help-28

[vast fossil]

For larger N, the sum is more precise

As N approaches infinity, we get the exact value

[inland snow]

ah

i have to write a narrative on this paper so can I say "A riemann sum can be performed because as N approaches infinity, the sum becomes more and more precise" @vast fossil @stable plover

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@inland snow Has your question been resolved?

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@inland snow Has your question been resolved?

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@inland snow Has your question been resolved?

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@inland snow Has your question been resolved?

[simple totem]

a riemann sum is being performed, and as N tends to infinity the approximation becomes more precise

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[radiant umbra]

What is the equation of the line containing the altitude of 🔼ABC from B to <-AC->

[radiant umbra]

I am stuck because I don’t really know where to begin or what they are asking really as well

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[stuck roost]

which are the positive integers that can be written as the difference of 2 cubes

[jade radish]

There are like... many

[stuck roost]

ik but if it were all odd numbers for example then i coul;d just say all odd numbers

[jade radish]

that's not true I read wrong

[stuck roost]

i know im just suing it as an exmaple

[jade radish]

any odd can be written as a difference of 2 cubes

well if it's true then it's true

what're you asking exactly

[stuck roost]

like every odd number and multiple of 4 can be written as a difference of 2 squares

but how about cube numbers

[jade radish]

that's not true

[stuck roost]

isnt it

[jade radish]

it's not

wait lemme re-read what ur saying

are you trying to say that if u have two odd numbers squared that the difference of those will be a multiple of 4?

bc then that's true

[stuck roost]

im trying to say that every multiple of 4 and every odd number can be written as a difference of 2 squared

squares

[wild sleet]

an odd number is a difference of 2 squares, always

[stuck roost]

yeah

im asking about cube numbers in my question

which are the positive integers that can be written as the difference of 2 cubes

[wild sleet]

https://cs.uwaterloo.ca/journals/JIS/VOL6/Broughan/broughan25.pdf

[stuck roost]

i need the difference

not sum

[wild sleet]

yeah i wanted to say

they focus on sum

and claim that difference is also characterized in the process

idk, no answer

[stuck roost]

its kinda confusing

i observed that every 4th prime number can be written as a difference between 2 consecetive cubes

but how do i prove it

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[torn jolt]

i need help with 6 (a)

[torn jolt]

how am i supposed to calculate the corresponding change in y if the change in x is 4.2

[onyx glen]

you should know the definition of slope as $m = \frac{\Delta y}{\Delta x}$

[glossy valve]

Ann

[torn jolt]

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[modern mountain]

how do i solve these

would 5a be $(3x - 3)^2 - 12$

[glossy valve]

MathematicsPractice

[torn jolt]

no

[modern mountain]

k

[torn jolt]

Green PFP moment

[twin wolf]

[torn jolt]

9(x^2 - 6/9x - 1/3) = 9((x-3/9)^2 - 1/3 - 9/81)

[twin wolf]

what in the

[torn jolt]

complete the square

[modern mountain]

can u put in in texit

[torn jolt]

i just factored out 9 at start

u'll have 9((x-3/9)^2 + C)

then turn that into

(3x-1)^2 + C

and solve for c

$9x^2-6x-3$

[glossy valve]

hibyehibye

[modern mountain]

$9(x^2 - \frac{6}{9} - \frac{1}{3}) = 9[(x-\frac{3}{9}^2 - \frac{1}{3} - \frac{9}{81})$

[torn jolt]

$9x^2-6x-3 = 9(x^2 - \frac{6}{9}x + \frac{1}{3})$

[glossy valve]

MathematicsPractice

hibyehibye

[modern mountain]

huh

[torn jolt]

wat

[modern mountain]

sorry i gotta get my head around it

[torn jolt]

i just factored out a 9

$9x^2-6x-3 = 9(x^2 - \frac{6}{9}x) + 3$

[glossy valve]

hibyehibye

[torn jolt]

then complete the square for this

[modern mountain]

yep

ah

[torn jolt]

and u can expand the 9 into the parenthesis

[modern mountain]

right right

[torn jolt]

u'll get something like

[modern mountain]

gimme a sec

[torn jolt]

$(3x-1)^2 + C$

[glossy valve]

hibyehibye

[modern mountain]

right right

brb

[torn jolt]

$9(x - 3/9)^2 = (3x-1)^2$

[glossy valve]

hibyehibye

[warm siren]

What about vertex formula?

[torn jolt]

wats that

[warm siren]

-b/2a

[torn jolt]

oh

that might be easier lol

[warm siren]

yeah lol

do that instead

[torn jolt]

@modern mountain

$(\sqrt{a}x-\frac{b}{2a})^2 + Z$

and just find Z i guess

[glossy valve]

hibyehibye

[torn jolt]

theres probably a formula that idk

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[quiet zenith]

can somebody check my solving

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[gritty rose]

where does N^2 + 2N come from?

i guess it doesn't matter since you're gonna take N >> 1 anyway

you should use that simplification in the next step

[torn jolt]

1 = 1^2 + 2(1)

1 = 3 QED

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[grim summit]

take luis' elevation equal to greg's elevation

and then solve for t

[hard agate]

confused

[grim summit]

lets say luis' elevation is L, and greg's elevation is G

for their elevations to be equal, L has to be equal to G right?

so L = G

[hard agate]

so add there t values?

[grim summit]

if you replace L with 480 - 15t and G with 200 + 5t you can solve for t

it would be 480 - 15t = 200 + 5t

[hard agate]

14t?

[grim summit]

you have to move the t's to one part and the numbers to another

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[drifting thorn]

In orbital mechanics, are vectors always assumed to be perpendicular to each other?

[drifting thorn]

<@&286206848099549185>

[gritty rose]

#old-network for physics server

most vectors aren't perpendicular to each other

[drifting thorn]

I joined it just wondering bc this server responds faster

well damn then

[gritty rose]

trivially, a vector isn't perpendicular to itself

except for the 0 vector

[drifting thorn]

well I mean if

they all are using cartisan coordinates?

I was hoping they were

but ty

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[brittle shard]

when given a function f which resolves around an axis x if the function f is for example x^2 then you could imagine that at any altitude x it forms a circle with a radius of x^2. So the area of the cross sectional area at any x is pi*(x^2)^2. Then the integral can be calculated by integrating from interval (a, b) on x to give the volume. This all makes sense but what I do not understand is how this logic still holds for more complex functions. For example, sin(x) with x on the interval (0, pi). When revolving this function around the x axis it creates a sorta bridge. But you can still just plug it into the area of a circle and integrate and still get the correct answer? How come this works? How come you dont have to break it into parts and compute monotone sections of it at a time?

[brittle shard]

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[gentle brook]

What did I do wrong? Why is it -1.4, 3.4 instead of 1.4, -3.4 like it looks more like on the graph?

[light sonnet]

How did you simplify that fraction?

[gentle brook]

Divide and turn to decimal

[light sonnet]

How did you do it? Because I got -1.4

[gentle brook]

I got the same answer

But on the graph it looks like positive 1.4

[light sonnet]

Right there, in the work, you factored out a -1, and you forgot to change the sign for +2x, to be -2x

[gentle brook]

Wait how would it become -2x?

[light sonnet]

Because you factored out a -1 from both terms

[gentle brook]

Okay thank you

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[muted quiver]

where would i start for this problem

limits arent my strong suit

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[unique peak]

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[polar cairn]

well for 3 GC = PT

I think

I think so

a parallelogram

has 2 opposite and equal sides

2 pairs of

opposite and equal sides

what is m

thats what im confused about

well

i think it would be 180-109

but im not sure

if its asking for the TOP RIGHT angle then

it will be 180 - BOTTOM RIGHT

opposite angles are equal in parallelogram

so bottom right angle = top left angle

and bottom left angle = top right

bottom left is 180- bottom right because angles in a straight line add up to 180

i think?

yes

if u have bottom left

thats equal to top right

opposite angles in this case are the same

in parallelogram

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@torn jolt Has your question been resolved?

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@torn jolt Has your question been resolved?

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[vernal crystal]

How do you get the points (-6, 10) and (10, -2)

[runic bloom]

substitute -6 for x

[vernal crystal]

But where would I get -6 from

This is a answer sheet but it doesn’t tell me

[runic bloom]

ig they just chose a random number

you could also think abt the perfect cube roots

8 and -8 for example

so to get x - 2 to equal -8, x=-6 is a nice number to work with

[vernal crystal]

Ohhh

I remember my teacher telling me that now

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[ancient haven]

can someone verify if my answer is correct? i couldnt break it so i think its correct

[severe linden]

looks fine

[ancient haven]

bet.

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[weak fern]

can anyone tell me why they went from minus to plus? Is there a rule for that? Im trying to understand the answer

[covert wing]

Yep

[hot herald]

which line are you referring to

[covert wing]

Take the minus out common.

and

[weak fern]

from second line to the third line

[covert wing]

Its just to ease that factoring process

You could do it with the minus nevertheless

[weak fern]

ah i see

[covert wing]

Its more like

[hot herald]

and/or multiplying both sides by -1

[glossy valve]

Muhammad Hussaini

[hot herald]

or going the long inefficient although still valid route,
add x^2 + 4x + 4
to both sides of the equation

[weak fern]

i see

Thanks for the help, I understand it better now

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[torn jolt]

You downvoted your own self

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[supple sequoia]

In triangle ABC, points M and N lie on sides AC and BC respectively.
a) If MN || AB, MN = 4 cm and CM : MA = 3 : 2, find AB.
I proved that the two triangles are similar, but then I can't think of how to find AB

[scenic yew]

You already got it if u proved that the two triangles are similar

But do you have any idea what the ratio (length) of the bigger triangle is?

[supple sequoia]

no, I only have the proportions so CM is 3x and MA is 2x, I only know MN 4cm

[scenic yew]

yeah the proportion

That's what i'm asking

And what is the overall proportion of CA

[supple sequoia]

5x

[scenic yew]

you don't actually need the x

just 5 would do

and 3

[supple sequoia]

but its not 5 santimiters its 5 of something

its lont like the 4

[scenic yew]

yeah

[supple sequoia]

thats why im typing it with x

[scenic yew]

but it would cancel out if you try to equate it

ok ok

let's use the x

CA = 5x

[supple sequoia]

yes

[scenic yew]

While MC = 3x

[supple sequoia]

yes

[scenic yew]

so 4 cm/ 3x = BA/5x

And what would you guess, the x were cancelled

leaving us with?

[supple sequoia]

NO WAY IT WAS THAT

I cant believe how dumb am I

[supple sequoia]

I spent the past hour trying to figure it out bc I didnt know that here the x cancels

[scenic yew]

yeah u were overcomplicating too much stuffs

[supple sequoia]

I though that the 4 and 5x were different

[scenic yew]

You can just substitute it either with any values

[supple sequoia]

Damn

[scenic yew]

You can use 2 or 1 or 5

The thing is, they are just the same shape scaled up

[supple sequoia]

no but bc the 5x is not 5 cm its 5 times scaled up and the 4 is the exact cm and thats what I though they were different

[scenic yew]

Yeah but since they're the same shape, even if x is any number you can still get the lengthof BA

[supple sequoia]

thanks so much

[scenic yew]

ur welcome

[supple sequoia]

I litterally got exam tmrw and this was the only thing I couldnt understand this server is really life saver 🙏🏽

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[fierce fern]

Im trying to work out this integral, I've attached my written answer and I've attached the ms answer, they are different functions, however when checking with my calculator they both yield the same answer. Checking in desmos shows that they are different graphs, so are both the answers right? And if so how come you can have multiple different functions be the correct answer to an integral?

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@fierce fern Has your question been resolved?

[hushed spear]

Try u = sec^4(u) @fierce fern

[fierce fern]

ye but im just wondering why the values are

different

they are both right, however the graphs are different

AHH SHIT

its because + c right?

the constants will be different and that would make the graphs the same?!?!??!

[hushed spear]

Yeah

[fierce fern]

♥️

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[torn jolt]

Does anyone know why it says (-infinite,infinite) ?

Shouldnt it be (-3/4,-1/4) ?

Thats the part where they overlap

[dark lark]

i don't know mathematic's 😦

[quaint prawn]

The absolute value can never return a negative number

it will always be 0, or larger

[dark lark]

😢

[quaint prawn]

so when we are solving for all x that make the inequality true

it is truly all values of x

because 0 is always greater than -1/2

[dark lark]

1+1=2

[torn jolt]

So what would i do now

Like whats the solution lol

[quaint prawn]

well

x can be anything

so a way that you could write the solution is

-inf < x < inf

[torn jolt]

Is there a reason for that

[quaint prawn]

The reason is , the inequality is saying

for what values of x

is the absolute value of (2x+1) greater than negative 1/2

We reasoned that, because the lowest the absolute value can ever be is 0, since it can never be negative

that x can be anything

any number

however large or however small

it will always make the absolute value of (2x+1) > -1/2

[torn jolt]

Thanks!!

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[orchid prawn]

Ayo help me out someone

anyone

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[rare stratus]

i am attempting this problem in my multivariable calc class, and i dont even know where to begin. i can very easily compute the dot product of w and a are but i have no clue what my professor is asking in relation to what the meaning of the vectors w and a are nor what the meaning of the dot product is

[rare stratus]

i have since figured out that the value of w.a is the weighted average of the class but still have no clue as to what the meaning of the vectors w and a are

<@&286206848099549185>

[full forum]

@rare stratus Has your question been resolved?

[rare stratus]

<@&286206848099549185>

[torn jolt]

well w is just the vector representing the weight of the exams
and a is vector representing the class average for each exams

[rare stratus]

well yeah but is there a deeper meaning?

I feel like the problem is implying something more complex for w and a

[torn jolt]

naah its just saying it to hint at what Ww.a could possibly be

[rare stratus]

oh word

ty

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[celest fulcrum]

How would I find the arc length of this angle

[celest fulcrum]

here is my work so far:

Idk where im going wrong

[atomic blade]

I'm not sure why you have a negative 3sqrt(5)/2

Otherwise it's fine

[celest fulcrum]

@atomic blade the answer according to the book is this

ah nvm

teacher emailed us that hte book is wrong

unfortunate

thank you so much fro your hlpe

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[celest fulcrum]

how would i solve 79

like what would the two bounds be?

[plush egret]

my guess is just their first region enclosed from x=0

,w plot sinx and cosx

[glossy valve]

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[plush egret]

alternatively, one half period

i would think that first one, though

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[runic bloom]

I saw this in my teacher's notes

but

we learned the nth term test later

but i thought nth term test can't test for convergence

isnt that what this is saying??

[gritty rose]

Sequence and series are different

[runic bloom]

oh

shit

what is the main difference?

[gritty rose]

tests apply to series

Ratio, root, nth term, integral

[runic bloom]

okay

ty

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[orchid parrot]

If I have a circle with the radius of 12 and a square that has the same side length and that square is inside the circle, how do I find the area of the circle that is not covered by the square

[orchid parrot]

I swear I'm going crazy

The circle's area should be bigger after calculating

But for some reason the square is bigger

Something is wrong

[shrewd hamlet]

So what’s the area of the circle u found

Square can’t have same side length as circle radius btw

It’ll have the diagonal length = radius but not the side

[orchid parrot]

It's 542.389

The diameter is 24

Ah

I se

[shrewd hamlet]

U mean 452?

[orchid parrot]

Yeah (rounded)

How would I get the length of the square then?

If I made it a triangle same answer

[shrewd hamlet]

Notice we have an isosceles 45 45 90 triangle

Use triangle 45 45 90 properties

[orchid parrot]

ah

Basically the side length is just the radius

But the line in the middle is straight 90 degree

Makes sense

[shrewd hamlet]

No

[orchid parrot]

🤔

[shrewd hamlet]

.

What are u confused abt

[orchid parrot]

I don't even know

So unconfusing it's confusing

[shrewd hamlet]

The diagonal length of square = radius of circle

Side length of square is not = radius of circle

[orchid parrot]

okay

that's obvious

[shrewd hamlet]

Soo

Do u see the 45 45 90 triangle

[orchid parrot]

yeah

[shrewd hamlet]

Do u know the ratio of sides in that type of triangle

[orchid parrot]

2:1?

damn bro my head

The diagonal length is the same as the 2 side lengths right?

this shouldn't even be that hard

[shrewd hamlet]

No

[orchid parrot]

compared to the other things I do

I'd love to see the way you solve it

[shrewd hamlet]

I mean u can use trig if u want

But using triangle properties is much simpler

Here

[orchid parrot]

never seen this in my life

🤯

[shrewd hamlet]

[orchid parrot]

lmao

I'm actually so confused

this some america only stuff

[shrewd hamlet]

What are u confused abt

[orchid parrot]

I swear

only thing I need

is the side length of the square

to get the squares area

but

my brain

is confused

[shrewd hamlet]

This is exactly how u get it lol

[orchid parrot]

somewhere

[shrewd hamlet]

So if the ratio of sides in such a triangle is $x : x : x\sqrt{2}$ and our triangle has a hypotenuse of 24, see how u can figure out the side lengths

[glossy valve]

Stephen

[orchid parrot]

I swear trig looks simpler

[shrewd hamlet]

Ok we can do that then

So we know the angles

And the hypotenuse

Just find the side lengths

[shrewd hamlet]

It’s all based on the same thing, really

[orchid parrot]

😭

16.9

😭

why do I find the first method harder man

[shrewd hamlet]

Yea about 16.97

[orchid parrot]

What does the X stand for in this formula it's like a new light

[shrewd hamlet]

Just watch a video on it one of these days

[shrewd hamlet]

Length of a side

[orchid parrot]

ah

[orchid parrot]

Straight to Khan Academy 🤣

the simpler things in life are always the most complicated

😭

bro

I just

figured it out

all that

down to 1 second

of realisation

[shrewd hamlet]

👍

[orchid parrot]

Thanks for the help man, widening my methods and understanding

[shrewd hamlet]

No problem

Have a good one

[orchid parrot]

You too

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[nova forum]

Don't know how to get vertex from function

[nova forum]

When I tried I got f(x) = -16(t - 3/2)^2 + 263/4

[deft zodiac]

,w expand -16(t - 3/2)^2 + 263/4

[glossy valve]

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[deft zodiac]

,calc 68*4

[glossy valve]

Result:

272

[deft zodiac]

ya um just add the difference

n u shld b good

[nova forum]

wait so what I got was right?

[deft zodiac]

aka (272-119)/4

no

the constant term is wrong

[deft zodiac]

it expands to

[nova forum]

ok, I'm really dumb. doesn

doesn't*

68 - (-3/2)^2 = 68 - 9/4 = 68 - 9/4 = 68(4)/4 - 9/4

= 263/4

?

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@nova forum Has your question been resolved?

[scenic yew]

Ah no ur already right here

[scenic yew]

This is ok now

that is the standard form for quadratic equation

and this is how it is written
y = a(x-h) + k

where (h,k) is the center

[nova forum]

so my equation for the standard form is right?

[scenic yew]

yes

[nova forum]

ok thanks 🥳

[scenic yew]

Since it is -16t^2 we can visualize that the equation is going downwards

[nova forum]

understood, thanks again

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[undone hemlock]

x+c=3x+2/x doesn't seem right

how do i combine these two together

[stable heart]

do you know about derivatives?

[undone hemlock]

no

[stable heart]

hmm. well what you need is to find the point(s) where the curve $y=3x+\f{2}{x}$ has the same slope as $y=x+c$. once you do this you can set the two equal with said value of $x$ to find what $c$ must be. i just dont remember how to find the slope of the curve without derivatives

[glossy valve]

Duh Hello

[undone hemlock]

then how do i start with this

y-x=c?

[stable heart]

issue is im not sure how to do it with the techniques that you know

[undone hemlock]

oh

u could teach me the way u do it too

[stable heart]

unfortunately derivatives isnt something that can just be taught in 10 min over text

usually you spend half a year learning about them

[undone hemlock]

alr

then could u explain more abt constants

like where r they found

[stable heart]

thing is you need to do the slope part first then follow up with finding the constants

the other order doesnt work

[undone hemlock]

ok

when i move 2/x to the other side it's -2x?

[stable heart]

if i tell you that there are 2 points, $x=1$ and $x=-1$ where the curves have the same slope would you be able to find $c$ in both of these cases?

[glossy valve]

Duh Hello

[undone hemlock]

using y=mx+c?

[stable heart]

well you already know that the tangent line, $y_1=x+c$ and you know that when $x=1$ and $x=-1$ the tangent line will just barely touch the curve $y_2=3x+\f{2}{x}$, hence when $x=1$ and $x=-1$ then $y_1=y_2$

[glossy valve]

Duh Hello

[stable heart]

i gave them a bit different names here since calling them both "y" will just be confusing

[undone hemlock]

oh ok

sorry how do i move 2/x when there's an equal sign?is it -2x?

[stable heart]

could you write the full equation that you have?

[undone hemlock]

x+c=3x+2/x?

[stable heart]

and which variable are you solving for?

[undone hemlock]

c

[stable heart]

so what can you do to get c to be the subject?

[undone hemlock]

c=3x+2/x-x

[stable heart]

yep

which can be simplified a tiny bit

[undone hemlock]

c=3x+2?

[stable heart]

not quite

[undone hemlock]

im confused with fractions with unknowns

[stable heart]

what you say there is that $$\f{2}{x}-x=2$$

[glossy valve]

Duh Hello

[stable heart]

you just keep the fraction there, you dont need to do anything with it

but we know that $3x-x=2x$

[glossy valve]

Duh Hello

[undone hemlock]

how bout the c

[stable heart]

since we know that $3x-x=2x$ we can rewrite $$c=3x-\f{2}{x}-x$$ to $$c=2x-\f{2}{x}$$

[glossy valve]

Duh Hello

[undone hemlock]

what do i do after?

[stable heart]

well now you can just plug in the values for $x$ that we "magically" know are true. the issue with this exercise is im not sure how you are supposed to show this

[glossy valve]

Duh Hello

[undone hemlock]

perhaps i could show the answer given

[stable heart]

also i realized i have written something wrong

it should be $$c=2x+\f{2}{x}$$

[glossy valve]

Duh Hello

[stable heart]

sorry about that

[undone hemlock]

the answer is c=±4 from the textbook

[stable heart]

yep, once we plug in $x=\pm1$ we get $c=\pm4$

[glossy valve]

Duh Hello

[undone hemlock]

how do we plug in?

btw is it always x=±1 if it's a tangent?

[stable heart]

nope, just in this case

[undone hemlock]

oh alr

[stable heart]

again. sorry that i cant help you with finding that

[undone hemlock]

but how do i know that?

[undone hemlock]

how do i know that in this case x=±1

[stable heart]

first: to plug in the x's we have $$c_1=2(1)+\f{2}{1}=4$$ $$c_2=2(-1)+\f{2}{-1}=-4$$ $$c=\pm4$$ for your next question ill get a way to ask it for you in a more precise manner. if you open a new channel with this same question and ask "How can I find when the slope of the curve y=3x+2/x is the same as the slope of the tangent line y=x+c without using derivatives" then maybe someone else can help you

[glossy valve]

Duh Hello

[stable heart]

so probably just close this channel, open a new one with the same picture and ask:

"How can I find when the slope of the curve y=3x+2/x is the same as the slope of the tangent line y=x+c without using derivatives"

since im just not sure how to do that

and then maybe someone else can help you there

[undone hemlock]

alr sorry for bothering

[stable heart]

nah no worries, honestly i should know how to do this but its been a long time and the later methods you learn are much faster so its easy to forget the old tricks

[undone hemlock]

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[ionic oracle]

chapter matrix and det i think the ans is 1/kA but in solution they have written specially 1/k A^-1

[thorny horizon]

There's no such thing as 1/A when A is a matrix

[ionic oracle]

oh thats why

ok then

thanks

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[torn jolt]

inverse matrix

not 1/a

[ionic oracle]

what is commute?

same chapter

[torn jolt]

okay

basically

wait

commute

just show me the page?

[ionic oracle]

ok

[torn jolt]

if A + b = B + a

wait

are these matrices

[ionic oracle]

YEAH

[torn jolt]

if a and b are matrices

[ionic oracle]

OK

[torn jolt]

are the matrices of a and b are shwn

[ionic oracle]

nope this is the q

[torn jolt]

okay

if a and b commute

its the same is a^2 + b^2 + 2ab

[thorny horizon]

Commute means something like "able to move around without changing the value of the expression"

[torn jolt]

like

-7 + 3 = 3 - 7

[ionic oracle]

oh'

i see

then is the ans a^2 + b^2 + 2ab

or ?

b^2 + 2ab +a^2

[hallow fern]

This is only true if AB=BA

[ionic oracle]

they have not given it'

in q

[hallow fern]

What do they mean by A and B commute

Is that not saying AB=BA

[ionic oracle]

it mean sable to move around without changing the value of the expression"

[hallow fern]

That’s the same thing

If 2 matrices A and B are commute then AB=BA

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[thorny horizon]

Ig rhe answer they are expecting is simply (B+A)²

[ionic oracle]

ok

[ionic oracle]

ok

[hallow fern]

Yeah I guess this

I was unsure if you were trying to prove the if and only if statement or not lol

[ionic oracle]

thanks this q was ass

[hallow fern]

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[ionic oracle]

i have only applied cramers rule when 2 eq are given of 2 variables

how do you do this?

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[ionic oracle]

i have only applied cramers rule when 2 eq are given of 2 variables
how do you do this?

[onyx glen]

by guessing what all of this notation is supposed to mean

presumably those are supposed to be the determinants that you'd calculate when applying cramer's rule, only they're given to you outright instead of left as computation.

[ionic oracle]

so how do i solve it

[ionic oracle]

help

[onyx glen]

learn telepathy and get into the author's mind

or maybe read the textbook and see how it explained cramer's rule, and take note of the notation it uses

and act accordingly.

[ionic oracle]

ok sure

[thick minnow]

I honestly clue what the notations means

[ionic oracle]

ok

[thick minnow]

maybe give some more context

[ionic oracle]

matrix and dets

chapter name

[thick minnow]

as in more context for the notation

[ionic oracle]

determinats | | sign

[lunar iris]

Yeah, so if you want people to help you you need to come in with actual work and a specific question.

[thick minnow]

alright, what's A, B1 and B2?

[ionic oracle]

matrices

[thick minnow]

and what's the cramer rule?

[ionic oracle]

ok sure

[ionic oracle]

its a way we solve questions of matrices

[normal tree]

cramer's rule is the whole thing where you replace a column and take the determinant

to solve a system of linear equations with a unique solution

I'm assuming B_1 means A with the first column replaced with b

but you should check on what the notation means

[ionic oracle]

notation means det

determinannt

[normal tree]

clearly I know that

but nobody knows what B_1, B_2 are

[ionic oracle]

variable ]

[normal tree]

nobody knows what x, and y are

[ionic oracle]

ofc bro u i see tags in profile

[normal tree]

is that the whole question being asked?

[ionic oracle]

yes

[ionic oracle]

variables

[normal tree]

that's not helpful

what are x and y in the context of this problem?

solutions to the system of linear equations?

[sharp flame]

I think your question is incomplete

[normal tree]

yeah I would think so too

[ionic oracle]

ok

[normal tree]

surely someone's defined what B_1 and B_2 are before

I'd conjecture it's A, but with the first and second columns replaced

but you need to actually check on that

[ionic oracle]

ok

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[ionic oracle]

help

[ionic oracle]

]

i know t is transpose

and reveses the order of colums and rows

of matrix

[normal tree]

(A^T-B)^T = A - B^T

see if that helps

[ionic oracle]

ok

(A^T+B)^T = A + B^T

is this also true

[normal tree]

yes it is

the ^T distributes over addition

you can prove this if you like

[ionic oracle]

ok

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[kind umbra]

I have 0 clue where to start with this

any ideas on how I begin to answers this?

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@kind umbra Has your question been resolved?

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@kind umbra Has your question been resolved?

[kind umbra]

<@&286206848099549185>

[kind umbra]

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[safe trench]

Solve mean value of f(x) = x^n for cases: (a) n=1, (b) n=2, (c) n is odd and (d) n approaches infinity

[safe trench]

I have solved (a) and (b) by mean value theorem

the mean value of the function I found is:

$\frac{1+(-1)^n}{2n+2}$

[fast peak]

\frac

[thick minnow]

use \frac

[glossy valve]

Diesel

[safe trench]

how should I solve c and d?

[fast peak]

what exactly do you mean with mean value. do you have an interval you are working with?

[safe trench]

oh

I forgot to mention

[-1, 1]

[fast peak]

then your expression looks right

[full forum]

@safe trench Has your question been resolved?

[fast peak]

what are you still wondering about?

surely plugging in n odd and taking the limit n->infty of that expression is doable

[full forum]

@safe trench Has your question been resolved?

[safe trench]

how?

[fast peak]

what is (-1)^odd

[safe trench]

-1

[fast peak]

what is 1+(-1)

[safe trench]

oh

so ignore the denom?

[fast peak]

well you can also work it out if you want but it doesnt matter

0/anything is 0

[safe trench]

yeah

[fast peak]

unless anthing= 0 I guess

but that's clearly not the case here

[safe trench]

and what about approaching infinity?

[fast peak]

I mean depending on how overkill you wanna do it, squeeze theorem I guess

[safe trench]

n = -1 does not hold right?

so all odds give 0 except that

[fast peak]

well I would assume they only mean n positive

for n negative the function isnt even defined at x=0

[safe trench]

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[quiet nimbus]

this is my attempted illustration

however I'm just stuck on how to approach the question

I know it's something with related rates

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[stark bobcat]

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[stark bobcat]

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[dense edge]

Is this true for all trig functions? All trig functions are composite therefor we must use chain rule on them to find the derivative?

[torn jolt]

you are always applying the chain rule, with every derivative

[onyx glen]

there is no such thing as a division of functions into "composite" and "not composite"

[dense edge]

Hmmm

[quaint prawn]

even f(x)=x^2 , you first apply power rule = 2x and then you apply the chain rule (derivative of x) = times 1

the second step of chain rule when the function is just an x is kinda pointless because it is a multiplication of 1

[dense edge]

With sin(x) I guess it feels more obvious as f(g(x)) because there is an outside function sin and inside function x

[quaint prawn]

that makes sense

[gritty rose]

there's almost 0 chance it'll be useful to think of sin(x) as a composition of two functions

[dense edge]

I thought this is called the General Power Rule, like a “fourth” derivative rule of the Chain Rule combined with the Product Rule

[onyx glen]

well ANYTHING can be viewed as a composition with the identity function

what is the "General Product Rule"?

[dense edge]

Oops typo meant to say General Power Rule

[quaint prawn]

^ I've never heard of that

[gritty rose]

that's just a stupid name for chain rule

[dense edge]

It comes from the chain rule yes

But it’s a real sub-rule

[torn jolt]

chain rule but it feels extra

[gritty rose]

real sub-rule
what?

[dense edge]

doesn't quite count as a fourth rule, but it has a name in math

it's called the General Power Rule

[spice orchid]

a name nearly no one uses 🤷

[quaint prawn]

What exactly is your question, or your point?

[dense edge]

just getting clarification on the math terminology

[torn jolt]

i wish semantics were this important, but they aren't

[quaint prawn]

ok. Technically sin(x) is a composite function , it is probably near useless to think of it as one though.

[dense edge]

Why tho?

It's important to know, you can't just take the derivative of the entire expression "sin(x^2 + x)"

[quaint prawn]

you can

its cos(x)

and there you go

now that's something that would typically be referred to as a composite function

[dense edge]

I thought you gotta take the derivative of the outside function, and the derivative of the inside function, and multiply together? f'(g(x)) * g'(x)

[quaint prawn]

that's exactly what you do. whats your point?

[dense edge]

so sin(x^2 + x) is not cos(x^2 + x)

[torn jolt]

no but we were talking about sin(x)

[quaint prawn]

yeah I am aware of how the chain rule works

[torn jolt]

not sin(x^2 +x)

[quaint prawn]

sin(x^2+x) is a composite function, so you must apply the chain rule

[torn jolt]

thats a different function entirely

[dense edge]

oh, I get what you are saying now

cos(x) is not worth looking at as a composite

but cos(x^2 + x) is

[quaint prawn]

yes

[dense edge]

alright

https://www.brightstorm.com/math/calculus/techniques-of-differentiation/chain-rule-the-general-power-rule/

fyi

this is how Professor Leonard teaches it too, with the extra "General Power Rule"

[torn jolt]

also try getting into Leibniz notation from now imo rather than Lagrangian, as a personal recommendation

helps you a lot more for the future

[dense edge]

d/dx?

I thought this was Newton syntax, not Lagrangian syntax

the way that extra ''' are added

[meager dew]

please god do not use newton's notation

[dense edge]

wow

I was taught wrong

I was thinking Langrange syntax was Newton syntax all this time

[torn jolt]

[
\parens{\map{f}{\map g x}}^{'} = \map{f'}{\map g x} \cdot \map{g'}{x} \longrightarrow \dv[y]{x} = \dv[y]{u} \cdot \dv[u]{x}
]

[torn jolt]

well i think it is better for when you get into multivariable stuff so

[dense edge]

I've never seen Euler syntax before

[gritty rose]

that shows up in math most people don't take

[dense edge]

I've heard some people use Lagrange with numbers instead of ''' prime symbols

[meager dew]

for higher order derivatives that is the notation used

[dense edge]

Leibniz does seem the most efficient..

won't confuse a prime for power 1 or something silly

Newton is doing Hieroglyphics

[torn jolt]

seems really funny to represent the integrals using Lagrange or Newton's; you just guess the variable of integration yourself haha

[dense edge]

https://tenor.com/view/hum-humanities-scum-kids-gif-19484647

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[meager dew]

is this a quiz

why exactly is it called quiz then

[torn jolt]

how are u on question 5 after 5 hours

[meager dew]

looks like a quiz

[torn jolt]

that's my favourite notation

only after

I think its 10 for question 5 and 20 for question 6

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[tulip marlin]

no solutions
if troll, no troll

[obsidian torrent]

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[hot mango]

How is this wrong

[clear lily]

i see what you mean

try writing abh

[hot mango]

wym

[clear lily]

on the second

question

[hot mango]

ok

any ideas for the third?

[clear lily]

remove the x

[hot mango]

ok

thrid was right, abh is wrong

[clear lily]

oh yeah my bad they specify in terms of b and h

[hot mango]

ah

[clear lily]

i genuinely dont know what is wrong

[hot mango]

me neither

[hot mango]

ig there was a random space somewhere, its right now. tysm

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[shadow storm]

I need some help factoring

[scenic wren]

well my go to here is always guessing
more often than not we have nice numbers anyway

if we think about it visually, at x=0 we have y=-7
however 2x^2 and 13x both have a positive slope
therefore the graph will rise indefinitely as x rises

therefore we must have a positive root

now lets just guess x=1
we get:
2+13-7=7

which is not 0

so lets go in between

for example 0.5

if we have found a root we can find the other one via polynomial division

alternatively we can just use complete the square to find the roots

alternatively we can just use the formula for the roots

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@shadow storm Has your question been resolved?

[shadow storm]

No I still don't get it

Is there nothing that multiplys to -7 and adds to 13

[scenic wren]

three options:
-guess a root
-complete the square
-use a formula

[shadow storm]

What if I were to write 13x as a difference and factor 2x out of the equation

So instead of 13x it would be 14x -x

And then it would be 2x(x+7)

@scenic wren

[scenic wren]

what

no

that doesnt work

that would imply that x=0 and x=-7 are the two roots

you can check that this is not the case

[shadow storm]

Ok ok but stay with me here

I did the equation that way and I this is what it showed

@scenic wren

I used a function calculator and yeah I got it right

@scenic wren

[scenic wren]

ah that is what you meant

i thought you meant
2x^2+13x-7=2x(x+7)

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[shadow storm]

Yeah sorry for the confusion.

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[dire flame]

I cant figure out how they got initial velocity

[brittle steeple]

Speed of the plane

converted from mph to feet per second

[dire flame]

huh

why?

omg youre right

gravity is feet not miles

bruh

imagine if their answer had units

thank you

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[brittle steeple]

yeah it's an oof

np

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[hollow moth]

could someone help me understand this proof please?

[hollow moth]

(ignore the strong math induction thing at the bottom)

i understand everything up to x^2n+1(x^2) +y^2n+1(y^2)

after that, i dont get how my professor factorized it like that

[undone yew]

I’m not even dyslexic and this is causing all letters to float in my eyes. Rewrite it and sort it neatly so we can easily help.

[twilit leaf]

the prof wrote

the proof

blue im ngl youve been kind of unhelpful

juan are you familiar with the concept of the sum of cubes?