help-0

[high rapids]

By my experimental mouse traps

[stone glen]

They prolly are dead anyways

[night pumice]

oh

.close

[lone heart]

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[stone glen]

Don't look like they last long

[night pumice]

lol

[lone heart]

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[magic osprey]

i need help with this

[magic osprey]

i just need someone to explain why there's work being done or none

i can take care of the computations

i just don't understand it

[prime badge]

it's really just if something moves

4 and 5 are no work, and the rest have work

force and movement

[magic osprey]

how will you explain the second one though?

[prime badge]

elevator is doing work on the woman

[magic osprey]

for example the lady is 40kg

oh wait

im stupid

lady = 40kg
displacement= 2m

then

w = (40)(9.8m/s)(2m)(cos0)

[prime badge]

400 N × 2m

[magic osprey]

right?

[prime badge]

yeah

[magic osprey]

OMG

I FUCKGNI GET IT NOW

[prime badge]

i honestly don't

[prime badge]

oh the ball kicking is interesting

cuz there's almost no displacement

[magic osprey]

isn't the displacement the distance traveled by the ball?

[prime badge]

no

[magic osprey]

or am i stupid?

[prime badge]

only the time when her foot is in contact would count

[magic osprey]

wtff\

[prime badge]

it's a messed up example

i can't just say oh it's zero work

it's totally non zero

but it's a tiny displacement and a tiny force too

hm

basically you calculate the kinetic energy of the ball, and that would be work

not via force displacement

[magic osprey]

that's so annoying

[prime badge]

and then number 1 is weird lol

[magic osprey]

this is an example our teacher gave us

which is basically number one

so i just basically copied it

[prime badge]

yes, all the relevant force is to cancel air drag on the tray

so no force honestly

if the intended answer for 3 is no work, i can't explain it

if you can do it with kinetic energy, that's correct

[lone heart]

@magic osprey Has your question been resolved?

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[foggy scroll]

<@&286206848099549185>

[foggy scroll]

can anyone help me with second part

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[high rapids]

What have you tried

[wanton nova]

Yoo

U helper now

Nice

[foggy scroll]

nothing yet

my teacher never really went over how to solve with intergral

i know how to do geometric equations that’s it really

[high rapids]

How are supposed to answer this question if you don't know integration?

[tacit arch]

triangles are enough

shade in the areas you're supposed to calculate, and find each one separately then add them all up in the end

[tacit arch]

1/2 * b * h

[high rapids]

Yeah but didn't they ask to use integrals?

[foggy scroll]

she wants me to use integrals tho

[tacit arch]

what formulas do you know

at this point, you know the answer and how to do it, but no one here knows what your teacher exactly wants besides you. go ask her

[lone heart]

@foggy scroll Has your question been resolved?

[lone heart]

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[small pine]

someone solve this exercise pls

[small pine]

I need to study for a test and got stuck in 22

[high rapids]

We are not here to solve for you

Only to help

[small pine]

ye but i dont know what to do

or you can explain how to solve it step by step without giving an answer

[high rapids]

Try drawing with the info provided

Why does the bird look like a cockroach lol

[small pine]

idk

[lime bobcat]

Are you sure that horizontal distance to the bird is rightly represented??

[small pine]

im asking!!!

and does not matter

[lime bobcat]

I'm asking you to help you think.

[small pine]

bc they dont grade graphs

[lime bobcat]

That's how someone learns, it's called formative assessment.

[small pine]

its annoying, if it is not right just tell me where it should be the point or whatever and why

[lime bobcat]

No.

Good luck, bye.

[small pine]

lol

just be like a normal teacher dude

[lime bobcat]

I hope a normal teacher helps you.

[high rapids]

Use angles

[small pine]

is it good this approach @high rapids ?

[high rapids]

And trigonometry

Yeah good enough

[small pine]

ok, i'll try

[clear stump]

@high rapids why are you green

[high rapids]

For self validation

[clear stump]

ok

[high rapids]

@small pine were you able to solve? I need to go sleep

It's easy peasy lemon squeezy

[small pine]

bro

im here

the book gives other answer tho

@high rapids

[high rapids]

Yes book is correct

For the first part all the angles of the smaller (narrower) triangle was found and the sine rule was used for the answer

For the the second part the whole right triangle was used to find the answer

[small pine]

ohhhh

i got it

ok done

.close

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[lone heart]

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[turbid juniper]

is counting rules and combinatorics the same/related?

[finite flax]

yes.

[turbid juniper]

oh okay

thank youu!

.close

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[wild talon]

when proving an equivalence between two expressions, do you have to only develop either LHS or RHS or can you develop both at the same time

[last ether]

Well

Depends

It really depends

[wild talon]

uhm

how do I know if i can

do both

or not

[last ether]

Kinda hard to give you a guideline

[wild talon]

because the answers provided only develop 1 side until its the same

[last ether]

Its more intuition

[wild talon]

if its like induction

and I just need to prove p(k+1)

could i do both sides?

[last ether]

Induction then I guess you develop one side

[wild talon]

oh..

[last ether]

But then like I said

It really depends

[lone heart]

@wild talon Has your question been resolved?

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@wild talon Has your question been resolved?

[cedar field]

Can you please find and do an algebra practice sheet with me?

[lone heart]

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[opaque hinge]

Did I draw this correctly

[lone heart]

@opaque hinge Has your question been resolved?

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@opaque hinge Has your question been resolved?

[opaque hinge]

<@&286206848099549185>

I don't know how to solve this question

[blazing saffron]

Shouldn't it just be the vectors added together

[blazing saffron]

https://www.youtube.com/watch?v=g9lgL6f3h90

[opaque hinge]

I did do that

[lone heart]

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[digital python]

does anyone know how to do the second one, from the graph, the limit tends to -0.5

[tacit arch]

guessing taylor expansion is not an option?

[digital python]

thank you, this should do it.

.close

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[narrow viper]

Dont understand how to do any of the problems that arent crossed out

[young finch]

Send the whole question

[narrow viper]

Alright

[young finch]

So you can tell which quadrant these points are in based of the signs

Like quad 1 is ++

Quad 2 is -+

Etc

[narrow viper]

Yea

[young finch]

What does is mean by trig ratio

Its already given?

[narrow viper]

No i think were supposed to determine it

Its not given yet

[young finch]

oh waif nvm

I see what its asking

So the first value will be the horizontal side of the triangle and the second value will be the vertical side of the triangle you can make

think unit circle

[narrow viper]

Oh

[young finch]

then you can find the hypotenuse of the triangle which is needed for cos and sin

For tan and cot you don't have to make the triangle I think

[narrow viper]

Could you go through one of the problems so I can better understand exactly how to do these?

[young finch]

So 1

-2,7

Needs the cosine trig ratio

based off the signs we know it is the second quadrant

[narrow viper]

Mhm

[young finch]

We can make a triangle

-2 is the base

7 is the height

[narrow viper]

Ill draw it right now

[young finch]

find the hypotenuse which is √53

cos is a/h

Adjacent is -2

hypotenuse is √53

-2/√53

simplify

[narrow viper]

Wait how do you know hypotenuse is 53 squared?

[young finch]

-2√53/53

[young finch]

Root*

[narrow viper]

mb

[young finch]

And I used Pythagorean theorm

[narrow viper]

Oh I see

[young finch]

Also theta is always going to be angle at the origin

[narrow viper]

Ohh so when I simplify it its -2/ 53 to the square root?

[young finch]

what

No you simplify by rationalizing

Which means multiplying both sides of the fraction by the same thing

√53×√53 is 53

[narrow viper]

Ohh to cancel the square root

[young finch]

And -2×√53 is just -2√53

Yes because you cant have a root in the denominator

[narrow viper]

Oh alright

that makes it simplier when the point is shown as a coordinate but

what would I do when it's shown in radians

like in problem 5

[burnt vortex]

could someone please help me finish up some questions I have for precalc

[young finch]

You know your unit circle right

[narrow viper]

Yea

[young finch]

#❓how-to-get-help

[young finch]

7π/6 has its own coordinates

[burnt vortex]

thx

[young finch]

-√3/2,-1/2

Both are negative which means it's in quadrant 3

[narrow viper]

Oh I forgot to use the unit circle

[young finch]

yeah

[narrow viper]

alright thanks a lot

I think I understand this now

[young finch]

okay good

[narrow viper]

.close

[lone heart]

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[lone heart]

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[eternal kestrel]

Okay so I am going over a few things for my calculus final and I have a few questions regarding rationalizing. I understand that you cannot have a radical in the denominator. But technically you’re allowed to have one in the numerator. This confuses me because there are still times when you rationalize the numerator, which makes no sense because then you end up with one in the denominator.

[vale wigeon]

I understand that you cannot have a radical in the denominator.
your understanding is wrong

there is nothing illegal per se with having a radical in the denominator.

you are allowed to have a radical anywhere you want within your expression

[eternal kestrel]

Then why rationalize?

[vale wigeon]

usually because it helps make cancellation happen

and that can, say, make it possible to calculate a limit by direct substitution when it was impossible prior

[eternal kestrel]

So do I just guess when it ends up in cancellation?

[vale wigeon]

no

[eternal kestrel]

Just do it and hope for the best?

[vale wigeon]

there's nothing wrong with doing it and finding out it wasn't helpful

you can always backtrack

[vale wigeon]

misleading

[tacit arch]

That's for 12-year-olds

Same logic why we tell children to never cross the street on red but adults do it all the time

[vale wigeon]

would wager the no crossing on red thing is a fair bit more important than rationalizing denoms

[eternal kestrel]

Im so confused, how come you cant have one but you can

[vale wigeon]

the reason why you rationalize denominators is not necessity but convenience, and there is an important difference between the two

you can

you can

there is nothing wrong with it

[eternal kestrel]

Why does it say you cant

[vale wigeon]

some people insist it's illegal because they confuse necessity with convenience or think children aren't able to grasp the difference

[tacit arch]

Read an appropriate math book for math rules, not some random website that doesn't tell you what level/grade/age its audience is targeted to

[eternal kestrel]

I was lied to my whole life

I thought u couldnt have a radical in the denominator

[tacit arch]

Indeed. Many of us were

Also Santa isn't real

https://c.tenor.com/HdLdTvcR_DEAAAAM/boom-anna-kendrick.gif

[eternal kestrel]

He isn’t?!?! 😧

[tacit arch]

,calc 1/sqrt(2)

[ocean seal]

Result:

0.70710678118655

[high rapids]

You are adopted

[tacit arch]

,w Santa clause

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[high rapids]

,w riemann

[ocean seal]

Results provided by WolframAlpha

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[vale wigeon]

are we done here

@eternal kestrel do you have anything else to ask?

[eternal kestrel]

Im moving on to trig but for now no

[vale wigeon]

ok

.close

[lone heart]

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[stone ruin]

Does this transformation exist, if not why not

if it does what is it

and it should say f(x) < x not f(x) < y

[lone heart]

@stone ruin Has your question been resolved?

[lone heart]

@stone ruin Has your question been resolved?

[tacit arch]

you can just try a piecewise transformation

[lone heart]

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[gentle lion]

If the cost price is 96% of the selling price, what is the profit%?

[simple current]

cost price=0.96sell price
sell price=100/96cost price
Profit=sell price-cost price
profit=sell price-0.96sell price
profit=100/96cost price-cost price
profit=0.4sell price
profit = cost price/24

[rapid nova]

cost price = 0.96 * selling price
profit = selling price / cost price - 1 = selling price / (0.96 * selling price) - 1 = 1/0.96 - 1 = 100/96 - 96/96 = 4/96 = 1/24

[simple current]

wait wouldn't that only be if the cost price was 1?

[rapid nova]

well, the question was about profit %, not its value

and the answer is that the profit is 1/24 of the cost price

[simple current]

huh true

Aya I misread the equation

[gentle lion]

Thanks guys

.close

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[misty bobcat]

what is the difference between degree of graph and degree of vertex

[misty bobcat]

degree of vertex is a number of incident edges with vertex

and degree of graph ?

[prime badge]

it's uh nothing, it's not defined, unless every vertex has the same degree

nvm, it can also mean maximum of the vertex degrees

[misty bobcat]

uhm

thanks

[rapid nova]

yeah, it's called a k-regular graph (k being the degree)

[misty bobcat]

.close

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[candid robin]

how do i do this

[candid robin]

i dont understand where to start

im looking at the answers, and i cant see why there are like 30 solutions

[rapid nova]

where did you get that?

your answer is correct

[candid robin]

those arent my answers

theyre the teachers

[rapid nova]

just solve sin(x) = sqrt(3)/2 and sin(x) = -sqrt(3)/2 separately

and then combine the answers

[candid robin]

???

where do i start

[rapid nova]

wdym

do you understand everything up to sin(x) = +- sqrt(3)/2?

[candid robin]

where did we get sin from

[rapid nova]

cosec(x) = 1/sin(x)

by definition

[candid robin]

ok

so then

ohh

ok that makes sense

so then why are we finding the values pi/3, pi-pi/3, etc

[rapid nova]

sin(x) = sqrt(3)/2 gives us solution of form arcsin(sqrt(3)/2) * (-1)^n + pi n = pi/3 * (-1)^n + pi n
in [0, 2pi] that gives us pi/3 * (-1)^0 + pi * 0 = pi/3 and pi/3 * (-1)^1 + pi * 1 = pi - pi/3 = 2pi/3

sin(x) = -sqrt(3)/2 gives us solution of form arcsin(-sqrt(3)/2) * (-1)^n + pi n = -pi/3 * (-1)^n + pi n
in [0, 2pi] that gives us -pi/3 * (-1)^1 + pi * 1 = pi + pi/3 = 4pi/3 and -pi/3 * (-1)^2 + pi * 2 = 2pi - pi/3 = 5pi/3

[candid robin]

what the hell

please explain

[rapid nova]

that's just how you solve sin(x) = a equation

i mean you can also do it visually

[candid robin]

yes please

[rapid nova]

just won't work for a general case

but ok

do you know that arcsin(sqrt(3)/2) is pi/3

[candid robin]

uhh

i guess yeah

[rapid nova]

does this help?

[candid robin]

what does that show me

[rapid nova]

it shows all the points where sin(x) is sqrt(3)/2 or -sqrt(3)/2

[candid robin]

ah i see

so basically we're trying to find the value of the thing at these 4 points?

[rapid nova]

yes

[candid robin]

ook cool

@rapid nova

how did my teacher come to this?

atm i only get that its 1-sinx and 1+sinx, which is difference of 2 squares

but why is it on the top and why is there a 1^2 - sin^2x at the bottom?

[north adder]

htey found a common denominator

done with q?

[candid robin]

so like they multiplied each one by the other

OH

okok thx

[north adder]

nw

[candid robin]

you can close it now if u want

[rapid nova]

it's you who is supposed to close it with .close

[candid robin]

.close

[lone heart]

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[tidal zealot]

is this equstion bernoulli or binomial?

idk what topic it lies under

[north adder]

this is a combinatorics quesiton

[tidal zealot]

ok thanks

.close

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[simple current]

can I just do elimination and have

[north adder]

thats one point of intersection

[simple current]

and then substitute for the rest

[north adder]

how would you find the second

[simple current]

for a +-

[north adder]

ah.

yes

[simple current]

ok

[north adder]

you can do that

[simple current]

thank you

so like i'd do quadratic formula for the rest

[north adder]

yea that would work

no worries

[simple current]

ok chill then

thanks

[north adder]

yea happy to help

[simple current]

.close

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[lost coral]

am i doing something wrong here?

[lost coral]

i see the mistake

.close

[lone heart]

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[candid robin]

where do i start with this

[plush ice]

transpose the cos to the other side

[candid robin]

what does that mean

[plush ice]

transfer

move

[candid robin]

so 3sinθ-2cosθ=0?

[plush ice]

no just the sin

[gray ingot]

I think they mean dividing by cos on both sides

[plush ice]

well i cant explain it without give away the answer

[candid robin]

hmm

can you write what that would look like after 'transposing'

[plush ice]

sin/cos=2/3

that's basically the answer

[lone heart]

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[scarlet shore]

I got this integral wrong but i dont know were I went wrong

[vale wigeon]

you forgor the -1/4 factor

[scarlet shore]

Still it says the solution is 1/8tg^2(x^4) +C

[lone heart]

@scarlet shore Has your question been resolved?

[fervent timber]

what is tg

and what is sen

I’ve only heard of sin cos tan sec csc cot

and apparently there’s something called cis

[lone heart]

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[prime ice]

Can someone pls look through my solution and correct me if I’m going wrong anywhere

[lone heart]

@prime ice Has your question been resolved?

[prime ice]

<@&286206848099549185>

[scarlet shore]

Its just different notantion, sen is spanish notation for sin

[prime ice]

<@&286206848099549185>

.close

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[small wave]

how to solve this?

[supple fiber]

let u = 2

u + u = u^2

hence u^2 = x

u = x^(1/2)

2 = x^(1/2)

ln_x(2) = 1/2 => by inspection x = 4 = 2 + 2 QED

[lone heart]

@small wave Has your question been resolved?

[opaque hinge]

pog

[lone heart]

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[kindred anchor]

,tex Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that exactly one is a king.

[ocean seal]

QuantumBee

[kindred anchor]

P(getting Exactly one King)=$\frac{4}{52}\cdot \frac{50}{51}\cdot {2}$

[ocean seal]

QuantumBee

[kindred anchor]

Is that right?

<@&286206848099549185>

[lone heart]

@kindred anchor Has your question been resolved?

[median oar]

shouldnt it be 4/52 * 48/51 * 2?

the 2nd card cant be a king right?

there are 48 non-king cards in a deck

[prime badge]

yes that's correct, it's equally important to draw a non king too

4/52 * 48/51 + 48/52 * 4/51 = what fro$t said

[kindred anchor]

Got it.

Thanks

.close

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[wintry kestrel]

Is there a way to simplify this down? I'm trying to find the average angle of two given angles given a 2d plane (x and y are points)

[lone heart]

@wintry kestrel Has your question been resolved?

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@wintry kestrel Has your question been resolved?

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@wintry kestrel Has your question been resolved?

[lone heart]

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[edgy cape]

Hello I am stuck on 6i

I am not sure how to start this

[stone glen]

Add the 2 vectors

[edgy cape]

I think I have to find the horizontal and vertical components produced by 6 and 10 first and then add those but i don'tknow what angle to use

[stone glen]

That will give u the resultant

[edgy cape]

i can't just add 6 and 10

[stone glen]

No

[stone glen]

And I'm not asking you to do that

Do you know how 2 vectors are added?

[edgy cape]

by adding their horizontal and vertial

[stone glen]

No

[wary stream]

You need the components, typically

The x and y components

[edgy cape]

so that is correct?

[stone glen]

Yes

[edgy cape]

.

[wary stream]

.

[stone glen]

Don't add the horizant and the vertical

[edgy cape]

ye so the magnitude 6 produces 6costheta and 6sin theta and same with 10

but what is theta

[stone glen]

I dknt even understand what u mean by that

The component in the x-axis

[wary stream]

They didn't specify x and y components, when they said horizontal and vertical components

[stone glen]

Exactly

[wary stream]

Normally horizontal is along the x axis

[wary stream]

Especially in a diagram like this

[edgy cape]

i mean horizontal and vertical around the given magnitude forces 6 and 10

actually i am wrong

[stone glen]

:/

[wary stream]

Law of cosine

[stone glen]

I don't understand

[wary stream]

Is how you find it

[edgy cape]

is that what i am finding,

[wary stream]

You have to find the magnitude first

Which applies law of cosine

[edgy cape]

how is magnitude law of cosine

oh wait ye

dam

so when two forces are at an angle that is not 90 then i can use trig for the resultant instead of pythag?

[wary stream]

Sure, I guess

Here's a useful video, if you're still confused, applies the same concept as your problem
https://www.youtube.com/watch?v=PNw4CTij2ok&ab_channel=SteveCrow

[edgy cape]

well i just need to confirm, i use 110 for the costheta?

[wary stream]

To find the resultant?

No

[edgy cape]

but 110 is the angle opposite to the 'side' I am finding

[wary stream]

And that is why I presented the video

So you can understand how to apply law of cosine with the resultant

The angle you'd be using is not 110

[edgy cape]

alright i will watch the video

[lone heart]

@edgy cape Has your question been resolved?

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[steep widget]

Hi, can someone explain to me what these 2 formulas are?

[steep widget]

(discrete math)

[lone heart]

@steep widget Has your question been resolved?

[lone heart]

@steep widget Has your question been resolved?

[hollow shale]

The left is read as "[something] choose [something else]." The right hand side is the expanded factorial definition of n choose r. n choose r computes the number of combinations of r things from n objects (no order).

$\binom{n}{r} = \frac{n!}{r!(n-r)!}$

[ocean seal]

castroploiin

[steep widget]

how about this one?

[hollow shale]

Replace n with r+k-1 and r with k-1

Works the same @steep widget

[lone heart]

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[vagrant rover]

Is 1 b?

[thick yoke]

No, 1 isn't B because of the horizontal asymptote

The horizontal asymptote of 1 is: y=1

[vagrant rover]

I thought it can't be A cause denominator has an odd leading degree.

[thick yoke]

its not A

[vagrant rover]

Ah okay okay

okay sec lemme tink

[vagrant rover]

Yeah that makes sense

Wait b isn't asymptote of 1?

[thick yoke]

B doesn't have a horizontal asymptote at all

C and D both have horizontal asymptote y=1

and A has horizontal asymptote of y=0

[vagrant rover]

Ah okay

makes sense

But how do we know c is y=1

The left side looks weird

How do we know it's approaching 1

[thick yoke]

you don't really know because of the qua

quality of the graph

[vagrant rover]

ah okay

so we make the inference based on the right side then?

Also, can we find the vertical asymptote with any of the information that we are given?

[vagrant rover]

We can't right?

since B isn't defined

Oh and so 1) is D and 3) is A?

[thick yoke]

yes

[vagrant rover]

tysm

[vagrant rover]

^

[thick yoke]

we know that the vertical asymptote is x=B but not more than that

[lone heart]

@vagrant rover Has your question been resolved?

[vagrant rover]

Okay tysm

.close

[lone heart]

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[river swallow]

hi im trying

but i got stuck there

[vagrant rover]

I think you forgot an x after 5

on the right hand side

also you should really be doing this with pen and paper or whiteboard/chalkboard

Cause it's really hard to do it using the online tools that you're using

And you'll get confused a lot

[river swallow]

im doing it with friends on discord thats why i use paint

im not sure if its this

[high rapids]

Damn I feel so old

Was about to say something "back in my days we had no discord friends to do math with"

~kids are ruined~

[river swallow]

we live in 2 different countries , we cant go to each others house @high rapids

it would be nice

nvm sorry i got it

.close

[lone heart]

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[alpine sable]

Why is this undefined?

[blissful breach]

Hey I was literally about to use this channel :(

[alpine sable]

.

And this here is defined 🤔

I don't get it

Shouldn't there be an equal sign for the function to exist

≥ or = to find f(c)

[summer sail]

because x = 1 is greater than 0 so the third function applies. In the first example x = 2 is undefined because 2 is not greater nor smaller than 2

[alpine sable]

Damn I feel stupid

Thanks

[alpine sable]

And if its smaller?

[alpine sable]

F(-1)

[summer sail]

then the first function applies

-1-1 = -2

[alpine sable]

Just realised this after the 3rd revision

Thanks

.close

[lone heart]

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[lone heart]

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[wanton nova]

hi

[median oar]

,rotate

[wanton nova]

do you know what a cubic number is?

[cunning star]

No.

[alpine kiln]

bound 600 between x^3 and (x+1)^3

[wanton nova]

its a number raised to the 3rd power

,calc 15^3

[ocean seal]

Result:

3375

[young dove]

Hi! I keep lurking here, just trying to solve a specific equation. Wolfram brings me to a solution but there is no step-by-step to get here. Is there other software that can help spell this out, or is it just an iterative estimate? log(e^x)+e^-x + x is really the underlying form. I figure ProductLog isn't applicable here, but maybe there is a sort of substitution that could get me by?

[wanton nova]

hi

you can type your question here

#help-4

[keen sandal]

Man must be typing for a while

[young dove]

I have been typing, someone just typed beneath me.

[wanton nova]

)

just copy paste it

[alpine kiln]

i have pro premium

if you want i can give you step by step for this one equation

[young dove]

I'll move over ty

I have pro premium too, still no dice

[wanton nova]

,calc 7^3

[ocean seal]

Result:

343

[wanton nova]

,calc 9^3

[ocean seal]

Result:

729

[cunning star]

oh I think i get it

9 is one

9 cubed?

[wanton nova]

yeah

[cunning star]

still more?

[wanton nova]

,calc 10^3

[ocean seal]

Result:

1000

[wanton nova]

nope

[cunning star]

I only need one?

[wanton nova]

yeah

thats what the question says

so the answer is 729

ok?

[cunning star]

So do I put that

or 729?

[wanton nova]

729 is a cubic number

so put 729

[cunning star]

?

[wanton nova]

yeha

but you have to show

[cunning star]

its 1 mark

[wanton nova]

adn?

[cunning star]

guess your right

[wanton nova]

,calc 8^3

[ocean seal]

Result:

512

[wanton nova]

write like this:

8^3 =512

[cunning star]

Alright.

[wanton nova]

9^3 =729

10^3 =1000

just these 3

[wanton nova]

what does dividing by a fraction mean?

[cunning star]

Im doing this on calculator btw because its a calculator test

25/2

[wanton nova]

yeah

ur right!

how did you do it?

[cunning star]

Just typed in my calculator

[wanton nova]

(

i had high hopes

[cunning star]

Was the answer right?

[wanton nova]

yeah

but why though?

[cunning star]

why did I type it in a calculator because its a calculator test. Your supposed to use a calculator

[wanton nova]

ok

dont mattah

[cunning star]

In my country, we have a test where we have to use calculators

[wanton nova]

do you know how to do it without?

[cunning star]

Yes.

[wanton nova]

how?

[cunning star]

But im not worried.

[wanton nova]

?

[wanton nova]

Ok

U here?

[cunning star]

yes

[wanton nova]

Ok

U here now?

[cunning star]

yes

[wanton nova]

Ok

So

What happenes when we multiply both sides by 2?

?

[cunning star]

8x?

[wanton nova]

?

Think of it this way

What is x÷2×2

?

[cunning star]

X/2?

X?

[wanton nova]

You get x

Right?

[cunning star]

Yes.

X times 2 is 2x?

[wanton nova]

So the ÷2 and ×2 cancel eachother out

Ok?

[cunning star]

Ok.

[wanton nova]

Yes

[cunning star]

Ok.

So do I do 4x/2?

[wanton nova]

Now we have

$\frac{4x-1}{2}$

[ocean seal]

Mike Oxbig

[wanton nova]

So basically (4x-1)÷2

Ok?

[cunning star]

ok

[wanton nova]

Its the same thing

Now we multiply by 2 on both sides

(4x-1)÷2×2

What do we get

What did i say about the ÷2 and ×2? What do they do to eachother?

[cunning star]

idk

4x-1÷1

[wanton nova]

Yeah

Which is just 4x-1

Right?

[wanton nova]

.

[cunning star]

yeah but that is very hard

[wanton nova]

They cancel and nothing remains

[cunning star]

so just divide by both sides

[wanton nova]

?

Now

We multiplied the left side by 2

[wanton nova]

Now the right side

[cunning star]

Whats the first step

[wanton nova]

Multiply both sides by 2

[cunning star]

what sides?

4x/2?

[wanton nova]

Everything that is left of the = is called the left side

And on the rightof the = is called the right side

[cunning star]

4x÷1÷1?

[wanton nova]

No

Dont rush

So

[cunning star]

Oh.

[wanton nova]

We multiply by 2 on both sides

What do we get on the left?

We just talked about this

...

[cunning star]

Oh I get that part

[wanton nova]

So what do we get on the lft

Left

?

[cunning star]

4x÷2?

[wanton nova]

F

Look above

[cunning star]

4x times 2?

[wanton nova]

No

This is the last time im explaining

(4x+1)÷2×2

What do the 2's do?

[cunning star]

oh ok im understanding

[wanton nova]

What do the 2's do?

[cunning star]

2x2=4

[wanton nova]

What do the 2's do?

[cunning star]

(4x+1)÷4?

[wanton nova]

Bro

Try to focus

Pls

[cunning star]

ok

[wanton nova]

If you add 2 to a number then you subtract 2, what do you get?

[cunning star]

the same number

[wanton nova]

If you divide by 2 then you multiply by 2, what do you get?

[cunning star]

same number

[wanton nova]

Good

Our number is 4x+1

We divide it by 2

Then we multiply by 2

What do we get?

[cunning star]

Yes, I get it.

[wanton nova]

BRO TELL ME

[cunning star]

1/2=0.5

0.5x2

[wanton nova]

F

I cant take this any longer

Sry bro

Im out

[cunning star]

Oh my bad lol

[wanton nova]

Bye

Fr this time

[cunning star]

Bro you got a video tutorial

.close

[lone heart]

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[lone heart]

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[thorny iris]

I am stuck on parts a and b

I used f'(x) = f(-4+x) - f(-4) / x

limit definition

but i am unable to get the slope or rate of change right

[abstract fractal]

Show your work

[thorny iris]

it super messy but i basically simplified the equation down to the equation: -4x-8

how would I get the instantaneous rate of change and slope from there?

[abstract fractal]

Again, show your work. You shouldn't have any variables at the end

Did you remember to take the limit?

[tender dew]

seems fine

just plug in -4 for x

[abstract fractal]

The problem is that theyre using lim h -> 0 (f(-4 + h) - f(-4))/h, except h is rebranded as x. There shouldn't be any variables after the limit

If they were just doing lim h->0 (f(x+h) - f(x))/h, then it'd be fine, but their comment seems to hint otherwise

[thorny iris]

yes thats what i did

i did that and then got to -4x-8

and then i subbed in 0

[abstract fractal]

Then why were there -4s here?

[thorny iris]

its asking at x = -4

i just switched h

for x

[abstract fractal]

That's what I was thinking

But if that's the case, you shouldn't get a variable. Plus, even if you take the limit x->0 now, you'll still get the wrong answer

You'll get -8, which isn't the slope of the tangent line

Wait, I made a mistake, lemme double check

Okay, the slope still isn't -8, even though lim x->0 -4x - 8 = -8, so there's an error somewhere in your working

[thorny iris]

yes I got -8 at first

and it said it was wrong

so i put in 8

[abstract fractal]

That's why I need to see your working so I can see what went wrong

[thorny iris]

here

also mb I got -2x+8

not 4

[abstract fractal]

Oh. Then everything's fine.

[thorny iris]

what would the slope be here

[abstract fractal]

Hold on

Second line

Nvm, you just forgot the ²

On the first line, it should be (-2(-4)² - ...), not just -2(-4)

[thorny iris]

yeah mb

Stil should be same answer tho

[abstract fractal]

Yep. The slope is 8

[thorny iris]

How did u find the slope

[abstract fractal]

Took the derivative. Same way you did, though with some shortcuts that you'll learn later

[thorny iris]

The derivative of what ?

[abstract fractal]

f(x)

[thorny iris]

But I get the formula -2x+8 from that

no ?

isn’t that the derivative of fx

[abstract fractal]

You're supposed to take the lim x->0

[thorny iris]

yeah

which gets 8

after u sub in zero

[abstract fractal]

No. It's the derivative of f(x) evaluated at -4, after you take the limit

[thorny iris]

oh

so if you take the derivative

of f(x)

without subbing in -4

?

[abstract fractal]

You'll just get the plain derivative. Though, you'll have to keep h as h

[thorny iris]

Ah ok

and then how would u find slope after solving that

would it just be the m value

[abstract fractal]

The derivative will end up being -4x - 8, and to find the derivative evaluated at -4, you plug in -4 for x

[thorny iris]

Ahh ok

[abstract fractal]

So the slope would be -4(-4) - 8

Which is 8

[thorny iris]

So basically I needed to take two derivatives

one w -4

limit 0

other just plain

w/o -4

[abstract fractal]

You don't need to take two derivatives. One will suffice. Both gave the same answer, you see

[thorny iris]

How so

The only derivative I took

Was -2x+8

and then I subbed in 0 to find rate of change

[abstract fractal]

Which was also 8

[thorny iris]

Yeah

But would that logic apply

To all types of questions ?

Would slope = instantaneous rate of change ?

[abstract fractal]

Sure. You just need to plug in the right value of x into the limit definition

[abstract fractal]

Slope of the tangent line would be, yes

[thorny iris]

OH

Ok

[abstract fractal]

That's the definition of instantaneous rate of change

[thorny iris]

That makes so much more sense

Ok thank you for the help lol

I have one more

if u wouldn’t mind rq

f(3) how would i determine the value

[abstract fractal]

Well, is there any red marks at x = 3?

[thorny iris]

yes but for x = 4

its hollow at x = 3

[abstract fractal]

In other words, it's undefined there

[thorny iris]

yeah thats what i thought

so it would be DNE right

[abstract fractal]

The hollow circle means it's not defined at that point

[abstract fractal]

Yes

[thorny iris]

yeah but its wrong apparently

thats what I had put at first

so would this question just be wrong?

[abstract fractal]

Well, it's definitely not defined

Not sure what they want

[thorny iris]

me neither bc they are for an integer value, dne, infinity, or -infinity

alright thanks for the help though

.close

[lone heart]

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[alpine sable]

they’re asking me to transform this formula so that x is isolated, is the answer : x = f + xf/y ?

[summer sail]

isnt it just x = f-y

[alpine sable]

i have no idea, i’m quite bad for now

i multiplied both sides by x, then both sides by f

[summer sail]

but then x isnt isolated

[alpine sable]

oh okay ?

[placid zinc]

Let's say you multiply both sides by f. Then you have:
1 = f/x + f/y

[alpine sable]

where have i made a mistake?

[placid zinc]

Then multiply both sides by x:
x = f + fx/y

[alpine sable]

oh so i was right?

[placid zinc]

There's an x on both sides, so no that doesn't work

[leaden jungle]

take it as a common factor

continue what you were doing and multiply by y

XY=fy+fx

xy-fx=fy

X(y-f)=fy

X=fy/(y-f)

[alpine sable]

so hold on

1. i multiply it by x, f and y?

on both sides

[summer sail]

or the easier way just subtract by 1/y

[leaden jungle]

multiply both sides by xfy

since that's the least common denominator

It's what kaynex and I did but over one step instead of 3

[alpine sable]

yeah i get u

and then we factorize the expression and move it to the other side?

[leaden jungle]

yeah

[alpine sable]

alright i see

[alpine sable]

does it only work with variables?

[leaden jungle]

wdym

[alpine sable]

hold on before that, i don’t understand how you factorized xy - xf

[leaden jungle]

X is a common factor

xy-fx= X(y-f)

multiplication distribution property

[alpine sable]

oh i see now lol

thank you a lot

[leaden jungle]

np

[alpine sable]

forget my question about the variables

.close

[lone heart]

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[slim iron]

If you are trying to use to log to find an unknown exponent would you use the absolute value of the base?

[slim iron]

For example I have 4782969 = -3^n-1

would i do log4782969 = log3 * n-1

then solve for n

aIt that wouldn't work