help-10

[timid silo]

|-x| = |x|

how?

[final python]

https://math.stackexchange.com/questions/1601430/prove-that-x-x/1601438

might help

[obtuse pebble]

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[tulip ginkgo]

How do I do this?

im not even fully sure what its asking me

[high lily]

its asking you to factorise the cubic

and you're given one of the (linear) factors

consider stuff iike polynomial long division

[tulip ginkgo]

cant i just use synthetic divison?

[warm shale]

H-Mobile

[tulip ginkgo]

x(x-3)(x-4)

i think

nvm apparently its wrong

i dont get it

[high lily]

why do you have x^3 - 7x^2 + 12x

you started with a cubic,
and the divided by a linear factor,
what degree is the quotient supposed to be

[tulip ginkgo]

oh

2?

[high lily]

yes

[tulip ginkgo]

ohhhh its meant to be

$x^2 -7x +12$

[warm shale]

H-Mobile

[tulip ginkgo]

wait but (x-3)(x-4) is still wrong 😦

[high lily]

because (x-3)(x-4) is a quadratic and is clearly not the factorisation of a cubic

[tulip ginkgo]

x(x-3)(x-4) is tho right?

that was wrong too

[high lily]

no

you forgot something very crucial

[tulip ginkgo]

:[

[high lily]

specifically the third factor that was given in the question and that you yourself also used to perform the division itself

[obtuse pebble]

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[autumn cloak]

really struggling with this question. Could someone give a explanation or better, a working out.

[obtuse pebble]

@autumn cloak Has your question been resolved?

[obtuse pebble]

@autumn cloak Has your question been resolved?

[mild ocean]

@autumn cloak just do the cross products

the cross product in the parentheses comes first

although this kinda looks like the vector a is defined in terms of itself

i guess just find what the vector a is and find what the ijk coefficients are

then put those in the answers for a_x, a_y, and a_z

i’m confused too actually

[obtuse pebble]

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[wary vigil]

hallooo :3 I need some help with partial derivatives. If i had a function that is defined as $f(x,y)$ if $(x,y) \neq (0,0)$ and as $0$ if $(x,y) = (0,0)$ is $\frac{\partial f}{\partial x}$ at $(0,0)$ dependent on the first part of the function or the second?

[warm shale]

Katharine

[hybrid gull]

I imagine the first part (limit definition?)

I'm assuming the limit definition holds for partial derivatives - I could be wrong.

[brave bramble]

Defined as f(x,y) if (x,y) ≠ (0,0)?

[wary vigil]

it's (x^3+y)sin(1/x^2+y^2)

[brave bramble]

Well, ∂f/∂x is dependent on the function lol

You'd need to know both

Specifically, you'd need the definition of the derivative's limit

Which needs f(0) and f(h) for small h

f(0,0) and f(h,0) I mean

[wary vigil]

😦

thank you 😄

i wanted easy life

i got derivative life

.close

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[vestal niche]

How do I write this with positive exponents, so I reciprocal everything or just the a-n

[vestal niche]

Do I *

Anyone?

[misty cedar]

just the a^(-n)

[vestal niche]

So it’d be 8/3a^n

?

[misty cedar]

$\frac{8}{3a^n}$ yes

[warm shale]

Peppermint Demon

[vestal niche]

Amazing thank you so much!

[misty cedar]

np

[vestal niche]

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[olive cypress]

hi

[olive cypress]

let's say there 60 people participating in a secret santa game
what is the probability that i and Bob draw each other's names

please help

@royal basin

[royal basin]

if the question asked for just the probability that you draw bob's name, would you be able to find that

[olive cypress]

1/(60-1)*1/(60-1)

is this right approach?

[royal basin]

no, and also you aren't answering my question.

[olive cypress]

yeah, that's probability

sorry

didn't understand the question

[royal basin]

if the question asked "What is the probability that you draw Bob's name?" would you be able to answer it?

i do not see what there is not to understand here.

[olive cypress]

oh yes

sorry my bad

it's 1/60

[royal basin]

correct.

now, are you also able to find the probability that bob draws your name, given that you have already drawn his?

[olive cypress]

ah it's 1/59

right?

[royal basin]

yes.

[olive cypress]

(1/60) * (1/59)

[royal basin]

yes, now you've got it.

[olive cypress]

hehe i see it now thanks!

please one quick question, too

if odd numbers of people play, is there a possibility one man doesn't receive a gift?

like statistically

[timid silo]

no

[olive cypress]

ok, thanks!

[royal basin]

under what conditions does someone not receive a gift?

is it if they draw their own name?

[obtuse pebble]

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@drifting ether Has your question been resolved?

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[soft marsh]

How does Delta r just disappear when -> 0

[spiral maple]

What?

[soft marsh]

Nvm I guess it was just another way of writing it my bad

[obtuse pebble]

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[tight violet]

Help

[hybrid gull]

.....

[tight violet]

Anyone can help me with these

Badly needed , its deadline is 2 hours from now

[hybrid gull]

Well if an ODE is homogeneous, then it is linear\

So first test for linearity

[tight violet]

Noted🎉

[hybrid gull]

Given this, or rather you can get this statement from the following:

If an ODE is not linear, then it isn't homogeneous/it can't be homogeneous

[tight violet]

do you mind showing me example solution for number 1?

So i could atleast able to solve myself the other solutions

[obtuse pebble]

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@tight violet Has your question been resolved?

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[tranquil rivet]

can someone help to explain why 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + ... = (pi^2)/6

[naive fossil]

https://www.youtube.com/watch?v=5iULOEZrjBA

[tranquil rivet]

ok thanks!

i tried to say uh it is the summation of 1/n^2

then summation of n^2 = [n(n+1)(2n+1)]/6

when I simplified I didn't get anything to do with pi at all

i got the 6 though

can someone explain why this is wrong

after I did the limit

and got something totally off

which is 0

<@&286206848099549185>

[obtuse pebble]

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[hybrid gull]

Do you have work?

[obtuse pebble]

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[broken sparrow]

im doing test corrections can i get help with this one?

[cerulean tartan]

interval of convergence is |x-3| < 2

thus radius of convergence is 2

[obtuse pebble]

@broken sparrow Has your question been resolved?

[broken sparrow]

@cerulean tartan howd u get the interval?

i was way off

[cerulean tartan]

[(x-3)/2]^n / n converges when 1 <= (x-3)/2 < 1

[broken sparrow]

thank you!

[obtuse pebble]

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[dim breach]

why is 6/10 = 3/5 my brain doesnt work rn i need an explanation

[dim breach]

.close

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[dim breach]

im so dumb

rn

thanks for ur help

[obtuse pebble]

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[timid silo]

How do I calculate A and B separately , I know how to find the average speed in total@but how do I do it for A and B

[high lily]

consider the line segments separately

and apply the same roc or slope formula

[timid silo]

so is this correct for A

2 over 20

iehj

so how do i do it <3

[high lily]

not 2/20

[timid silo]

hjkdaksH

[high lily]

how are you getting 2/20

[mild ocean]

the graph isn’t 1 to 1 so they’re confused

[timid silo]

🙃

[timid silo]

from 0, y2 - y1, 40 - 20

x2 - x1 = 4 - 2

for A

[high lily]

40-20 is 20 and 4-2 is 2
but why did you say 2 over 20 representing 2/20?

[timid silo]

uieq

so its 20/2 then

help

[high lily]

yes

[timid silo]

Ok ty

[high lily]

(which can be simplified)

[timid silo]

yeah

ok ty

.close

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[worthy stag]

Hey guys I had a question

[worthy stag]

I was doing my homework and I can’t understand if I did this one question right

Did I do d right?

If not how can I improve?

I’m pretty sure it’s correct but I just want to confirm

<@&286206848099549185>

[obtuse pebble]

@worthy stag Has your question been resolved?

[worthy stag]

no

<@&286206848099549185>

finna sleep now hopefully yall answer my question tomorrow 🥱

[short spruce]

you're correct, sleep well

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[steel wave]

helmp

[high lily]

what have you tried

[obtuse pebble]

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[timid silo]

are these two calculations for the convergence radius correct?

[timid silo]

<@&286206848099549185>

[obtuse pebble]

@timid silo Has your question been resolved?

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@timid silo Has your question been resolved?

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@timid silo Has your question been resolved?

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[thorn sage]

I have an interesting question from my math core team training that I did not really understand.

"Let A be
3^2008-3^2007+3^2006-3^2005+...+3^2-3^1,
and Let B be
3^12-3^11+3^10-3^9+...+3^2-3^1"

find the HCF of A and B

ill appreciate if anyone could help me, thanks!!

[obtuse pebble]

@thorn sage Has your question been resolved?

[thorn sage]

<@&286206848099549185>

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[thorn sage]

.reopen

[obtuse pebble]

✅

[thorn sage]

<@&286206848099549185>

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[spark thunder]

im not sure how to properly substitute x = 1 into here, im trying to learn implicit differentiation

[spark thunder]

my professor said this is the result, could someone explain how to get here?

[spiral maple]

they plugged x=1 into the curve, not the derivative.

[spark thunder]

!

you're right, thanks for pointing this out

.close

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[wintry stream]

can someone please explain how to do this step by step

[mild ocean]

$\int_{x}^{4x} = \int_{a}^{4x} + \int_{x}^{a} = \int_{a}^{4x} - \int_{a}^{x}$

@wintry stream

[warm shale]

quantum

[mild ocean]

use this and the chain rule

[obtuse pebble]

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[viscid flume]

hey can i please get help

[viscid flume]

I need to determine the exact value using compund angle formulas

[obtuse pebble]

@viscid flume Has your question been resolved?

[viscid flume]

<@&286206848099549185> please help

[viscid flume]

someone please help

[carmine bear]

tbh I have limited knowledge on this topic since I've only just started learning it but I think I have a solution. Ill use degrees to explain because it's easier for me since im not used to radians. Basically -13pi/12 is -195 degrees, now using a CAST diagram you know that cos(-195) = cos (165) since cos(360 - 195) = cos (-195). Now you also know that cos(165) is the negative of cos (15) as shown in the CAST diagram again. To calculate cos 15 you use the compound formulas with either cos(60 - 45) or cos(45 - 30).

i suppose now you can use these since you just need to calculate cos (15)

[viscid flume]

its kinda confusing since I was taught in radians and ur telling me in degrees lol

[carmine bear]

ok ill try my best

[viscid flume]

alright thank youy

[carmine bear]

cos(-13 π /12 ) = cos (11 π /12) as can be shown in the CAST diagram

[viscid flume]

yea

[carmine bear]

then also in the cast diagram you know that cos(11 π /12) = cos( π /12) since cos (11 π /12) is in a quadrant that is negative for cos

and that π - π/12 = 11 π /12

[viscid flume]

yes

[carmine bear]

you can rewrite cos ( π /12) as either cos ( (π /3) - ( π /4) ) or as cos( ( π /4) - ( π /6) )

since you have A and B

you can use the compound angle formulae to find cos( π /12)

and then to find the cos(11 π /12) you just have to multiply by -1 since it's in the negative quadrant

[viscid flume]

which formula would I use?

because for compound angle formula

[carmine bear]

you'll use the one for cos (A-B)

[viscid flume]

why?

if I have cos(pi/12)

[carmine bear]

ill have to go back to degrees to explain this bit since it's easier to understand

π /12 = 15 degrees

π / 3 = 60

π / 4 = 45

60 -45 = 15

so you're basically breaking down so that π /12 = π /3 - π/4

I believe you should be expected to know the cos, sin and tan values of π /3 , π /4 and π /6

[soft sail]

wouldn't it be simpler to use the fact that negatives don't matter for cosine to solve for cos(-13pi/12)=cos(13pi/12)=cos(12pi/12+pi/12)=cos(pi+pi/12)?

[carmine bear]

I didnt really know that, I'm still fairly new to the topic myself, only just learnt it. But this is the way id do it since it just seems clearer to me.

[viscid flume]

to be honest I understand what u did

i got it

thank you so much

[carmine bear]

np

[viscid flume]

.close

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[sharp lantern]

Hi, can anyone show me the workout for this?

[timid silo]

What have you figured out so far?

You're trying to simplify this, right?

[sharp lantern]

yeah

[sharp lantern]

just that the first one would be x

[timid silo]

You are saying that (cbrt(x))^2 = x? Why would that be?

[sharp lantern]

um

[timid silo]

What's (cbrt(27))^2?

[sharp lantern]

i just mean how do u simplify this? its from indices. i dont know wheres cbrt something is coming from so ...

[mild ocean]

rewrite roots as fractional exponents

[timid silo]

The first part of the expression you posted is (cbrt(x))^2
cbrt(x) just means cube root of x by the way, I am typing on my phone so I obviously cannot draw it exactly as you posted on the paper

[sharp lantern]

hmm

i was confused by cbrt

[harsh sentinel]

the square root of x is just x^1/2

similarly, the cube root of x is just x^1/3

[sharp lantern]

ok

[obtuse pebble]

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[regal wyvern]

Hello everyone. I've been doing some indefinite integrals on my own accord and tried attacking $\int \frac{\sqrt{x^4 + x^{-4} + 2}}{x^3} dx$. I've attempted to do a substitution $u = \frac{1}{x^4}$, (and further, $u^{-1} = x^4$ and $\sqrt{u^{-1}} = x^2$, $du = -\frac{4}{x^5} dx \implies dx = - \frac{x^5 du}{4}$), which produced the solution as follows:
$\ \int \frac{\sqrt{x^4 + x^{-4} + 2}}{x^3} dx = \int \frac{\sqrt{u^{-1} + u + 2}}{x^3} \cdot (- \frac{x^5 du}{4}) = -\frac{1}{4} \int \sqrt{\frac{u^{-1} + u + 2}{u}} du = -\frac{1}{4} \int \sqrt{\frac{u^2 + 2u + 1}{u^2}} du = -\frac{1}{4} \int \frac{u+1}{u} = -\frac{1}{4x^4} + ln(x) + C$.

[warm shale]

JarrGarde

[regal wyvern]

I have two questions:

1. Is the substitution done valid, since it relies on getting an interim result x^2 which can be further subbed in terms of u?
2. Do we take liberties by saying sqrt(u^2) = u (and sqrt((u+1)^2) = u+1) because the substituted value is strictly positive?

[obtuse pebble]

@regal wyvern Has your question been resolved?

[regal wyvern]

<@&286206848099549185>

[hybrid gull]

That looks good to me

I don't think we worry about the exact values of x and u here, we just care about their relationship

Feel free to check this integral on integral calculator, or on Desmos

Desmos:

Set f(x) = your answer
Look at the graph of f'(x), see if it's the same as the original integrand. (There may be domain issues, but the idea remains the same)

[regal wyvern]

This is actually... clever, never would have thought of this, even though it is obvious

[hybrid gull]

Thank you!

[regal wyvern]

So this is something that should be a concern only when solving definite integrals?

[hybrid gull]

In my experience, yes

[regal wyvern]

Fair enough, thank you so much!

.close

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[hearty parrot]

An oil company bores a hole 240m deep. Estimate the cost of boring if the cost is £70 for drilling the first metre with an increase in cost of £3.50 per metre for each succeeding metre.

Would n = 239 since the first metre is included in the initial cost (a=70)?

[carmine bear]

I would presume so

[obtuse pebble]

@hearty parrot Has your question been resolved?

[hearty parrot]

the formula i am using is sum = n/2 [2a+(n-1)d],
would i need to include the -1 after the n if i have already taken the first metre into account? or is n-1 standard for any arithmetic progression?

[obtuse pebble]

@hearty parrot Has your question been resolved?

[carmine bear]

it's standard for any arithmetic progression

[obtuse pebble]

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[errant quest]

need some help on this question

i have the partials of x y and lamda

but i dont know what to do after that

[obtuse pebble]

@errant quest Has your question been resolved?

[errant quest]

.

and this one idk how tf to set this up

[obtuse pebble]

@errant quest Has your question been resolved?

[errant quest]

is the x just negative infity positive infity

[mild ocean]

,w plot y = x and y = 3x

[warm shale]

Results provided by WolframAlpha

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

Requested by quantum#6320

[mild ocean]

never mind

best to do it on desmos

@errant quest plot it on desmos and find the x and y intervals

the upper bound for y should be obvious

[obtuse pebble]

@errant quest Has your question been resolved?

[errant quest]

what does the bar notaion mean ?

[mild ocean]

no clue

i just assumed there

[errant quest]

oh thats fine

i can ignore it and see what happens

maybe it doesnt really matter

let me try it out

[mild ocean]

i suggest doing that at first

[errant quest]

so if i plug it into desmos i should get the intervals?

[mild ocean]

yes

well you have to manually find them

it’s really easy though

[errant quest]

like this/

[mild ocean]

yeah

but with the appropriate functions

[errant quest]

there we go

[mild ocean]

the bar above x probably means something then

because these functions only intersect at x = y = 0

[errant quest]

how would i set up the intervals then?

it goes from 0 to x

and 0 to 3x?

wait no i lied we just dont have x bounds

[obtuse pebble]

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[obtuse pebble]

@errant quest Has your question been resolved?

[obtuse pebble]

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[ruby minnow]

Consider $$y= \sqrt{1-x^2}$$ over interval [0,0.5]

Then $$(\frac{\sqrt{3}}{4} \le \int_{0}^{ 0.5} \sqrt{1-x^2} dx \le (?)$$

Could anyone please tell me how they got sqrt(3)/4 and how should I figure out (?)

[warm shale]

màe

[obtuse pebble]

@ruby minnow Has your question been resolved?

[plain owl]

$\sqrt{1-x^2}\geq \frac{\sqrt{3}}{2},\forall x\in [0,0.5]$

[warm shale]

Euclid31415

[ruby minnow]

Sorry I'm still confused

[plain owl]

$\implies \int_0^{0.5}\sqrt{1-x^2},dx\geq \int_0^{0.5}\frac{\sqrt{3}}{2},dx=\frac{\sqrt{3}}{4}$

[warm shale]

Euclid31415

[ruby minnow]

Oh

Thank you!

.close

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[plain owl]

You got how to figure out (?) ?

[obtuse pebble]

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[ruby minnow]

Um, nope I'm still stuck

[ruby minnow]

Could you please help me with that?

[plain owl]

Assuming similar argument, \$\sqrt{1-x^2}\leq 1,\forall x\in [0,0.5]$

[warm shale]

Euclid31415

[ruby minnow]

Ahh okay, got it, thank you so muchh!!

.close

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[jagged spear]

hi, I'm stuck on this problem. I don't even know where to start

[jagged spear]

I assume $dz = (\frac{\partial z}{\partial x})_y \cdot dx + (\frac{\partial z}{\partial y})_x \cdot dy$

[warm shale]

Almeric Lo

[jagged spear]

but then I don't know how to proceed

[obtuse pebble]

@jagged spear Has your question been resolved?

[jagged spear]

<@&286206848099549185>

[jagged spear]

.close

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[lusty vigil]

How can I solve this equation
dh/dt = k · √h

[celest pike]

you can use variable separable , take all the h terms to one side

and if there were any t terms to the other

so , here

dh/√h =k . dt

and now we integrate both sides

to get

√h/(1/2) = kt + c

i.e.

2 √h =kt +c

this is the final equation

hope this helped!

[lusty vigil]

thanks a lot!

.close

[obtuse pebble]

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[celest pike]

np!

[obtuse pebble]

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[wicked stag]

Hi, how can I define the formation law of F and G? I know what to do after, but I'm a little stuck on how to transform this into a ax + b function.

[obtuse pebble]

@wicked stag Has your question been resolved?

[wicked stag]

<@&286206848099549185>

[timid silo]

Those are interval defined functions. Assuming they are polynomials, you can use a certainnumber of points to find their expressions in their respective domains

[wicked stag]

Are they polinomial bc of the parabol before the rising on F?

[timid silo]

The straight lines are also polynomial functions

[wicked stag]

i get that its interval defined, but i still didnt get on how i should extract the function

[timid silo]

You have to sample some points, insert them in a generic polynomial function, and get the value of the coefficients

[obtuse pebble]

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[timid silo]

Hey i have a question how do i find the formula for this sequence?

[timid silo]

Do you know abel’s theorem?

i have not heard of it

Hmm might not be helpful then lol

[obtuse pebble]

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[crude root]

Are these values correct?

[crude root]

is the height in 0 = ∞ or is it = 0

[obtuse pebble]

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[crude root]

damn gtg

.close

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[vivid oxide]

i need to prove the following statemen

[vivid oxide]

i understtand why its true, im just not sure how to approach the proof

#discrete-math <@&286206848099549185>

[nocturne minnow]

You have to wait at least 15 minutes before pinging helpers

[calm quail]

Verbally or...?

[obtuse pebble]

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[short spruce]

when what

chain rule = composite function

[spiral maple]

if there's a composition, chain rule is applicable

[obtuse pebble]

@tough light Has your question been resolved?

[spiral maple]

you have a composition...

sqrt(x) and you put x^2-1 into it

$f(g(x))=(f\circ g)(x)$

[warm shale]

Mosh

[spiral maple]

composition

cause... there's a composition of functions

chain rule is purely used for compositions

$\sqrt{x^2-1}=f(g(x))$ with $f(x)=\sqrt{x}$ and $g(x)=x^2-1$

[warm shale]

Mosh

[spiral maple]

no

it isnt

o is composition, not whatever you just wrote

[obtuse pebble]

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[devout gust]

pleaseee, i change the equation but i dont know how put that in the grapich

someone can help me? 😞

[jolly ginkgo]

Wdym changed

[nocturne minnow]

What did you try?

[devout gust]

equatiooon

r = 3

and

[nocturne minnow]

Show your work

[devout gust]

sure

x² + y² - 14x -12y = -76
x² - 14x + y² - 12y = -76
x² - 14x + ? y² - 12y = -76 + ?

x² - 14 + 49 + y² -12y = -76 + ?

so 49

its

-76 + 49

so

( x-7)² + y² - 12y = -27

and then is the same

BUT

[nocturne minnow]

That looks good for the x term, but what about y?

[high lily]

what do you have after completing the square for y too?
(give the full equation)

[devout gust]

(x-7)² + y² -12y ´+ 36

ahh

[nocturne minnow]

You didn't complete the square for that

[devout gust]

ahh sorry guys my english is bad

im from mexico

then???

guyyys help 😭

[high lily]

what do you have after completing the square for y too?
(give the full equation)

[devout gust]

oh

sure

full? 😭

[nocturne minnow]

Yes

[devout gust]

from the beginning??

😭

[nocturne minnow]

No

[devout gust]

😔

[nocturne minnow]

You did part of it

[devout gust]

oh

siii

[nocturne minnow]

You completed the square for just x, you need to do y now

[devout gust]

(x-7)² + y² - 12y + 36 = -27 + 36

(x-7)² + (y-6)²

= 9

(???

[high lily]

yes

[devout gust]

SIIIIII

SO

[nocturne minnow]

Do you know the equation of a circle and what it means?

[devout gust]

r = 3 right??

[high lily]

yes, your r is correct

[devout gust]

yes yes

buttt

[high lily]

however you will need to identify your centre

[devout gust]

idk how ubicate!!

[devout gust]

yes i did!!!

[nocturne minnow]

No you didn't

[devout gust]

centre is 7,6

no?

[nocturne minnow]

If that's the center, relook at the drawing you did

[high lily]

parentheses
(7,6)
yes

[nocturne minnow]

Where is the center in that graph?

[devout gust]

amm

(? 😭

[nocturne minnow]

Where did you put the center for this graph?

What is the center in that?

[devout gust]

amm i dont know 😭

😔

[nocturne minnow]

How do you identify the center of a circle?

[devout gust]

for the equation

[nocturne minnow]

In general

[devout gust]

x - 7

huh

wdym

[nocturne minnow]

Look at the graph you drew

What is the center of that circle?

[devout gust]

OH

now 😁

[nocturne minnow]

Nope

[devout gust]

(7,6)

a

NOO 😭

😁 ?

[nocturne minnow]

No

[devout gust]

whereeeee 😭 😭

I HATE MYSELF

I HATE GRAPHIC

WHEREEE 😭 💔

WHY ITS SO HARD

[nocturne minnow]

If the center is (7, 6) what is the x coordinate and the y coordinate?

[devout gust]

sorry 😔 👌

[devout gust]

x is 7

and

y is 6

OH

OMG

NOW? 😭

[nocturne minnow]

Yes

[devout gust]

OMG

[nocturne minnow]

That's it

[devout gust]

WOW

REALLY

HEY

GUY

DONT LEAVE

ME

I NEED MOREEE EXERCISE

AAAAAAAH

THAK U SO MUCHO

MUCH

I DONT WANT CLOSE THAT I WILL BE USED LIKE IN SOME MINUTES

[obtuse pebble]

@devout gust Has your question been resolved?

[devout gust]

@nocturne minnow

how do this?? 😭

its ( -1, 3 )

i think

[autumn adder]

Hi!

[devout gust]

OMG

HI

you can help me?!?!

[autumn adder]

Do you have to graph the following parabola?

[devout gust]

siiiiii

yes

[autumn adder]

There are many ways, lemme just show you one.

[devout gust]

omg thank u!!

🤭

[autumn adder]

Okay, see...

[devout gust]

YES

[autumn adder]

We will find intercepts for the parabola.

For example, the y-intercept of the parabola

[devout gust]

siisisi

i find!

[autumn adder]

Is that value of y where x is 0

So put x=0 in parabolic equation

And find value of y

[devout gust]

😯

[autumn adder]

What does it come to be?

[devout gust]

huh 😭

OH

7

y = 7

[autumn adder]

Okay, so that means

the graph must be passing through (0,7)

Now you have to find the lowest point of the parabola

[devout gust]

ohhh

[autumn adder]

As in the eqn. a > 0

SO the parabola opens upwards

Find the discriminant

[devout gust]

wait i translate

ohhohohh

[autumn adder]

Its
$ax^2+bx+c=0$

[warm shale]

Muhammad Hussaini

[devout gust]

🤯

[autumn adder]

$If a>0, parabola opens upwards$

[warm shale]

Muhammad Hussaini

[autumn adder]

Here a is greater than 0

It is 4

[obtuse pebble]

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[autumn adder]

So it opens upwards

[devout gust]

WOOA

[autumn adder]

.reopen

[obtuse pebble]

✅

[devout gust]

so its

4?

[autumn adder]

No.

[devout gust]

oh 😭

[autumn adder]

You have to find the vertex now

The lowermost point

[devout gust]

omg

SIISIS

WITH THE EQUATION?

[autumn adder]

You can find the discriminant first

If the equation has a solution, then we dont need to find a vertex

[devout gust]

y = 4² + 8x + 7

[autumn adder]

$D=\sqrt{b^2-4ac}$

[warm shale]

Muhammad Hussaini

[devout gust]

oh 😭

[autumn adder]

Use this to see whether you get real values or not

[devout gust]

a = 4

right?

and

b = 8

[autumn adder]

Yeah

[devout gust]

or not?

AHH

[autumn adder]

c=7

[devout gust]

thank u so much

if you see

[autumn adder]

Well its not this much

[devout gust]

that

im

dumb

is for

[autumn adder]

Nah youre not

Just practice

[devout gust]

im not speke english very well 😭

im from mexico so

its more hard still 😭

[autumn adder]

$D=\sqrt{8^2-4(4)(7)}$

[warm shale]

Muhammad Hussaini

[autumn adder]

You can easily see, that D does not exist in real numbers

So parabola has no x intercepts

[devout gust]

woaa

[autumn adder]

Or values where y is 0

Now you need to find vertex

[devout gust]

so 🤔

SIII

sososo

seee

see

y = 4x² + 8x + 7

x =

😭

OH

x = - 8/2x4

[nocturne minnow]

The easiest method, plug in some x values

[autumn adder]

Remember, the x-coordinate of vertex is always
$x = \frac{-b}{2a}$

[warm shale]

Muhammad Hussaini

[devout gust]

SII

[nocturne minnow]

Like 0, 1, and -1

[devout gust]

SIIIII

[autumn adder]

Well @nocturne minnow

[devout gust]

x = -1

[autumn adder]

The vertex lies above x axis

[devout gust]

y = 3

SOO

( -1, 3 )

[autumn adder]

Yeah

Nice

[devout gust]

OMG

YEA

[autumn adder]

So you got the vertex?

[devout gust]

I DO IT?

[autumn adder]

Now you have two points

Yeeahhh

[devout gust]

🥳

[devout gust]

SIIIIIIII

FINALLY

😭

😔

[autumn adder]

You got y-intercept, and the vertex

You can make it now

[devout gust]

emmmmmm

how i

how i

ahh

[autumn adder]

?

[devout gust]

how find that

😭

i mean 😭

how like

how find

yea

[autumn adder]

Now you just drag those points

On your screen

To the points we just found

[devout gust]

-1 and 3?

[autumn adder]

First we found (0,7)

[devout gust]

omg

[autumn adder]

...

Then we found (-1,3)

So, you can do it now!

[devout gust]

? 😁

[high lily]

you're not plotting your points correctly

[devout gust]

😞

[autumn adder]

No

[devout gust]

😭 WHY ITS SO HARD UBICATE POINTS FOR ME

[autumn adder]

That rightmost point

Take it to 0,7

[devout gust]

sii

[nocturne minnow]

It seems like the main concept you are have trouble with is plotting cordinates

[autumn adder]

And the vertex (lowermost point) take it to (-1,3)

[nocturne minnow]

What is the x and y value of (0, 7)

[devout gust]

YES

[devout gust]

OH

[nocturne minnow]

They are coordinates, (0, 7)

[autumn adder]

I guess he/she had the same problem in the prev. question...

[devout gust]

soooooooooo

[nocturne minnow]

You don't pick it individually

[devout gust]

? 😭

[autumn adder]

YEAh

[devout gust]

OMG

WHAT

RLLTy?

OMG 😭 👏

[devout gust]

XDD YES

😭

[autumn adder]

Take some exercises on plotting points

You'll be all good

[devout gust]

OMG THANK U SO MUCHO

MUCH

ALL

ARE SO SWEET

[autumn adder]

Welcome!

[devout gust]

THANK UUU!!!!!!!!1

OMG

AHH

RLLY THANKS

!!!!!!!

.close

[obtuse pebble]

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[crystal stream]

Hi

[crystal stream]

I need some help here, maybe someone can help? Thanks.

I don't know about c and b.

[royal basin]

consider: A * adj(A) = det(A) * I

[crystal stream]

Hi Ann

I used that for proving that adj(A) is invertible

The thing is that I don't know if my explenations are enough

[royal basin]

ok but you didn't post any of your work

[crystal stream]

It came out that adj(A) is equal to det(A) (which is not 0) multiplied by A^-1 (which is invertible)

[crystal stream]

I do. It is a part of the university requirements. I don't get any grade for that but it is.

[royal basin]

i think you misunderstood me

you didn't post any of your work here.

also, A*adj(A) = det(A)I should be something you have proved when first dealing with the adjugate.

[crystal stream]

Oh

Sorry

[crystal stream]

isn't that enough to say?

invertible matrix multiplied by a scalar is also invertible isnt it?

[crystal stream]

Thats because I write in Hebrew.

I can't change it to English anytime I want to post something

I did it it calculus though but it is a lot of work 🙂

[royal basin]

we're walking in circles now...

[crystal stream]

What do you mean?

@royal basin

[crystal stream]

Isn't that true?

[royal basin]

invertible matrix multiplied by a nonzero scalar is invertible.

[crystal stream]

Yeah

Then thats ok

but proving the other way

I suppose towards a contradiction that A isn't invertible

Which means that det(A) = 0

which means that adj(A) * A = 0

since adj(A) is invertible, it can not be 0

Contradiction

BUT, I did not know if I can say that if A = 0 then adj(A) = 0

and thats my question

[royal basin]

as in if A is the zero matrix?

[crystal stream]

yeah so I get confused here

because when we say det(A) = 0

it means the number 0

but not the zero matrix

So what is the meaning of adj(A) * A = 0 (the number)

[royal basin]

if you're gonna be pedantic

[royal basin]

this is incorrect

and the 0 should be O

[crystal stream]

when you say O you mean the zero matrix

OH

it is since 0 * I = O

ok

but if A = O, does it mean that adj(A) = O automatically

?

[royal basin]

yes

[crystal stream]

Gotcha

now another question

that I have something I wrote to show you

Thats for (c)

The thing is, that I don't know why det(det(A)) is det(A)^n

[royal basin]

det(det(A))??????

[crystal stream]

yeah

[royal basin]

you realize this is nonsense right

the step marked by the blue asterisk is nonsensical

you can't take the det of a NUMBER

it's $\det(kM) = k^n \det(M)$

[warm shale]

Kanga Gang Annihilator Ann

[royal basin]

so $\det(\det(A) A^{-1}) = \det(A)^n \det(A^{-1})$...

[warm shale]

Kanga Gang Annihilator Ann

[crystal stream]

Is that obvious ? I can see where that n comes from

[crystal stream]

Is that ok to say that det(A^-1) = det(A)^-1?

@royal basin

[royal basin]

there's nothing here i can say without feeling like i'm lying or being dishonest

[crystal stream]

What do you mean?

Isnt that true?

About those questions, they all seem true to me, but I don't know to prove that.

[crystal stream]

I don't get it

[royal basin]

i mean what i said please stop pinging me please stop pinging me please stop pinging me please stop pinging me please stop pinging me

[crystal stream]

Ok, mb

You're busy now then?

[royal basin]

no i'm just unable to help you

[crystal stream]

WhY?

[nocturne minnow]

People aren't required to help you, they help when they feel like it, and Ann doesn't feel like helping you

[obtuse pebble]

@crystal stream Has your question been resolved?

[crystal stream]

.close

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[fallen girder]

I know the harmonic series diverges, but what if we multiply it by a sequence that converges to 0?

[obtuse pebble]

@fallen girder Has your question been resolved?

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[obtuse pebble]

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[steady atlas]

How to calculate limit of x approaching -1 and 1

In step 4 I calculate asymptotes of the function in the top

I can figure out x approaching to infinity but not really when denominator equals 0

[obtuse pebble]

@steady atlas Has your question been resolved?

[warm shale]

Jawa

[steady atlas]

and

[warm shale]

Jawa

[obtuse pebble]

@steady atlas Has your question been resolved?

[steady atlas]

.close

[obtuse pebble]

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[fickle isle]

hi can i get some help with this question https://media.discordapp.net/attachments/331586246583386113/916982103571316736/unknown.png

[fickle isle]

honestly i dont even understand the question itself

is matrix b supposed to be the transformed matrix

[obtuse pebble]

@fickle isle Has your question been resolved?

[fickle isle]

<@&286206848099549185>

[obtuse pebble]

@fickle isle Has your question been resolved?

[lean sigil]

matrix B is the matrix that represents the transformation

Tv = B * v

and you need the find the kernel of the transofmation

and the image

Do you know how to calculate these things? @fickle isle

[fickle isle]

honestly

no

[final python]

https://youtu.be/NVohRlwmrBQ

this might help

[obtuse pebble]

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[cold thorn]

Can someone help me?
I want to differentiate this.
sin(ax+b) / cos (cx+d)

[timid silo]

Don't u have exam tomorrow?

[cold thorn]

?

no?

[timid silo]

Where are you stuck

[cold thorn]

i watched those videos people recommended me and now i trying some questions

and here i dont get what rule to use

like its division here

[timid silo]

Use chain quotient rule

[cold thorn]

chain quotient?

i can use chain rule on both

[timid silo]

Wait I'll show you

[daring marlin]

chain and quotient

[cold thorn]

but how to do vboth at same time?

[timid silo]

No u don't

[high lily]

take it one step at a time

you have a quotient of two functions

[cold thorn]

ok plz guide me what to do one by one

[high lily]

apply quotient rule first

worry about the chain rule later

[cold thorn]

wait

but how can i apply quotient rule

since theres no multiplicat6ion, right?

sin(ax+b) / cos (cx+d)

[high lily]

you have a quotient of two functions

[cold thorn]

Isnt sin(ax+b) part of one function?

and same for cos?

[high lily]

you literally have a fraction

[cold thorn]

uhh so

[timid silo]

Do u actually know how to use quotient rule?

[cold thorn]

yes

[timid silo]

Tell me

[cold thorn]

derivative of first (second) - derivate of second (first)
divided by
second^2

i think?

[high lily]

whut

[cold thorn]

sin(ax+b) / cos (cx+d)

[high lily]

please don't use first and second here

makes it sup[er confusing to read

[cold thorn]

sin' (ax+b) - cos (cx+d)' / cos^2