help-10

[sweet cobalt]

I gtg now sorry, does that make sense?

[weary horizon]

ohhh

yea

thanks

.close

[obtuse pebble]

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[wanton dagger]

How would I solve this inequality graphically?

[royal basin]

do you know the geometric meaning of absolute value?

[wanton dagger]

Nope

[royal basin]

|x| is the distance from x to zero on the number line

(alternatively, it may sometimes be helpful to think of |a-b| as the distance from a to b on the number line)

[wanton dagger]

Ok I see

Ok I got it thanks

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[hot iris]

.

I tried solving it till

[hot iris]

Now I'm stuck

[hot iris]

All of this is just the LHS

Ok i simplified it

@compact shadow

[obtuse pebble]

@hot iris Has your question been resolved?

[hot iris]

nvm

i figured it out

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[tepid lagoon]

How do I do this

[obtuse pebble]

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[wanton quartz]

These two rectangular triangles have the same perimeter. The slanted side of the lower triangle is the adjacent side of the triangle above it. The smallest angle of the bottom triangle is 20°, what is the value of the angles of the triangles above it? Can anyone help me? I've been searching for a really long time but can't find anything.

[obtuse pebble]

@wanton quartz Has your question been resolved?

[obtuse pebble]

@wanton quartz Has your question been resolved?

[obtuse pebble]

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[scarlet locust]

Is there an injective function from R to [-1,1]?

[desert sparrow]

Any ideas?

[scarlet locust]

sinx but that isn't injective 🗿

[desert sparrow]

What do you look for in an injective function

[scarlet locust]

a transformation of arctan might work I think

[desert sparrow]

Oh

Good

[scarlet locust]

horizontal line should only intersect the graph once at all points

[desert sparrow]

Try this

[scarlet locust]

isn't arctan's range (-pi/2, pi/2)

even if I squish it

it'd be (-1, 1)

🗿

this is really close to what I'm looking for tho

but I don't think any inverse trig functions would work

polynomials won't either

no idea @desert sparrow

[desert sparrow]

Hmm

I missed the point about closed intervals

[scarlet locust]

Practically though if I think about it if R is being mapped to [-1, 1] then we'd actually never be able to find an x numerically such that f(x) = -1 or 1 right

[desert sparrow]

I'm googling a lot harder now, essentially you cannot use a continuous function

So there is o en

one*

but you need construction 🗿

[scarlet locust]

wdym

[scarlet locust]

why not?

wait will this work
$$2\left(\frac{1}{1+e^{-x}}\right)-1$$

[warm shale]

Swas.py

[desert sparrow]

http://mathonline.wikidot.com/preservation-of-compactness-under-continuous-maps
R is not compact but [-1, 1] is. So you cannot use continuous functions

[scarlet locust]

this is a transformation of the sigmoid function

[desert sparrow]

Won't achieve -1, 1

Same issue

[scarlet locust]

yeah I guessed

[desert sparrow]

So you need to construct a magic function

Usually by hijacking the richness of the reals lol

[scarlet locust]

what is compact

[desert sparrow]

in here it's just closed and bounded

[scarlet locust]

interesting, how?

[desert sparrow]

Is this homeworok?

Homework*?

[scarlet locust]

nope

[desert sparrow]

lol

ok

[scarlet locust]

just curious

[desert sparrow]

mathematically or in an applied context?

The sigmoidal functions will work fine for anything since (-1, 1) works

[scarlet locust]

^

[scarlet locust]

mathematically

[scarlet locust]

yep

[desert sparrow]

By 'anything' I mean 'anything in a practical context'

[scarlet locust]

yeah

I get it

how would you do that magic construction

[desert sparrow]

It would be something like
https://math.stackexchange.com/questions/160738/how-to-define-a-bijection-between-0-1-and-0-1/160741#160741

I think this makes for an explicit solution
||https://math.stackexchange.com/a/3244494||

[scarlet locust]

I see

so it has to be non continuous

but wait if f(1) = 0
will 1/2 + arctan(1)/pi ∉ Range(f)

[desert sparrow]

no

The point of the construction

is to abuse the infiniteness of $\mathbb{N}$

[warm shale]

pepper

[desert sparrow]

$\mathbb{N}$ does not end

[warm shale]

pepper

[desert sparrow]

Oh by the way

For that

You just change the 0 and 1 to your endpoints lol

[scarlet locust]

yeah I get that

[scarlet locust]

yes but then what x will give 0.75

[desert sparrow]

It's basically the same function?

[scarlet locust]

wdym

we let f(1) = 0, if that wasn't the case the image of 1 would be 0.5 + arctan(1)/2 = 0.75

but since we let f(1) = 0, what would the pre image of 0.75 now be

[desert sparrow]

it doesn't matter

you take a finite subset of N

the starting members

to fill in special values

like -1

then you displace the future subsets as necessary

for example, you remap f(0) = lolwhatever

then you remap f(1) = 0

since f(0) would originally have been 0

[scarlet locust]

then shouldn't it be f(n -2) instead of (n+2)

[desert sparrow]

then you remap f(2) = g(1), where g would be the original function, or whaever

[scarlet locust]

so that f(3) now gives 0.75

[desert sparrow]

Well I'm not sure

since that question is [0, 1]

the idea is the same though

[scarlet locust]

oh nvm f(3) will give 0.75 with f(n+2) only

I get it

[desert sparrow]

Yeah it just uses the infiniteness of N

imo concept is more important than the detail

[scarlet locust]

so technically we could pick infinite elements out of N and still be left with infinite elements?

[desert sparrow]

That's a feature

not a bug

[scarlet locust]

😳

does that mean we could also map N to R surjectively somehow?

@desert sparrow are you here?

[obtuse pebble]

@scarlet locust Has your question been resolved?

[obtuse pebble]

@scarlet locust Has your question been resolved?

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[scenic flare]

Hello I am doing a practice involving cosine and sine rule and I got stuck on a question can anyone help

[cedar flicker]

can you share the question

[scenic flare]

Here

Question 21

[royal basin]

a or b?

[scenic flare]

A

[royal basin]

and where did you get stuck?

[scenic flare]

basically i ttrieddifferent ways to solve it but disnt get it right so i was asking for help

[cedar flicker]

try opening it

[scenic flare]

i did the general cosine rule and got 3.4 but the answer is 3.97

[royal basin]

"general cosine rule"?

can you show your work?

maybe you were on the right track and simply made an arithmetic mistake for all we know

[scenic flare]

sure let me get an image, its kind of all over the place but ill show it

[royal basin]

oh boy

[scenic flare]

I mostly do it in my head and write on calculator so I don’t write as many things down

[scenic flare]

It’s not many things it’s just that I don’t write much things

[royal basin]

,rccw

[scenic flare]

do you know if the length is affected by the curve

[royal basin]

well ok like

i see you have a triangle with sides 3, 1.5 and x marked

you are on the right track

[scenic flare]

i felt so as well but this curve is driving me crazy idk if it affects the line or if it doesnt

[royal basin]

imagine unrolling the surface of the cone onto a flat plane. the result will be a circular sector whose radius is 3 (the original slant height) and whose arc length is the circumference of the original base

i.e. 2 * 2pi

[scenic flare]

ok

ill draw it to help me see it better

ok @royal basin i drew it but then what would the line AB be in this plane

it would be from half of the sector to the other correct ?

[royal basin]

it would unroll into a straight line

and arc AC would unroll into an arc of length 2 * pi

so in fact the angle opposite x in your triangle will be 2pi/3 radians, or 120 degrees

[scenic flare]

im sorry im not understanding is there a way you could draw it cause im getting mixed up

[royal basin]

one moment

[scenic flare]

ohhhh ok

c would be the perimeter of the cone base

and AT would be 3

right ?

[royal basin]

AT is 3, but i don't know what you mean by lowercase c

[scenic flare]

AC and A'C would equal the perimeter of teh cone base

each being half of the original perimeter

would B be at the exact middle mark ?

@royal basin

[royal basin]

AC and A'C would equal the perimeter of teh cone base
yes

well

together they make up the whole perimeter of the base yes

and yes B is the midpoint of TC as indicated in the problem

[scenic flare]

yes thats what i meant

[scenic flare]

let me try and solve it now

i think i might be able to

just a second

@royal basin something went wrong. I had the height of the cone which was 10xpi or 31.4159 but when i tried dividing by two ad=nd doing pythagoreon theorem it didnt work and gave me 7.6

i most likely did the wrong height formula

[royal basin]

the what???????

the height of the cone is not 10pi???

where the hell did you get that from lmao

[scenic flare]

this is the formula for height of cone correct

here image again to help

yeah i messed up the formula sorry

[royal basin]

???

this formula involves the volume

you don't have the volume of the cone and you don't need the volume of the cone

[scenic flare]

what would be the formula then

lmao im so sorry im very lost

been trying this qiestion for like 40 minutes now

[royal basin]

idk about anyone else but asking "what is the formula" is a great way to piss me personally off.

i was trying to offer you some explanation as to how to get angle ATB (see my diagram)

[scenic flare]

yes i know i messed the formula and i couldnt find it

ill just ask my teacher when i see her in class

sorry for the bother

.close

[obtuse pebble]

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[split laurel]

Hello

[split laurel]

I want to know what an array with a two dimensional axis means.

Like

[[1]]

How can there be a single element in a 2d array

??

[royal basin]

well this is a somewhat degenerate example of a 1×1 array

[obtuse pebble]

@split laurel Has your question been resolved?

[split laurel]

@royal basin what is a 1 * 1 array?

[royal basin]

an array with a width of 1 and a height of 1...

[split laurel]

Does it mean that this array value can be accessed using row index as well as column index

like [1]

and [[1]]

??

@royal basin

Am I right ann??

[royal basin]

i don't know what you mean

[split laurel]

Can I explain

A bit

?

[royal basin]

i don't know if i have enough energy to listen to what might be nonsense

but sure, go ahead and explain what you mean...

[obtuse pebble]

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[faint merlin]

@open granite stuck on maths sba too?

[open granite]

On a question? Yes I am!

[faint merlin]

Same here bro

[open granite]

sba...?

[faint merlin]

School based assessment

for cxc

[open granite]

Ooooh, no actually 😛

[faint merlin]

Oh

Im almost finished with my sba just to do the analysis and im done but idk how to do it just need some help, on a tight deadline and im trying not to let down my team

Data analysis

[obtuse pebble]

@faint merlin Has your question been resolved?

[faint merlin]

<@&286206848099549185> sorry for the ping, need some help plz

[obtuse pebble]

@faint merlin Has your question been resolved?

[faint merlin]

.close

[obtuse pebble]

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[obtuse pebble]

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[fathom lion]

I don't understand what happens here

1)why do the boundaries flip

2)why is the "1" positive and the "u" positive

^if you multiplied that bracket by -1/u^2

(im sure they are somehow linked but i haven't came across this idea formally)

[robust sleet]

$-\int_{a}^{b} =\int_{b}^{a}$

bruh

$test$

[timid silo]

RIP Tex

[robust sleet]

negative of a integral swaps boundaries

[fathom lion]

Could you have solved it without swapping boundaries

[robust sleet]

yes

I never do it

[fathom lion]

would it be harder

than this

[robust sleet]

no

[fathom lion]

wait so you can multiple the integrand by negative 1 and change the boundaries flip?

[robust sleet]

yes

[fathom lion]

ok intresting

thanks

.close

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[timid silo]

hello i need help with a multi step problem you have to look at the other pages to understand this one page so here

[timid silo]

that’s the question i need help with

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[cerulean plaza]

how do you quickly solve for x and find the radian values of something like tanx=1

[cerulean plaza]

like whats the best way to do it, do you have to memorize some values or does it have to do with understanding the tan graph

what are some strategies in general for trig questions like this

[tardy epoch]

memorize unit circle values

,calc tan(45 deg)

[warm shale]

Result:

1

[obtuse pebble]

@cerulean plaza Has your question been resolved?

[obtuse pebble]

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[cerulean plaza]

i get that but how do you determine the radian values

[cerulean plaza]

like is there a way to determine the values of pi/4 and 5pi/4

[burnt scroll]

You gotta memorize those sadly

[cerulean plaza]

i see

.close

[obtuse pebble]

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[cerulean plaza]

i just need more practice i suppose

[burnt scroll]

Well you only have to memorize the values in the first quadrant really

After that you can use equivalent angle stuff

[cerulean plaza]

right but my question is how do you look at tanx=1 and determine the values?

is that all thru memorized values?

[burnt scroll]

Remember that

Tan x = sinx/cosx

[cerulean plaza]

right

[burnt scroll]

which means sinx=cosx

In order to get tanx = 1

[cerulean plaza]

ok i get that, but how do u use that info to get the x values

[burnt scroll]

sinx = cosx happens in a 45 - 45 - 90 triangle

[obtuse pebble]

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[young marlin]

odd question........ does anyone know what this shape is called ?

[young marlin]

hilbert curve

.close

[obtuse pebble]

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[clear locust]

can anyone help?

[primal lark]

question?

[clear locust]

In a marriage ceremony of pembas daughter he has to make arrangement for accomodation of 150 persons.for this purpose he plans to build a conical tent in such a way that each person has 4 sq.cm of the space on the ground and 20cu.m of air to breadth.what should be the height of the tent

yea

this

[primal lark]

ok is it ok to think of the tent as a pyramid?

like its shape

ig so?

[clear locust]

yea maybe

[primal lark]

well i will go with the assumption then coz i am pretty sure

do you know the formula of the area of a pyramid?

i mean

volume

[clear locust]

yea

[primal lark]

$\frac {l w h}{3}$

[warm shale]

Sus

[clear locust]

1/3 × area of base × height

ik this

[primal lark]

now notice the area occupied by each person on the floor is 4 sq cm and the area of the floor is $lw$ and you have 150 persons so whats $lw$?

[warm shale]

Sus

[clear locust]

600

?

[primal lark]

yup

now

the amount of air inside the tent

is the volume of tent

ig?

[clear locust]

yea

[primal lark]

can you find the volume in terms of h first?

[clear locust]

the volume comes like 3000

[primal lark]

in terms of h i mean

[clear locust]

i dont get it

could you do it?

[primal lark]

your correct!

[primal lark]

you have the formula $lw*\frac {h}{3}$

[warm shale]

Sus

[primal lark]

lw=600

then whats the volume in terms of h?

just plug in 600 in lw

[clear locust]

200h?

[primal lark]

do you get it?

[primal lark]

yup

now try to form a equation

[clear locust]

oh ok

thanks

[primal lark]

for h

[clear locust]

all ring

right

ill do it

it seems

ive done a mistake

its a cone

[primal lark]

oof

was it mentioned?

[clear locust]

150 into 4

[primal lark]

somewhere

[clear locust]

is the base area

so height comes 15

thanks for the help tho

[primal lark]

wow

was it a coincendence

when i used pyramid

i also got 15

[clear locust]

damn

ig it works both ways

[primal lark]

ya

[clear locust]

aight cya

[obtuse pebble]

@clear locust Has your question been resolved?

[obtuse pebble]

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[stark perch]

Dumb question but how did they go from that step to the step shown in the box

[civic zealot]

u = 1 + cos(theta), so 1 - u = -cos(theta)

[stark perch]

Wait so what happened to sin theta

[royal basin]

it was cancelled out

[stark perch]

Ah makes sense

But how comes I’m changing to -cos theta? Am I missing out something here?

[obtuse pebble]

@stark perch Has your question been resolved?

[tardy epoch]

Read the whole solution and follow the algebra

[obtuse pebble]

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[verbal prawn]

Can someone construct that for me

[high lily]

what exactly are you struggling with?

are you able to draw something that looks like a rectangle

[verbal prawn]

I’m not understanding the question lol

Should I just draw a line of 90 deg then a diagonal of 8cm with base 7cm?

[high lily]

how accurate do you need this to be?

[verbal prawn]

As accurate as possible

[high lily]

you could start with what you described above

[verbal prawn]

Alr I’ll do it now

Nope

Couldn’t do it

[obtuse pebble]

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[obtuse pebble]

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[misty cedar]

if W={O}, then W wont have a basis and a dimension of 0 right?

[slim lake]

Yes

To it just use a contradiction

Assume there is a non zero vector v that spans the vector space W = {0}

Then show why v has to be the zero vector and hence the vector space doesn't have a basis

[obtuse pebble]

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[verbal prawn]

Can someone help?

[alpine raven]

maybe expand (x-1/x)^2 first

[slim lake]

No need you can solve for x in x+1/x=5

Just a quadratic

[scarlet locust]

there's an easier method

square both sides of x+1/x = 5

[alpine raven]

^

[scarlet locust]

the 2ab term will just be 2

and you can find the value x^2 + 1/x^2

[scarlet locust]

and substitute that in this expansion

[verbal prawn]

Got it

Thanks

[obtuse pebble]

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[distant moth]

how do i solve the equations in red

[scarlet locust]

to begin with you can factor a 3 from the 2nd and 3rd equation

it'd make them cleaner

[distant moth]

i get

c=-x

then if i put that in the 2nd eqn

i get y=-x/2

WTF

okay its working now

i think previously my brain wasnt working

.close

[obtuse pebble]

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[silent sail]

hello i was doing a non calc paper and had gotten as far as the markscheme shows with using tan ect but i dont understand how to get the answer 4 without using a calculator

[teal prawn]

you want to solve for k?

[silent sail]

yes

[teal prawn]

do yk the value of tan(30°)?

[silent sail]

nope

[verbal prawn]

It’s root 3 isn’t it? Or 1/root 3

[silent sail]

Im a little confused tho as we never needed to know it for class

[verbal prawn]

Use that

[teal prawn]

its a standard angle

you should know it

[teal prawn]

1/√3 yeah

[silent sail]

ok thank you

.close

[obtuse pebble]

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[verbal prawn]

You want the answer?

[silent sail]

4 right?

[verbal prawn]

Yes

[silent sail]

but isnt it pretty hard to find that answer non calc

[verbal prawn]

No..

It’s relatively easy

Which grade?

[teal prawn]

not really, since 30° is a standard angle, you should know the value of all its trig functions memorised

[silent sail]

aight

im 15

[teal prawn]

atleast 3

sin, cos and tan

[verbal prawn]

Oh..

[verbal prawn]

Ye

[silent sail]

oh yeah found it in the syllabus we need to know the exact value for trigonometric ratios of 0 30 45 60 90 i assume thats it

[verbal prawn]

Yes

Those are standard angles

I also need to remember them for my finals lol

[obtuse pebble]

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[solar stump]

Is $\frac{d}{dt} \frac{M}{2} (y_t (0, t))^2 = M y_t (0,t) . y_{tt}(0,t)$, where $y$ is a function $y(x,t)$?

[warm shale]

Waes (Wires)

[obtuse pebble]

@solar stump Has your question been resolved?

[obtuse pebble]

@solar stump Has your question been resolved?

[solar stump]

<@&286206848099549185>

[warm canopy]

i think you're good, just the chain rule right?

$\frac{d}{dt}(y(t)^2) = 2y(t)\cdot\frac{dy}{dt}$

[warm shale]

iCaird

[solar stump]

Cool cool

It's the blend of partial and full derivatives that keeps throwing me

[warm canopy]

$y_{t}(0,t)$ is just a function of t, so the partial and full derivatives are the same

[warm shale]

iCaird

[solar stump]

Ah great, cheers

,close

.close

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[timid silo]

How do I solve any sort of Quadratic Equation?

[obtuse pebble]

@timid silo Has your question been resolved?

[past pecan]

Quadratic formula

That is, $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

[warm shale]

Chris24

[past pecan]

This will give you the roots of a quadratic function. In other words, where the function is equal to 0.

[timid silo]

Thanks

.close

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[clear idol]

For all real numbers x, x is less than or equal to x²

I'm supposed to choose between 4 choices on what could prove the conjecture wrong. Namely:

b.) All whole numbers.
c.) Set of integers.
d.) Set of negative integers.```

However, I've tried all those but none of the choices proves the conjecture wrong (?)

[clear idol]

a.) Counting numbers:

Assuming x = 1, then 1² = 1. Which makes it equal to x².

Assuming x = 2, then 2² = 4. Which makes it less than x².

b.) All whole numbers, same as the previous choice.

c and d.) Integers:

Assuming x = 0, then 0² (x²) = 0 which makes x equal to x².

Assuming x = -1, then -1² (x²) = 1 , which makes x less than x².

Assuming x = -2, then -2² (x²) = 4, which makes x less than x².```
I would assume the same happens for every lower negative integer.

Am I doing something wrong?

[pine sail]

I mean do you have to only use these choices?

The statement

For all real numbers x, x is less than or equal to x^2
Is incorrect.

But for all integers, it's correct.
For all whole numbers, it's correct.
Since it's true for all integers it's also true for a set of negative integers of course.
And its of course true for the counting numbers as well.

So your choices are not what you should have.

And btw,
-1^2 = -1
(-1)^2 = 1
Kindly refrain from using -x^2 for (-x)^2 those are two different things.

[scarlet locust]

None of those actually prove it incorrect, you're right

Set of rational numbers would

[pine sail]

Or irrational.

[clear idol]

Oh, okay, thanks guys :))

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[warm shale]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[final sky]

Bruh

[obtuse pebble]

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[torpid crescent]

What is the Taylor series of this in sigma summation form? (where “a” is some constant)

[robust sleet]

u can rewrite e^((x(a+1))

[torpid crescent]

mhm but the Taylor series tho

[robust sleet]

how did u rewrite it

[last storm]

Is a a natural number? Because then I think you can write it as a geometric sum

[obtuse pebble]

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[torpid crescent]

wdym

[robust sleet]

e^(xa)e

for e^(xa) use taylor series of e^x with x=xa

for 1/(e^x - 1 )

use the taylor series of 1/(1-x)

the negative of it

with x=e^x

[obtuse pebble]

@torpid crescent Has your question been resolved?

[torpid crescent]

huh?

What is the Taylor series of the whole thing

[torpid crescent]

That’s not the Taylor series- Taylor series is made up of only powers of x

<@&286206848099549185>

[eternal bloom]

,w taylor (e^[x(a+1)]-1)/(e^x-1)

[warm shale]

Results provided by WolframAlpha

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

Requested by 1345631#4969

[torpid crescent]

Thanks

but

that’s 1 series over another I needed the entire thing as 1 series (if that’s possible)

[eternal bloom]

Then differentiate etc

[torpid crescent]

wdym

[eternal bloom]

f(x) = f(0) + f'(0) x + f''(0) x^2/2 etc

[versed turret]

$f(x-a) = \sum_{n=1}^{\infty} \frac{f^{(n)}(a)(x-a)^n}{n!}$

[warm shale]

castroploiin

[versed turret]

where f^(n) (a) is the nth derivative of f evaluated at a.

[obtuse pebble]

@torpid crescent Has your question been resolved?

[obtuse pebble]

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[misty valve]

Idk how my 10 rectangle midpoint answer is wrong

I wrote a program that game me 2x the answer

And then divided that by 2

[forest sinew]

2 times the answer 👀

in what language?

@misty valve

[violet compass]

the file says .py

so python

[misty valve]

Oh crap I found the mistake

[forest sinew]

oh i just noticed you posted the code too sorry

[misty valve]

Wasn't with the code it's in what I was intending

This calculates 5 rectangles

[forest sinew]

yes

if you can import you could try to generalize your code

w linspace

or just manually feed in your delta

[misty valve]

Ok ty

.close

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[craggy stirrup]

Hello can anyone help me with my homework

[misty terrace]

just post it

[craggy stirrup]

This is the question

So can u help @misty terrace

[tame berry]

what are nickels and what are dimes

assuming that
nickel = 5c
dimes = 10c

let N = #nickels and let D= #dimes

simultaneous equation

16+D=N
10D+5N=395

#dimes = 21
#nickels = 37

[warm canopy]

there are pennies too

[tame berry]

oh wait

there are pennies

lol

ok then

16+D=N
P=6D

10D+5N+P=395

3 equations

ok so

im assuming you know how to do simultaneous equations? @craggy stirrup

10(D)+5(16+d)+6D=395

so D=#dimes=15

#nickels=31

#pennies=90

[craggy stirrup]

I’m really sorry I just saw your answer

Can u explain again

[tame berry]

u know how to do simultaneous equation right?

[craggy stirrup]

Like solve them right

[tame berry]

ye

[craggy stirrup]

Yes I know

[tame berry]

the question is like a riddle

I think

[craggy stirrup]

So I solve this

[tame berry]

so you can form 3 equations from the riddle

[craggy stirrup]

Yes

[tame berry]

and then solve it to find the number of one coin

[craggy stirrup]

Ok

[tame berry]

ye do u know where it comes from?

[craggy stirrup]

From the “let” statement right?

[tame berry]

yeah

i just substituted stuff in from the previous equations

[craggy stirrup]

Ok I’ll solve it and tell u the answer

[tame berry]

ok ping me

[craggy stirrup]

Ok

[craggy stirrup]

I’m getting a decimal

@tame berry

@tame berry

[tame berry]

what steps are u doing?

ur just solving for D right?

@craggy stirrup

also if you think about it in real terms lol you can't have a decimal number of coins

[craggy stirrup]

Yes I’m solving for d

[tame berry]

can u show ur steps?

[craggy stirrup]

This equation

[craggy stirrup]

Sure

Never mind I got 15

Sorry I made a mistake in the end

So The answer is
D = 15

Now I just solve the rest of the word problem right

@tame berry

[tame berry]

yes

[craggy stirrup]

I got 31 nickels , 90 pennies and 15 dimes

Is it correct @tame berry

Is it correct

@tame berry

[tame berry]

yeah that's what I got

[craggy stirrup]

Yes thanks for your help
I also have another question

[tame berry]

he's been santa?

damn

[obtuse pebble]

@craggy stirrup Has your question been resolved?

[tame berry]

@craggy stirrup

I added 1/3+1/4+1/5 which gives 47/60

there's a 13/60 missing in his life

so 60 years

so hes 75 years old

i think

his working life has to = 1

so add all the fractions

and the remainder = 13

[craggy stirrup]

So add them and get 75

[tame berry]

13/60 = 13 years

[tame berry]

add wat

[craggy stirrup]

Nvm

I read it wrong

[craggy stirrup]

Do we add 47/60 to 13/60 @tame berry

@tame berry

Can u explain it again

[obtuse pebble]

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[craggy stirrup]

.reopen

[obtuse pebble]

✅

[craggy stirrup]

@tame berry

[obtuse pebble]

@craggy stirrup Has your question been resolved?

[tame berry]

wdym

so i added the fractions of his life

and got 47/60

so 1-47/60=13/60, right?

and he still has spent 13 years working as santa claus which is unaccounted for in those fractions

so 13/60 is = 13 years

which means that 1/60 = 1 year

so 60/60 = 60 years that he's spent working

[obtuse pebble]

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[frozen swift]

42

[frozen swift]

No calc solve fast

I need way

[fierce lagoon]

Good job, you're showing us a test

That's against the rules

Is this for points

[frozen swift]

Not a test

It’s my friends binder

He had me borrow it for practice for test

[fierce lagoon]

I see

[frozen swift]

Also it’s the weekend

LIL

[fierce lagoon]

42, use Pythagorean theorem to find either a possible leg or hypotenuse

Oh taht is true

I forgot

Actually no it's Nunday

[tame berry]

30

[fierce lagoon]

Don't just show the answer you gotta show them how

[tame berry]

oh its a test

[fierce lagoon]

It's not

[tame berry]

lul

[fierce lagoon]

It's a sample test

[tame berry]

i used trial and error

[craggy stirrup]

Why did u do 1 - 47

[tame berry]

because total working years = 60/60=1

its 1-47/60

which is 60/60-47/60

[frozen swift]

Ummm

Help

[craggy stirrup]

Oh ok

[tame berry]

sqrt(34^2-16^2)

[craggy stirrup]

Now I get it

[tame berry]

bet

[frozen swift]

Oh there is no fast way

Thx

.close

[obtuse pebble]

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[autumn delta]

Hey

[autumn delta]

so what does the f(x) represent here

I get the normal definintion with f(a+h) - f(a)

and h gets closer to 0

is x just a+h in this case?

or

[versed turret]

It's just the value of the function as it approaches x = a

[versed turret]

Yep

[autumn delta]

Okok ty

[versed turret]

So the lim would turn into h -> 0

[obtuse pebble]

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[autumn delta]

hey

[autumn delta]

so I get that the limit doesnt exist becuase both sides approach a different number

but isnt it approaching 0 on the graph

[alpine raven]

the limit of |x| when x approaches 0 at both sides is indeed 0, but it has nothing to do with differentiability

[autumn delta]

hmmmmmmmm

then why is it saying 1 and -1 here

isnt the algebra supposed to match the graph

[alpine raven]

and of course, we have two limits for |x| since the function isnt the same in all intervals

[autumn delta]

So this is a continiuous graph

[alpine raven]

yes, but not differentiable in 0

[autumn delta]

but the limit does not exist at x = 0 so therefore the derivative does not exist?

[alpine raven]

the limit of the rate of change, not the function itself

[autumn delta]

OHHHH

lmfao im so sped

[alpine raven]

if the limit of the rate of change (f(a+h)-f(a))/h when h-->0 isnt a constant or if it has two differents values, then its not differentiable

[autumn delta]

okay yeah that makes sense ty

[obtuse pebble]

@autumn delta Has your question been resolved?

[eternal bloom]

#❓how-to-get-help . This channel is occupied

[obtuse pebble]

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[winged bronze]

Can someone tell me

[winged bronze]

If I have done correctly

[torpid crescent]

Yes but what is the Taylor series of the original expression in sigma summation form

[brave bramble]

That's probably more detail than needed

Like good to me!

[winged bronze]

Okay, can I ask one more ?

Have I done right this one

[obtuse pebble]

@winged bronze Has your question been resolved?

[obtuse pebble]

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[digital fjord]

this is my teachers work

but i was curious what the critcal numbers were

from x^3+2 / x^3

[flat anvil]

well critical numbers by definition is where the derivative is either 0 or undefined

so clearly it would be undefined at x = 0 (division by 0)

and then you can solve x^3 + 2 = 0 to find the other one

[digital fjord]

im not sure how i would to solve it?

for critcal numbers

like how do i solve for a rational function like this

like normally i set demoninator = 0

so x^3=0

x=0

so thats one critcal number but its undefined there

but howw did my teacher get -sqrt ^3/2

as a critical number

@burnt scroll

or anyone idk

<@&286206848099549185>

[burnt scroll]

@digital fjord ok so

critical numbers are when the slope is equal to 0 or undefined right

[digital fjord]

yea

@burnt scroll

f'(x)=0

[burnt scroll]

what did you get for f'(x)

[digital fjord]

x^3+2 / x ^3

[burnt scroll]

ok so

the critical numbers would be when x^3+2 = 0

and also when x^3 = 0

[digital fjord]

oh

and i would use the critical numbers sqrt -2 ^3/2

and 0

when doing my first derivative test

for local and min?

[burnt scroll]

uh

-2 ^3/2

whats that

[digital fjord]

what

wdym

[burnt scroll]

-2^ 1/3 would be cube root -2

[digital fjord]

yea

so would i use cube root -2

and 0

[burnt scroll]

ye

[digital fjord]

as my critical numbers when using first derivative

test to find local min and max?

[burnt scroll]

ye

[digital fjord]

also what does it mean in my teachers sheet when its undefined at 0?

[digital fjord]

.

is it because thats the V.A?

and the critical number cannot lie there?

[burnt scroll]

this is the derivative right

whats the derivative equal to at x = 0

[digital fjord]

0

2/0 = 0

[burnt scroll]

uh

you cant divide by 0

[digital fjord]

oh

im not sure trhen

[burnt scroll]

so the derivative

is undefined at x = 0

[digital fjord]

but why

is it undefined at x=0

like howd u know

[burnt scroll]

well

f'(x) is equal to this right

f'(0) would be dividing by 0

but you cant do that

[digital fjord]

yea

so

i have to

idk

[burnt scroll]

like

since you cant do that

it does not exist

DNE

undefined

[digital fjord]

yea

1/0 = dne

or x/0

[burnt scroll]

ye

so since you dont know what the slope is at x = 0

you're trying to sketch the curve or something right

[digital fjord]

yea

[burnt scroll]

so you check what the slope is approaching

on the left side and on the right side

so that you can draw it

[digital fjord]

ohh with

cube root -2

[burnt scroll]

with that one you know the slope is 0 at that point

[digital fjord]

ooo

i think i get sorta

ilemme try myself

[obtuse pebble]

@digital fjord Has your question been resolved?

[obtuse pebble]

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[eternal nexus]

Would someone please help me to infer this line?

[eternal nexus]

This statement is true if it’s impossible for P to be true while Q is false.

[brave bramble]

So it's worth seeing the truth table:

So the only instance where a statement P → Q is false, is when you find some P that is true, and Q that is false

There's a common math term called the vacuous truth, for cases where there are simply no examples of P

So for example, for all x where x < 2 and x > 3, x = fish

[drifting wraith]

you can always replace it with "not P or Q" it doesn't mean anything else

[brave bramble]

Think that's false? Find me a counter example

[eternal nexus]

Haha

Got it.

You are awesome @brave bramble

Thank you 😊

[brave bramble]

Np, feel free to ask if you have anything else!

[eternal nexus]

.close

[obtuse pebble]

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[lost breach]

The length of a rectangle is the sum of the width and 1. The area of the rectangle is 72 units. What is the length, in units, of the rectangle?

[lost breach]

.close

[obtuse pebble]

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[lucid flume]

If three vectors a, b, c has magnitudes of 4,3,5

[lucid flume]

respectively

and the sum of them is '0'

then what will be the magnitude of $?$ c x (a x b) $$

[warm shale]

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

[lucid flume]

$$ c x (a x b) $$

[lucid flume]

here, the 'x' means cross product

Please help me understand how to solve the 98 no question

<@&286206848099549185>

[alpine raven]

there is a formula for c x (a x b) if im not wrong

something like that :
$\vec{c} \times (\vec{a} \times \vec{b}) = (\vec{c} \cdot \vec{a})\vec{b} - (\vec{c} \cdot \vec{b})\vec{a}$

[warm shale]

Ｈｅｒｅｌｓ

[vapid hamlet]

This won't help much, I think

Use the fact the the vectors are linearly dependent

And $|a\times b|=|a||b|\sin(\theta)$

[warm shale]

Zanarcane

[alpine raven]

well what is theta here ? 🤔

[vapid hamlet]

The angle between a and b

[alpine raven]

yes i know that

[lucid flume]

that is also my question, here theta is not mentioned

[vapid hamlet]

This is where collinearity plays a role

[lucid flume]

ok, but here a+b+c=0

that means it is colinear?

[alpine raven]

no

[lucid flume]

how?

[alpine raven]

colinear means there is a constant k such that a = kb

[lucid flume]

oh ok

[alpine raven]

and if they are colinear then theta = 0 or pi

[vapid hamlet]

Sorry, I meant something else

a, b, c lie on some plane

[alpine raven]

coplanar or idk how it said in english

[lucid flume]

you're right

it is called coplanar

[vapid hamlet]

So c is collinear to a × b (assuming a and b are not collinear)

[lucid flume]

ok, then?

[alpine raven]

we are talking about cross product tho, so they can't really be coplanar I think

[alpine raven]

yes thats true

or...

[vapid hamlet]

Then the magnitude would be zero... Sorry, let me think again

[lucid flume]

I found a wierd connection, so text book suggests that the answer is 60 and the product of the magnitudes of the vectors is also 60

[vapid hamlet]

Argh

[lucid flume]

[vapid hamlet]

I meant

[alpine raven]

its a physic books 😮

[vapid hamlet]

c is orthogonal to a × b

[lucid flume]

yes

[vapid hamlet]

So

$|c\times(a\times b)|=|c||a\times b|$

[warm shale]

Zanarcane

[lucid flume]

how you got that?

[vapid hamlet]

Because of orthogonality $\sin(\theta)=1$

[warm shale]

Zanarcane

[lucid flume]

Ok, then what about the a x b?