help-10

[obtuse pebble]

@woven quartz Has your question been resolved?

[woven quartz]

thank you, i think i got it. am i supposed to proceed like this?

[tardy epoch]

,w int 0 to pi/2 of |sin(x) - cos(x)|dx

[warm shale]

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[tardy epoch]

looks good

[woven quartz]

thank you very much

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[woven quartz]

help, please. this should be a fairly simple LPP, however i got it wrong
i) the feasible solution should be at a corner
ii) 2y-x is to be maximized, so i need to check which corner point has the highest value of y and lowest value of x
that gives me (2,7) as the feasible solution. where did i go wrong?

[obtuse pebble]

@woven quartz Has your question been resolved?

[woven quartz]

no, but i think i get it.

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[low pagoda]

idk

[tardy epoch]

you're just supposed to differentiate all the choices and see which one equals f(x)

[low pagoda]

ew

[tardy epoch]

oh i guess you can also use u-sub on your integral

try u-sub here to see if it's equal to any of your choices

[low pagoda]

wait since I have -ln|cos(e^x + pi/2)| I can make it ln|sec|

[tardy epoch]

you can check your answer by doing this

probably only takes like a minute to differentiate each choice

[obtuse pebble]

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[low pagoda]

would this be 10?

[static beacon]

yea

[obtuse pebble]

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[low pagoda]

.reopen

[obtuse pebble]

✅

[low pagoda]

this is correct right?

[rigid lintel]

,w d/dx -arctan(x-2)

[warm shale]

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[rigid lintel]

yeah its b

,w d/dx arctan(x-2)

[warm shale]

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[low pagoda]

I think the first time I did the problem I chose D because I forgot to distribute the negative

[rigid lintel]

you dont actually need to integrate

you can just differentiate the possible answers

work smarter

not harder

[tardy epoch]

@rigid lintel great minds

[rigid lintel]

think alike ❤️

[obtuse pebble]

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[hollow grail]

.

[hollow grail]

what happened in the first question

[elfin burrow]

they made the substitution u^2 = 4-x^2

you can think of it as u = sqrt(4 - x^2)

except i think that needlessly overcomplicated the question

u = 4 - x^2 works fine

the integrand becomes (4 - u) u^(1/2) (1/2) du

[hollow grail]

ok what about

this

where did this come from

[elfin burrow]

that's the expression for dx

in terms of du

the previous line

[hollow grail]

dx = 2.sqrt(x) du

right?

how do i sub x in that?

[elfin burrow]

no

how are you getting this?

u = sqrt(x) - 1

=> du/dx = 1/(2sqrt(x))

[elfin burrow]

correct

but you are changing variables from x to u

you don't want to keep any x's in your expression for dx

you want it in terms of u and du

[hollow grail]

yes how do i change the x inside the sqrt?

[elfin burrow]

use your definition of u

u = sqrt(x) - 1

so can you rewrite 2sqrt(x) in terms of u?

[hollow grail]

x = (u+1)^2

?

[elfin burrow]

u = sqrt(x) - 1

so sqrt(x) = u + 1

[hollow grail]

ohh

thats why

yesyes i see it now

Thank you

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[uncut karma]

translate it to English if u don't are Brazilian to know what it mean

[timid silo]

Ah yes I can see the pixels on the letters. This is also 3 pages of questions, what is your specific question?

[uncut karma]

6

[tardy epoch]

screenshot and send one question only. your images are too small to read.

[timid silo]

Okay now we wait for our philanthropic Portuguese friends to come translate this for us

[teal turret]

Lol

[uncut karma]

here this in english

6. Mark the TRUE alternative.

a) The number 1 is multiple of all numbers.

b) The set of dividers of a number is infinite.

c) The zero number is a divisor of all numbers.

d) The set of multiples of a number is infinite.

[obtuse pebble]

@uncut karma Has your question been resolved?

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@uncut karma Has your question been resolved?

[obtuse pebble]

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[warm olive]

is the black-scholes equation considered a linear differential equation

[warm olive]

?

here is the equation for reference

[tardy epoch]

linear in what variable

[warm olive]

umm

im not sure tbh

im just doing an essay

on linear and non-linear differential equations

[twin sapphire]

this seems to be the solution of the equation

not the equation itself

[warm olive]

ohh

[tardy epoch]

https://en.wikipedia.org/wiki/Black–Scholes_equation

where V is the price of the option as a function of stock price S and time t, r is the risk-free interest rate, and {\displaystyle \sigma }\sigma is the volatility of the stock.

So in this case yes it is linear

[warm olive]

what was said in the {}?

[tardy epoch]

should follow this for the definition of linearity:
https://en.wikipedia.org/wiki/Linear_differential_equation

just the bottom sentence right below

[warm olive]

ahh okay

[tardy epoch]

$\displaystyle \sigma$

[warm shale]

riemann

[warm olive]

thank u very much

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[inland matrix]

heep

I tried summing twerk but i can figure it out

i tried putting the pivot on the left side since i think im trying to find the force of the fulcrum

I know the answer is 8.33% i just need help figuring it out

i tried this

$\tau = r \times F_{fulcrum} - r \times F_g$

[warm shale]

allarkvarkk

[inland matrix]

the one without shit would just be

$0 = 0.25F_{fulcrum} - 0.5mg \text{ and } 0 = .24F_{fulcrum} - .5mg$

[warm shale]

allarkvarkk

[inland matrix]

I got no clue how to do this

[narrow vault]

you're making this way too complicated

what's the two lengths of the two arms when the fulcrum is in the centre
vs
what's the lengths of the two arms when the fulcrum is shifted by 1cm

[inland matrix]

center is .25 and .25 and shifted is .24 and .26

[narrow vault]

and what happens to the torques when the scales are balanced in both cases

[inland matrix]

wdym?

= 0

[narrow vault]

and why are your equations 0.25F_{fulcrum} - 0.5mg if your arm lengths are 0.25, 0.25

[inland matrix]

i moved the pivot because i cant figure out how to do it when its in the middle

because if it is

$.25F_g - .25F_g = 0 \text{ and } .24F_g - .26F_g = 0$

[warm shale]

allarkvarkk

[narrow vault]

the easy way to do this is to think that when scales are balanced torques on both sides are equal

ye like that

[inland matrix]

wait but how do i solve this?

F_g is the same for all of them

[narrow vault]

obviously you can't have the same variables

the entire point is that since your fulcrum moved one of the weights must adjust

[inland matrix]

oh is that what the question is asking

omg u right

$.25F_g - .25F_g = 0 \text{ and } .24F_g - .26F_{g_2} = 0$

like this?

[warm shale]

allarkvarkk

[narrow vault]

ye, and find g2 in terms of g

well one in terms of the other, and the larger one is the counterfeit value

[inland matrix]

Fg2 = .24/.26 Fg

i got it to work only one way though

nvm got it

says marked up

by bad im sorry i went a little stupid

thank you so much

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[dusky lichen]

How can you find the equation of a parabola given the vertex and the x intercepts

[bold bane]

A parabola is composed of two linear factors of the form (x-a) and (x-b). a and b are the roots of the polynomial, ie. the x-intercepts.

Now that parabola can be compressed or stretched vertically by some constant k. You can use the vertex to determine that constant k.

[warm shale]

Kookiemon

[dusky lichen]

How can i find the constant k

Can you help me

The x intercepts are

x1 = -3

X2 = 6

[late stump]

you can plug in the coordinates for the vertex into the equation and isolate k

[dusky lichen]

And the vertex

3/2 , -5

[dusky lichen]

I dont understand what the x stands for

[sharp pecan]

look at the equation Kookiemon gave you

fill it out with what you have

they explained it quite well

[dusky lichen]

y = k(x+3)(x-6)

[sharp pecan]

well, but you know x and y right?

[dusky lichen]

X and y of the vertex?

[sharp pecan]

...

yes

[dusky lichen]

Ok

-5=k(3/2+3)(3/2-6)

[late stump]

yup now isolate k

by rearranging

[dusky lichen]

So the k is 20/81

What can i do now

[nocturne minnow]

Plug it back into here now that you have k

[dusky lichen]

y= 20/81 × x^2 - 20/27 × x - 40/9

[nocturne minnow]

You don't need to expand it

[dusky lichen]

Wow ok

Ok

I tried to find it

With the formula

y= a( x-h)^2 + k

But it didnt work

Shouldnt i use that

[nocturne minnow]

You can still use that

[dusky lichen]

Instead of 40/9 it showed 20/9

Anyway ill try and do it gain

To see if i made a mistake

Thank you guys

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[hallow umbra]

I got x = pi, but the textbook answers have x = pi/2 x = pi, 3pi/2

I solved cosx = -1 which doesn't match the other two

[tardy epoch]

show your work

[trail musk]

what is 1+tan^2

hmm

[hallow umbra]

sec^2x

[trail musk]

how do you know?

[hallow umbra]

It is an identity that we were supposed to memorize

[trail musk]

sin^2 + cos^2 = 1
(divide through by cos^2)
tan^2 + 1 = sec^2

i had trouble keeping it straight until i realized that

hopefully that helps

[hallow umbra]

huh interesting, I do always have problems remember the 3 inverse pythagorean identities so that will help

tysm

[tardy epoch]

when you divide by cos(x) here, you first have to say cos(x) is not 0

[trail musk]

factor, don't divide

[tardy epoch]

just work with the first equation

$\cos^2(x) + \cos(x) = \cos(x)(\cos(x)+1) = 0$

[warm shale]

riemann

[tardy epoch]

so now use the zero product property of two numbers: ab=0 implies a=0 or b=0

[hallow umbra]

ahhh

okay that makes much sense

tsym I got it

I appreciate the help

If I have another question do I ask here again

ill just do

Work.

I know thags wrong but i was going somewhere ?

Just get stuck with these seemingly unsolvable equations and I’m stuck

I changed it all into sine now I’m here

[tardy epoch]

just factor out sin

[hallow umbra]

Like this?

[tardy epoch]

you just need to start all over

solutions to these problems should not be more than 3 lines

[hallow umbra]

Will do

[tardy epoch]

factor out sin

[hallow umbra]

ahhh there

gotcha

Can you start solving for the zeros from here?

,rotate

[hallow umbra]

That tanx supposed to be squared

Okay I got it

It does work like that

Thank you

Okay so then this one as well

I tried solving this via QF but I can't get anywhere because it is a nonreal answer

,rotate

,rotate

[obtuse pebble]

@hallow umbra Has your question been resolved?

[hallow umbra]

I’m following mathway

But there’s gotta be a simpler way to to do this no?

,close

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[west field]

https://cdn.discordapp.com/attachments/801452104438120480/1054564133615439882/IMG_9904.jpg

[west field]

idk how to prove pt congruent to ru

<@&286206848099549185>

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[ruby wave]

Very confused

[ruby wave]

3x3 magic square problem

<@&286206848099549185>

Help please

[obtuse pebble]

@ruby wave Has your question been resolved?

[obtuse pebble]

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[storm vale]

Question about finding vertex from standard form for quadratics

[storm vale]

is it -b/2a
or -(b/2a)

because if i have a negative for both b and a, does it cancel otu and they both become postiive and the number is positive or does the whole thing stay negative always

[nocturne minnow]

They mean the same

The negative only gets distributed to one of the terms

[storm vale]

so if my problem was
y= -2x^2-4x+5
what would the vertex be

[nocturne minnow]

Apply that formula

[storm vale]

im 90% sure its wrong

when i calculate it i get -1, 13
but on calculators like photomath it shows -1,7

[nocturne minnow]

when i calculate it i get -1, 13
How did you get this?

[storm vale]

-2(-1)^2 = 4
-4(-1) = 4
4+4+5 = 13
i messed up somewhere

[nocturne minnow]

-2(-1)^2 = 4
Explain

[storm vale]

-2 times -1 is just cancelling the negatives so ti becomes 2
2 to the power of 2 is 2 squared so 4

[nocturne minnow]

No

Improper use of order of operations

[storm vale]

would it be then -1^2 so
-2 times 1
so -2 + 4 + 5

so the coefficient waits until exponent is done first

[nocturne minnow]

Yes

[storm vale]

oh
i see
thank you

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[meager hull]

Guys pls I hope the image works

[meager hull]

Ah bet, anyways: so like I'm supposed to ig estimate the values of c and like I got this far

And I'm realizing I could just like idk, take a guess to see what happens

It says estimate in the question after all

[rigid lintel]

you could mentally draw a line like this

[meager hull]

1/6 is such a small slope 💀

[rigid lintel]

and move it up and down

(mentally)

[meager hull]

Ah

Wait yeah cus the interval 3xists

[rigid lintel]

so theres multiple possible values of c

[meager hull]

I mean 2 is kinda close

Sorta

Wait not 2

3

[rigid lintel]

yeah

or 6

[meager hull]

Not 6 cus that's where the horizontal thing is

That's the local min, I know it's hard to see it's okay my drawing skills are 💀

BUT TYY

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[rigid lintel]

sorry the what

6 works

or 6 and bit

6.2

[meager hull]

Yeah it just can't be 6 on the dot cus horizontal tangent line is 0

.close

Yeah it's closed alr

[obtuse pebble]

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[sour coral]

Can someone help make this formula excel friendly? = (1/3)πB2*(C2^2+C2*D2+D2^2)

[obtuse pebble]

Please don't occupy multiple help channels.

[nocturne minnow]

Don't open multiple channels

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[ancient stag]

can someone clarify this

[ancient stag]

so basically the error term for taylor series if its 0 it just means the series converges to f(x) as n goes to infinity as the function we're trying to estimate has 0 error?

[twin sapphire]

yes if the error term goes to 0 then the series converges to the function but no the function doesnt have 0 error (it doesnt mean anything for a function to have an error in itself)

[ancient stag]

i dont understand what you mean by the 2nd part that the function doesn't have an error

am i supposed to just say that the approximation doesn't have error

[twin sapphire]

no

just your sentence doesnt make sense

[ancient stag]

ohh i see what you mean

[twin sapphire]

this bit

[ancient stag]

yea i see why it makes 0 mathematical sense

well thanks man

apprecaite it

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[hushed olive]

can i have help with calculating ratio, im stuck on the translation part

[obtuse pebble]

@hushed olive Has your question been resolved?

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[timid silo]

"A fair dice is rolled twice consecutively. If this experiment is carried out 450 times, how many times will it at least a multiple of 3 be obtained."

[narrow vault]

..on average, right?

you can't give a definitive answer to something that's probabilitic

[timid silo]

This is my current work
.
.
Since there are only two multiple of 3 in the dice, the probability I will get it is 2/6 and if I do it twice it will become 4/36 or 1/9.
If it is carried 450 times. I have to multiply 1/9 with 450 to get the answer.

But the answer from my teacher is 250.... Is it actually 250 or 50?

[narrow vault]

first of all unless your question specifies on average the answer is undefined

because you can't predict the future :p

then let us assume you're calculating the number of pairs that contain at least one multiple of 3 on average

if you only roll a dice twice, what's the probability at least one of them is a multiple of 3?

[timid silo]

If it is rolled once then it is 2/6 but twice will be 4/36 ?

Oh wait

[timid silo]

Hmm I'm not really about this

This is from what I learned

[civic zealot]

this calculates the expected number of times both dice have a multiple of 3

you want at least one of them, not just both

[timid silo]

Ah I see

[narrow vault]

a nice trick to know is when you're asked about something happening at least X times

think about the scenario where it doesn't happen (the complement), which is sometimes easier to calculate

what's the probability that you roll 2 dice and you don't get at least one multiple of 3?

[timid silo]

I dont have any idea😅

[narrow vault]

if you don't get at least one multiple of 3, how many multiples of 3 can you get?

[timid silo]

1 ?

[narrow vault]

is 1 not at least 1?

alright wording at this point might become a problem

if you want to calculate the probability other than getting 2 multiples of 3 or 1 multiple of 3 (these being at least one multiple of 3)

what's the only probability you're worried about

[timid silo]

It's not

Hm

Wait the probability that I won't get atleast 1 multiple of 3 is 4/6 ?

[narrow vault]

that's only for one dice

what's the probability to not get at least 1 multiple of 3 for two dice?

[timid silo]

16/36 = 4/9

Ah I understand now

P(getting at least one multiple of 3)= 1 - 4/9

[narrow vault]

at leaset one multiple of 3 but yes

and now you can calculate the expected number of pairs with at least one multiple of 3 when you repeat this 450 times

[timid silo]

P(at least one multiple of 3)= 1 - 4/9 =5/9
5/9 x 450 = 250 times

Finally understood it

Thank you very much!

.close

[obtuse pebble]

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[distant rampart]

$$
\begin{tabular}{c|c|c|c}
p & q & r & \left(p \implies q\right) \implies r \ \hline
T & T & T & T \
T & T & F & F \
T & F & T & T \
T & F & F & T \
F & T & T & T \
F & T & F & F \
F & F & T & T \
F & F & F & F \
\end{tabular}
$$

[distant rampart]

is this right?

[timid silo]

,w truth table of (p implies q) implies r

[distant rampart]

why is it true for p->~q->r

[twin sapphire]

what are your brackets?

[distant rampart]

wdym

[timid silo]

^ it is kind of vague lol

[twin sapphire]

$(p \implies q) \implies r$ or $p \implies( q \implies r)$

[warm shale]

Benjamin

[distant rampart]

oh i just meant p->q->r for the fourth column

[timid silo]

then probably the first

[narrow vault]

clarification needed because apparently wolfie thinks it's the latter and conventionally i thought it's the former

[twin sapphire]

yeah its confusing

like implies are not associative

[warm shale]

Results provided by WolframAlpha

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

Requested by ♡LexQa♡#5050

[distant rampart]

better now?

[timid silo]

Sure

Then u got a few wrong

[distant rampart]

now why is it T for (p->~q)->r

let's start there

[narrow vault]

because F-> T results in T

[twin sapphire]

if p is true and q is false

[distant rampart]

i see

[twin sapphire]

p->q is false

then F implies anything

is always true

[distant rampart]

yea

and for T -> F -> F?

Or, F->F

that's T

[twin sapphire]

its very confusing

[narrow vault]

this is why instructors will yell at you (i assume your also did) to also include truth table columns for intermediate expressions

[twin sapphire]

like write what are p, q and r

[narrow vault]

because trying to do everything in your head gets complicated real fast

[twin sapphire]

dgh

[twin sapphire]

like what are those

[warm shale]

dgh
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[distant rampart]

okay now i got it

thanks amigos

[twin sapphire]

bybye

[distant rampart]

intermediate expressions
what's that

[narrow vault]

parts of your whole expression

[distant rampart]

i see

[twin sapphire]

a column for (p=>q) in this case

[distant rampart]

yeah

will think of that for the future

[obtuse pebble]

@distant rampart Has your question been resolved?

[obtuse pebble]

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[frozen token]

Hey im in honors alg 2 right now and i was going to try to take pre calc over the summer and wanted to start learning now for fun. I was wondering on what i should try to learn specifically, i have this calculus book by james stewart.

[timid silo]

Start off with trigonometry I guess

[frozen token]

Yea this is what the course ill be taking over the summer has as the description

Trigonometry is like more indepth geometry?

[obtuse pebble]

@frozen token Has your question been resolved?

[loud tangle]

its basically tying angles and side lengths together

and trignometry is found basically everywhere where rotation is

[obtuse pebble]

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[winged crown]

hi can anyone help this question?

[winged crown]

is it 5* 2^3

or 2^3

[timid silo]

Use the exponents properties of
[
a^{m} \cdot a^{n} = a^{m +n}
]

[warm shale]

♡LexQa♡

[winged crown]

so if its 1/2+-1/2 its 0

then is it 2^3

or 5 * 2^3

[timid silo]

Yes

[winged crown]

oki ty

.close

[obtuse pebble]

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[white jasper]

hello may i ask how to solve this?

[royal basin]

do you know in general how to calculate line integrals

[white jasper]

yes

[royal basin]

ok, then what is posing you trouble in this one?

[white jasper]

i dk how to find the x

[royal basin]

what do you mean by "how to find the x"?

[white jasper]

in my knowledge, I need to have the x and y equation to solve the line integral, and now I dont know what is the x

[royal basin]

you need a parameterization of the curve along which you're integrating.

in this case, of the parabolic arc from (0,0) to (pi, pi^2)

it would be strange that you have only half of said parameterization.

[white jasper]

oh so using x=rcos(theta) and y =rsin(theta)?

[white jasper]

so like how I solve for a circle?

half circle I mean

[royal basin]

no what

no

oh my god

what the actual shit

just because i said "arc" doesnt mean im talking about circles!!!

your curve isnt a piece of a circle!!! it's a piece of a parabola!!! parabolas aren't circles!!!

and you're overthinking it!!!

do you know how parameterizations of curves work in general?

[white jasper]

I think it is 1/4 of circle

[white jasper]

I guess not now

[royal basin]

https://www.youtube.com/results?search_query=parametric+equations+of+curves

also, no, i will reiterate, parabolas aren't circles. NO part of a parabola is shaped the same as an arc of a circle. and no, you are wrong about your parabolic arc being the same as a quarter-circle arc.

your parabola has the very straightforward parameterization x = t, y = t^2 for 0 ≤ t ≤ pi.

[white jasper]

ohhhh I got it

thank you so muchhhh

.close

[obtuse pebble]

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[warped flume]

i got 765.8m^2

is it a difference to worry about

[stable rain]

um

well

ur main steps i think should be right

u prob just rounded too much early?

like in ur earlier steps did u round?

try maybe doing them to 4 or 6 sf

5 or 6

[warped flume]

yeah i rounded to 3sf

[stable rain]

yea that

u shldnt round to 3 as well if ur final answer wants 3sf

personally i would leave it as its exact values

eg leave it as sin65 etc

[warped flume]

makes sense makes sense

[stable rain]

but if u wanna round try to use > the amount needed for the final ans

4 is generally safe but not always

5 is quite safe

6 is if u feeling idk

very very safe

3 is pretty bad

[warped flume]

aight ty <33

[stable rain]

np

💕

time to

purge

.close

[obtuse pebble]

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[gray topaz]

sup

[gray topaz]

-1, 8, 16, 32

whats the pattern?

[vapid hamlet]

is it 16 or -16?

[gray topaz]

16

<@&286206848099549185>

[vapid hamlet]

it could be anything, also ping helpers only after 15 minutes

[zenith raft]

lol

[timid silo]

https://oeis.org/search?q=-1%2C8%2C16%2C32&language=english&go=Search

[zenith raft]

nothing even comes up with those 4 exactly

[narrow vault]

seems like a copypaste or printing error ngl

[obtuse pebble]

@gray topaz Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[topaz spruce]

Hey! What does this notation mean?

[topaz spruce]

$\int_{C}$

[warm shale]

sentinel

[topaz spruce]

I kind of made a guess when calculating, which was correct

[lost tree]

I guess C is like a path

or curve

u integrate along this curve

[topaz spruce]

Is it normal in integrals for them to be specified with a curve?

[lost tree]

what do u mean "normal" it depends on the integral

afaik

[topaz spruce]

Yeah right, so it's 'normal' notation, to say, integrate f along C

Which is what it states?

[lost tree]

yeah lol to the best of my knowledge yes (idk much abt line integrals), but unless it is maybe clear from the context that the integral is along a specific curve, it will be indicated in subscript like that

[obtuse pebble]

@topaz spruce Has your question been resolved?

[obtuse pebble]

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[proud cargo]

I need some help with this

[rigid lintel]

what would the best fit line look like with and without Q

[proud cargo]

it would be a positive slope

right

in both cases

[rigid lintel]

yes

[proud cargo]

q is just dragging it down

[rigid lintel]

exactly

[copper spade]

Bro contradicting himself

Atleast close the new one

[proud cargo]

i found one place else

its not here anymore

[rigid lintel]

look its closed now

[proud cargo]

ok thank u

[proud cargo]

so then shouldnt the slope value change?

[rigid lintel]

yeah the slope value changes

if you include Q or dont include Q

[proud cargo]

sorry i meant sign

the sign changes right

because its influential?

[rigid lintel]

the sign is either + or -

[proud cargo]

okay so if you remove q its still positive?

[rigid lintel]

the slope should still be positive with Q

[proud cargo]

ohhh okay

[rigid lintel]

yes

[proud cargo]

i c now

okay so the value changes sign doesnt

okay

thank you

.close

[obtuse pebble]

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[silver plover]

..

[silver plover]

i sketched this

is this how youd write the range?

[rigid lintel]

[0,2) is a set

and y is a real number

so it doesnt make sense to say $y \neq [0,2)$

[warm shale]

Gijs

[rigid lintel]

do you mean $y \notin [0,2)$

[warm shale]

Gijs

[silver plover]

what about range is (-inf,0) U [2,inf)

@rigid lintel

does that work

[rigid lintel]

-1 is element of (-inf, 0) and f(1) is not defined

did you flip the positive and negative x haha

[silver plover]

is my graph wrong then

?

no imean

[silver plover]

this is for y

not x

[rigid lintel]

oh yeah

[silver plover]

lmao

so im correct?

[rigid lintel]

yes thats totally correct

[silver plover]

SUIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII]

gijs u scared me for sec

lol

[rigid lintel]

hahah

not to be pedantic

but usually its written as

${f(x) : x \in \mathbb{R} without {-1, 1}}$

[warm shale]

Gijs

[silver plover]

thats domain

no?

[rigid lintel]

no because its the set of f(x)

which are y values

[rich tapir]

${f(x) : x \in \mathbb{R} - {-1, 1}}$

[warm shale]

alihsaas

[rich tapir]

ah

[silver plover]

lol

@rigid lintel just out of curiosity

if i was to find range without the graph

what would i do next

complete square?

[rigid lintel]

thats an interesting approach

i dont really think you need to do any algebra to find the range of a function

[silver plover]

can u spot my mistake

cuz thats surely not correct

[silver plover]

just curious

[rigid lintel]

the red part isnt quite right

y - 1 <= -1 and y - 1 >= 1 is right though

so you can still make the right conclusion

[silver plover]

so y <= 0 and y >= 2

but thats not true

since y cant = 0

[rigid lintel]

oh yeah

you make a good point

[silver plover]

mhm

[rigid lintel]

im not sure how to resolve that

[silver plover]

hmmmm

this method should work tbh

[rigid lintel]

it definitely should

[silver plover]

hmmmm

[silver plover]

anyway ill have a go later

for this

does it have any horizontal asymptotes

since when x tends to infinity, we get infinity over infinity

which is undefined

[rich tapir]

at 4y(y-2)
you can just take y>0 and y>-2
no need to expand solve a polynomial, also you know y isnt 0 cause you took a=-y to solve your polynomial above

[rich tapir]

if you reach undefined or indeterminate form, use HR or in this case just take from the numerator and dominator the term with highest degree

[silver plover]

ok cool

and secondly

to find the turning point

is there another way faster way rather than differntiating it

[rich tapir]

is turning point the point you get from second derivative?

[silver plover]

first

[rich tapir]

ah so like the maximum and minimum

[silver plover]

ye

[rich tapir]

don't think so, it is pretty much defined as the point where the first derivative is zero

[silver plover]

i differrentiated

butwhen i plug in 0

its undefined

[rich tapir]

wdym

[silver plover]

nvr mind

im dumb

[silver plover]

i get turning point at (2,5)

is that correct?

[rich tapir]

that is correct but it has 2 turning points

you got the minimum

[silver plover]

2

?

how

[rich tapir]

just a moment

[silver plover]

how do i find the second one lol

i did he derviative

subbed 0

what else do i do

lmao

@rich tapir

[rich tapir]

i assume you divided by x

[silver plover]

wait

wait

wait

hold up

a minute

i made a mistake

by subbing in 0

instead of making it equal to0

but i still got the TP correct

how

[rich tapir]

just a coincidence

your work is wrong

[silver plover]

ik

cuz i subbed in 0

[rich tapir]

now you know how it should be done 👍

[silver plover]

ok i got the TPS

how do i know

which one is a max and and which is a min

[rich tapir]

from graph or table of variation

[silver plover]

the question is to draw the graph tho

lol

[rich tapir]

table of variation

you study the sign of first derivative and see when f is increasing/decreasing, with the addition of asymptotes

actually I used the terms maximum and minimum wrong here, i apologize

[silver plover]

wdym

[rich tapir]

i assume local minimum/maximum would be a correct, but not sure

so let's just go with turning point

[silver plover]

got this so far

correct so far?

[rich tapir]

yah correct so far

[silver plover]

idrk how to draw the othr one now

[rich tapir]

how did you draw the first part

[silver plover]

plotted the tp

then just used the asympottes

to guide me

hows this

[rich tapir]

just like if you take x tends to 1-, the limit will go towards -infinity, take the limit as x tends to 1+

[rich tapir]

yah correct

but consider writing a table of variation, makes work alot easier

[silver plover]

nice letsgooooo

[silver plover]

ok ok

there was a lot of work

to draw that lmao

[rich tapir]

yah rational functions are a bit hard to draw at first

[silver plover]

is this correct for the range?

[rich tapir]

yah right 👍

[silver plover]

thanks a lot mate

appreciate the help

[rich tapir]

you're welcome anytime ❤️

[silver plover]

does this graph have vertical asympototes

i dont think it does

cuz u cant make the denomiator = 0

[rich tapir]

yah but you have log

[silver plover]

sry

log means ln

here

my uni defines log as ln

[rich tapir]

log x, you get a vertical asymptote

yah i assumed it is ln x

[silver plover]

the process here says to make denominator approach to 0

and i did that

[rich tapir]

take x as it tends to 0+, ln 0+ goes to -infinity

take the limit over the bounds of the function, 0+ and +infinity

[silver plover]

wait

lets go back a bit

could u read my definition and tell me if u agree with it?

[silver plover]

^

[rich tapir]

yah i agree with it, but it doesn't really work here cause the function isnt rational

[silver plover]

what does that part mean

dont really get that

[rich tapir]

anything other than zero, 3, -3, infinity

it's so you dont get 0/0

[silver plover]

but what is x tending to?

if that makes sense

so for example

say we have x/(x+1)

is the numerator approaching a non zero value here?

and how do u know

[rich tapir]

x tends to some constant a

a finite

[rich tapir]

for the limit as x tends to -1, yah the numerator tends to a none zero value

[silver plover]

so back to this. since this isnt rational, how would u find the vertical asymptote

what process

[rich tapir]

you look at the domain of this function, you see it is
(0, +inf)
you take the limit at x tends to 0+ and x tends to +inf, if a vertical asymptote exists, as x tends to 0+, y will tend to -infinity/infinity (specifically -infinity here)

[silver plover]

a limit at x tends to 0 wont exists no?

since log(0) is undefined

acc

hmm

[rich tapir]

x cant be 0 or 0-

that's why we took 0+

[silver plover]

would it tend to -infinity?

as x tends to 0

?

[rich tapir]

yah ln(0+) -> -infinity

[silver plover]

and for x tends to infinity

would it be undefined

since log(infinity)/1+(infinity)

cant really do much with that

[rich tapir]

you use Hôpital's rule here

[silver plover]

havent done that

[rich tapir]

derivative of numerator divided by derivative of dominator

[silver plover]

i dont think we can use that here

as this question is from a chapter where we havent learnt it yet

acc i can use it uf u want

[silver plover]

is it just this?

[rich tapir]

that's how it's done, don't recall any other way to solve this

[rich tapir]

yah

with the limit ofcourse

[silver plover]

what the derviative of 1 + modulus x?

[rich tapir]

cause x>0, it's the same as derivative of 1+x

[silver plover]

ok

[silver plover]

^^

[rich tapir]

write the limit where you write derivative over derivative

but yah correct

[silver plover]

so whats the vertical asympotote

[rich tapir]

the vertical asymptote is x=0 and you have a horizontal asymptote y=0

you get a horizontal asymptote when limit to infinity ends up at a finite,
and you get a vertical asymptote when limit to a finite ends up at infinity/-infinity

[silver plover]

yh that makes sense

wait so

can u always use lhopitals rule

like anytime

seems cool

[rich tapir]

only when you reach an intermediate form

[silver plover]

what does that mean

[rich tapir]

and you must have a fraction

[rich tapir]

undefined

0/0 inf/inf

[silver plover]

ight

asympototes done

and i got one intersection at (1,0)

not really sure how to sketch this

[rich tapir]

start with drawing table of variation

[obtuse pebble]

@silver plover Has your question been resolved?

[silver plover]

should i do values from 0 to 10 for x?

[rich tapir]

0 to infinity

[silver plover]

no u said to to table of variation

[rich tapir]

you never learned about table of variation?

[silver plover]

like picking points?

and poltting them?

[rich tapir]

no you don't take specific points

you study the function over the domain

increasing decreasing

[silver plover]

i havent done table of variation then no

i dont think

[rich tapir]

just a moment, ill show you how it's done here

[silver plover]

ok

thx

@rich tapir it has an asymptote at y = 0
but intersects at (1,0)
how does that make sense

[rich tapir]

it increases to a maximum then decreases to the asymptote

[silver plover]

but it intersects the axis at (1,0)

it cant intersect asymptotes

and we said y = 0 is an asymptote

[rich tapir]

it can if it is increasing to a maximum or decreasing to a minimum

[rich tapir]

yah that is correct, but make the curve stick more to the vertical asymptote

[silver plover]

ight cool cheers mate

that was pretty tough icl

[rich tapir]

npp

table of variation came out to be more difficult than I expect

expected

for this function

[silver plover]

ah rip

[rich tapir]

this is the table of variation of another function, but it's the same idea

you should also include the limits/asymptotes, i didnt include them

[silver plover]

final question for this worksheet

would this not have any vertical asymptotes

since if u made 1 + x^2 = 0

its not real

[rich tapir]

yah it doesn't have any vertical asymptotes

[silver plover]

would we use hopitals rule to find horizontal asymptotes?

[rich tapir]

with rational functions, you can just take the term with highest degree

from numerator and denominator

[silver plover]

they both have same degree

[rich tapir]

yah what will the limit be

then

[silver plover]

1?

[rich tapir]

you take the entire term with its coefficients

[silver plover]

dont really understand what ur saying soz

[rich tapir]

for example: ax, x is a variable, a is its coefficient

[silver plover]

could u explain what u mean here

[rich tapir]

the term with highest degree from numerator is -x^2
the term with highest degree from denominator is x^2
(-x^2)/(x^2)

[silver plover]

ok

then do u sub infinity?

for x?

as we wanna find what it is when x tends to infinity

[rich tapir]

simplify or you will reach the same result inf/inf

[silver plover]

oh

its -1

[rich tapir]

correct

[silver plover]

so thats a trick then, with rational functions, u can ignnore everything else and just simplify the highest degree term from num and denom?

[rich tapir]

yes

[silver plover]

is this how the graph looks?

for this

[rich tapir]

correct

[silver plover]

LESGOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

SUIIIIIIIIIIIIIIIIIIIIIIIIIIIII
SUIIIIIIIIIIIII]

SUIIIIIIIIIIIIIIIIIIIIIIIIII]SUIIIIIIIIIIIIIIIIIIIIIIIIIIII]

[silver plover]

alright thats me done for now

cheers mate

[rich tapir]

🫡

[silver plover]

.close

[obtuse pebble]

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[coral wing]

i cant find any answers on this online surprisingly

[coral wing]

and i kinda need to know this

whats the difference between a point frequency table and a binned one

i thought they were the same thing but you need to use different formulas when calculating the measures of em

[proven zephyr]

Ok so

the main difference is how they list the values

if you have a data set with the heights of 100 people, a point frequency table for this data set will list each value of the variable individually (e.g., 60 inches, 61 inches, 62 inches, etc.) and the number of people with each height.

A binned frequency table is similar to a point frequency table, but instead of listing each value of the variable individually, the values are grouped into "bins" or "intervals." For example, a binned frequency table for the heights data set might group the heights into intervals of 5 inches (e.g., 60-64 inches, 65-69 inches, 70-74 inches, etc.) and list the number of people in each interval.

The main difference between a point frequency table and a binned frequency table is the level of detail they provide.

[proven zephyr]

ok second part

In a point frequency table, the values of the variable being analyzed are listed individually, and the measure of central tendency (e.g., mean, median, mode) can be calculated directly from these values.

In a binned frequency table, the values of the variable are grouped into bins or intervals, and the measure of central tendency cannot be calculated directly from these values. Instead, you need to use a different formula that takes into account the width of the intervals and the number of observations in each interval.

[coral wing]

alright, thank u so much!

.close

[obtuse pebble]

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[proven zephyr]

You're welcome!
credits: ChatGPT

[obtuse pebble]

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[proven snow]

https://cdn.discordapp.com/attachments/990415514213965844/1054844529603256400/image.png

[fierce lagoon]

Yeah so use parallel-transversals laws

[proven snow]

i was thinking its B

or another side would be the A-B line

like this

so would it be SAS?

that's what I'm confused about is the order the Sides and angles are counted.

[fierce lagoon]

Well why would angles JAB and KBA be congruent

That would only work if AJ || BK

That's not given

[proven snow]

.close

[obtuse pebble]

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[timid silo]

I used the Pythagorean theorem but I think I'm missing something. Should i use derivatives?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[upbeat gazelle]

I think Pythagoras is enough here

You could use the derivative to see the angle for the which the width occupied by the vehicle is maximum

[timid silo]

How can i compute it with derivative?

[obtuse pebble]

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[royal karma]

If

[royal karma]

If
$A \subseteq B \ so \ B-A=B\Delta A$

[warm shale]

Kingo