[lilac storm]

4 times more than Io?

[viscid thistle]

you are eating the word "intense" now

which i purposefully highlighted and wrote in caps

[lilac storm]

4 times more intense than Io

[viscid thistle]

yeah?

what equation can you form with that piece of info?

"4 times more intense than I_0"

[lilac storm]

4Io

[viscid thistle]

that is not an equation.

that is an expression

what is equal to 4*I_0 that they are talking about? if they are talking about more intense?

[lilac storm]

D = 10/ln10 (lnI/4Io)?

[viscid thistle]

once again, don't know what that is

is it ln(I) at the top somehow?

[lilac storm]

so taking the original eq and just changing Io to 4Io

[viscid thistle]

no, that is nonsense, you are saying that I_0=4I_0

which is blatantly untrue

[viscid thistle]

the word intense should really give you everything you want to know about this question

[lilac storm]

i don't get what 4 times more intense means mathematically, if you can explain me using the eq and numbers that are given?

[viscid thistle]

i'm trying for you to get it mathematically

[lilac storm]

simply saying 4 times more intense is not helping me at all

[viscid thistle]

this isn't even math at this point, what i'm asking you is about reading comprehension

if i insist repeating something valuable it is because i know you are able to get it at some point, but you only need to try some attempts to it

and actually processing down what a sound to be 4 times more intense than I_0 is

let me just try with a simpler example

[lilac storm]

is it determining the relative loundness of a sound which is D, that is 4 times more intense than Io?

[viscid thistle]

no but that answer is kind of understandable due to the bad wording of b

the key is, may i repeat on the word intense which is represented with the letter I

and not with the letter I_0

[lilac storm]

ok, so i get it intensity is I so what now?

[viscid thistle]

if, once again, intensity is I and we are given that the sound is 4 times more intense than I_0, what is that thing that it is equal to 4*I_0

[lilac storm]

I

[viscid thistle]

yeah.

really all i ask is to process what i say and read what the problem says about the words mentioned

it was purely reading comprehension

but once again, i may agree that it was kind of an iffy wording

a better wording could've been "an intensity sound that is 4 times as I_0"

so now that you finally know that ${\color{green}{I}}=4I_0$, you should be able to find $D$: $$D=\frac{10}{\ln(10)}\left(\ln(\frac{\color{green}{I}}{I_0})\right)$$

[obsidian monolith]

Al𝟛dium

[lilac storm]

so how would i start off?

[viscid thistle]

do you not read my messages?

[lilac storm]

do i use 0.01 from the previous part?

[viscid thistle]

no

[viscid thistle]

is there something you don't understand about this or did you just completely ignored this?

[lilac storm]

there are so many variables so how do i solve for D?

[viscid thistle]

you know I_0

[lilac storm]

yes

[viscid thistle]

there are no unknowns except D

[lilac storm]

oh, i think i got it

[viscid thistle]

so yeah, i'm glad to hear, if you want to check with me your "plug in the calculator part", you should be getting ||≈6.02db||. but for the record, when someone helps you, try to read all of the messages, being patient, and try to think when they propose you to do so instead of saying anything to get to the "give me the answer i don't know what to do".

[lilac storm]

yes, your right

ok, thank you so much for your help, i really appreciate it

your right about being patient, reading everything carefully, i will keep this in mind going forward

thanks again

[lilac storm]

so i have solved this question but i just want to make sure that i did it right

so first i started off by listing out all the things that are given which are, A=58750, r=0.05 and t=4

then i used the A=Pe^rt formula and plugged everything in and rearranged the eq accordingly to find P and the answer i get is 48100.43 or simply 48100, i just want to ask that did i do everything correctly?

[lilac storm]

anyone there to help?

is anyone there?

is anyone there...?

i have posted a question above a little while ago which i have solved but i just need somebody's help to make sure that i did it right

[odd rivet]

Yes

That's right

[wispy aurora]

woah 4 hours without anyone there. That's rare af

[echo wagon]

My friend.

It's 7 hours.

[odd rivet]

They were talking about difference in time between question and answer

[echo wagon]

Hmm

[wispy aurora]

Ye I was

I did notice the time difference after that

but like ehh

[viscid thistle]

Anyone help with critical points?

[olive pawn]

hey i am self taught can someone tell me exactly what i have to learn in precalculus

[uncut mulch]

mostly:
functions, graphing, sequences and series, trig, logs and exponents

[olive pawn]

can you tell me what exactly to study in each of those topics( if you want you can dm them)

[uncut mulch]

look up khan for a basic intro / outline,
search up more in-depth stuff from people like Prof Leonard or Organic Chem Tutor

[olive pawn]

ok thank you

[dark sky]

does this graph have a horizontal asymptote?

no right?

how do i find the end behavior of this function

[lilac pier]

you can factor out x^5 from the numerator and denominator

and take the limit as x approaches +infinity

[crystal osprey]

If you remember the rule of finding horizontal asymptotes, you'd know that since the largest degree of the numerator is equal to that of the denominator, you'd isolate the leading coefficients to find the horizontal asymptote.

In this case, it's -4

You can also do what Sup said, which is to take out x^5 respectably. This'll lead you with the top x^5 and bottom x^5 cancelling out, and leaving you with their leading coefficients left alone, and the other terms divided by a power of x.

Dividing anything by x which in this case substituted by infinity (using limit laws) would get you 0. So the only thing left over are the 2 leading coefficients from x^5; the largest term in both the numerator and denominator

Both methods will lead you with an answer of 4/-1, which is simplified to -4.

@dark sky

The top method is far easier to remember since it's always true for any rational function, and you won't have to go simplifying with infinite limits. But the bottom is a way to do it with limits if you're instructed to show the steps.

It depends on what level you're at in Pre-calculus. It's possible to come across this type of question if you haven't gone into the limit unit, in which case you're probably only required to use the rule of finding horizontal asymptotes.

[knotty echo]

Dont paste the same question in 2 different channels

#rules message

Do not spam your questions in the wrong channel or across multiple channels. Be patient and wait for someone to answer.

[harsh cipher]

Hi

I have a question.

this question. What is the equation of the parabola

[wooden hornet]

y^2 = 4ax

just put in the values

[unborn nimbus]

im not sure if this is the right place but, does anyone know how to solve f(x)= sqrt(x-2)? or the whole 'domain of a function' in general

[uncut mulch]

consider what would make your function undefined

[unborn nimbus]

ahh tyty

[viscid thistle]

How do I set up cases to solve an inequality like |x-5| < |x+1|? I've forgotten how to approach absolute valur Inequalities and equations with two absolute value terms

[unborn nimbus]

does any1 know how this works?

[echo wagon]

I would say this is easiest to do with inspection

Since you start with a polynomial, and end with a polynomial, g(x) is a polynomial too

Now take the highest order term you have, 2x, and think how you change it into the highest order term of g(f(x)), i.e. 4x^2

[unborn nimbus]

omg thank you so much!! i believe this is what i'm supposed to do:
since (2x)^2 = 4x,
and (2x+1)^2 = 4x^2+4x+1,
i just need to add +2 to get 4x^2+4x+3

thankuuu!

[echo wagon]

@unborn nimbus Good job!

So what is g(x)?

[unborn nimbus]

x^2 + 2 right?

[echo wagon]

Yep, perfect

[unborn nimbus]

thank you!!

[echo wagon]

Np

[pastel dust]

is getting two parallel lines from a degenerate parabola possible through a slice of a double cone

no, right?

[viscid thistle]

Can anyone help me?

[sick steppe]

dont ask to ask

[viscid thistle]

Can somebody check my answers?

@sick steppe

[sick steppe]

why did you ping me?

also dont cross post

[viscid thistle]

sorry

[north pagoda]

@knotty echo yeah why did no one answer then

[stable yacht]

So I solved for the terminal velocity by finding the limit as t approaches infinity for the given equation, but I am confused on what it asks after that. The problem asks how long it would take to reach 58% of the terminal velocity.

I’m just blanking on what that actually means in terms of what I just solved for.

[hallow thunder]

if your $100%$ terminal velocity is $\frac{162}{1.1}$ if i read that right, you just need to find $58%$ of that and then find a time $(t)$ that returns that value when plugged into $v(t)$

@stable yacht

[obsidian monolith]

jedben2

[winter quartz]

So first @vale urchin , let's consider the two parametric equations seperately.
Do you agree that there graphs look roughly like this?

[vale urchin]

Yes except I thought 4 was positive

[winter quartz]

I changed it to work with my graph xp

[vale urchin]

okay that looks good

makes sense so far

[winter quartz]

So think about what x(t) means.

Notice how 2 is our starting point

[vale urchin]

like the center okay

[winter quartz]

Also, we'll let t refer to seconds so it's easier to process

[vale urchin]

t = 2 seconds

okay

[winter quartz]

So what this tells us is if we move to the right for t seconds, we end up moving t spaces to the right.

[vale urchin]

so increase okay for x

[winter quartz]

Yes. Since x(t)=x+2, we start at x=2 and every second we move 1 space to the right

[vale urchin]

so if x(t) is x(2) we are 3 to the right

[winter quartz]

Wait no, that should be 2 to the right

[vale urchin]

wait

haha

I just saw it

should be 4\

when t = 2

in that equation at least

[winter quartz]

x(2)=4, that is correct

[vale urchin]

okay good thats a good diagram

[winter quartz]

So this function is telling us how much distance (left/right) we are moving given a certain amount of seconds passing.

[vale urchin]

I see okay and y is the same?

except upward/downward?

[winter quartz]

Yes. But let's draw it out

[vale urchin]

okay yep

so when t is 0 for y(0) its at 7 up

[vale urchin]

ahhhhhhhh

but goes down by 4

interesting

[winter quartz]

So we start at 7 and every second we move down four spaces

[vale urchin]

because -4t

[winter quartz]

Correct!

[vale urchin]

Correct

oh yes

okay so it will create a curve then

but just one line

[winter quartz]

So what is x(t) and y(t) when t=0?