help-49

[pine brook]

@atomic magnet I hope you have a great rest of your day

[atomic magnet]

haha thank you so much thats very nice for you to say :), let me know if you have any other questions, id be happy to help in any way i can

[pine brook]

No worries at all man! Yeah I will! Have a good one mate, although I'll probably be back with a new query later on haha

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[midnight plank]

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[blissful canyon]

Question:
It is known that when executing the instruction sage euler_phi (302303) was obtained 301200 as result. The is_prime(302303) instruction results in:
False or True?

[blissful canyon]

I know the answer is False just can’t understand what does euler_phi do

this is on Sage Math Cell btw

I see a correlation that every time I do euler_phi of prime I get the prime - 1

[unique forge]

amount of natural numbers smaller than and coprime to n

look up euler totient function

[blissful canyon]

thanks my teacher didn’t talked about that and it’s very easy to visualize it like this

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[last slate]

-4+8p-6p-5+20p

[last slate]

Ned help

[neon rune]

what do you need help with?

[last slate]

Don’t exactly know where to start

[humble swan]

Do you know how to add numbers

[last slate]

Yes

[humble swan]

So you can see that there are two groups of numbers

One normal numbers and other numbers with p

Correct?

[last slate]

Yea I see it

Is it -5 and -6p?

[humble swan]

which group do you want to do first

[last slate]

Which ever?

[humble swan]

Yes thoes r the 2 different groups

[last slate]

Ummm

-5?

[humble swan]

ok

what else is there which is in the same category as -5

[last slate]

-6p

[humble swan]

no

-4

[last slate]

Oh

I see it now sorry I’m blind

[humble swan]

Or even better look what I do

[last slate]

So then we add those 2?

[humble swan]

-4+8p-6p-5+20p to

-4 -5 + 8p -6p +20p

[last slate]

Yup

That’s i how I had it

But I didn’t know if I was correct

[humble swan]

Ur correct :>

If you do
-4 -5 + 8p -6p +20p what would you get?

[clever sedge]

Substraction is the addition of inverse (2 - 3 = 2 + (-3)). Addition is commutative, so you can rearrange the terms as you wish.

You should.

[humble swan]

No i understand how it works i just cant understand thoes words

[clever sedge]

You can't just blindly move terms if you don't know why you can in the first place

$3 - 2 \neq 2 - 3$

[grand pond]

USS-Enterprise

[clever sedge]

But 3 - 2 = 3 + (-2) = -2 + 3

[humble swan]

^ That means this is all the same

[last slate]

What are we typing here

[humble swan]

just differently written

[last slate]

I’m confused lol

[humble swan]

Ill tell you after your question

[last slate]

Ok

[humble swan]

ok so from here

-4 -5 + 8p -6p +20p

[last slate]

Yea

[humble swan]

If you were to solve it what would you get?

do you know how to start

[last slate]

22-9

=o?

[humble swan]

no

[last slate]

0

22p-9

[humble swan]

yes

[last slate]

Ok

[humble swan]

now I assume you would have to find what p is equal to?

right

[last slate]

Are you asking me?

[humble swan]

yes

I dont know the question

You just gave me half of it

[last slate]

Oh so what you do next is you add 9 to both sides

[humble swan]

.

[humble swan]

Your question

What just this

Thats not a question

What are you trying to find, the value of p?

[last slate]

So (22p-9)+9=0+9

[clever sedge]

Just a note, we aren't solving anything here. We are simplifying an expression. We solve equations. It's better to use proper terminology. Also can not find the value of p from this because it's an expression

[last slate]

Then simplify the arithmetic

22p=0+9

[clever sedge]

If you are just told to "simplify" you do what you did right there. You don't make equations out of thin air.

[last slate]

Oh ok

[clever sedge]

$-4+8p-6p-5+20p$

[grand pond]

USS-Enterprise

[clever sedge]

This is an expression

[last slate]

But I got 22p-9

[clever sedge]

$-4+8p-6p-5+20p = 30$

[grand pond]

USS-Enterprise

[clever sedge]

This would be an equation and you can solve for p here

[last slate]

22p=9

Is that correct

?

[clever sedge]

You can only simplify the expression, which you did and got 22p - 9

That's all you can do

[clever sedge]

No.

As I said, you can't just make equations

If you are told to simplify the expression, there should be no talk about equations at all

[last slate]

Do you know my original question?

[clever sedge]

You said to simplify, no?

[last slate]

Yea

[clever sedge]

Well then

You simplified the expression.

By "collecting like terms" is what you did

[last slate]

That all I need

[clever sedge]

No equations

Yes.

[last slate]

Just to simplify

[clever sedge]

-4+8p-6p-5+20p is just an expression

Expressions and equations aren't the same thing

As I said earlier, you simplify expressions and solve equations.

An expression is something like 3x - 5

An equation is something like 3x - 5 = 2

[last slate]

Is it 22p-9?

[clever sedge]

See that you can solve for x in the equation

Yes

[last slate]

Ok cool

[clever sedge]

That's simplifying the expression

Collecting like terms (collecting the terms with p and constants)

[last slate]

That it that’s all I needed

Ty

[humble swan]

In level 1 english it means

The only thing you can do with -4+8p-6p-5+20p
is simplify to 22p -9

If you had something like
4p+6p+4=8
You can do 10p +4 =8 then 10p = 4 p = 4/10

[clever sedge]

Yes. Don't make equations out of this like 22p = 9 because that's not correct

[last slate]

I know but you confused me

Idk how

[humble swan]

https://tenor.com/view/captain-america-marvel-avengers-gif-14328153

[clever sedge]

Just remember the difference between expressions and equations 😄

[last slate]

Ok

Bye Ty

[humble swan]

Also thanks for clarifying that

Also learnt somethin

teheh

[clever sedge]

No problem! We all learn every day

[humble swan]

do .close

[last slate]

.close

[midnight plank]

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[clever sedge]

It's just not good saying "solve an expression" because you can not physically do that

[midnight plank]

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[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

@last slate Has your question been resolved?

[weak bay]

Can you try moving all the terms to the left and see if you can simplify the expression?

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[hearty rune]

oops

[midnight plank]

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[kindred token]

Does this make any sense

I guess not because I should do it by contradiction

But can someone give a pointer

Suppose f is continuous at 0 so the limit is c is 0

Then we can pick this epsilon and that’s a contradiction since |f(x) - c| = epsilon

[midnight plank]

@kindred token Has your question been resolved?

[kindred token]

<@&286206848099549185>

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[kindred token]

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[kindred token]

.reopen

[midnight plank]

✅

[kindred token]

Here

[kindred token]

Great thanks

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[ornate sonnet]

Determine the rank of the matrix [image] depending on the real parameter c.

[ornate sonnet]

this seems little bit tricky , to be honest I would be really glad if there is a video on how to solve matrices that are like this (that have this confusing stuff like -a-1 and a-2 in them )

[midnight plank]

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[stark zodiac]

Can someone help me with this problem?

[modest mango]

Where are you confused

or what part do you need help with

[stark zodiac]

Setting up the inequality

[modest mango]

I would seperate the inequality

[stark zodiac]

is y+1>x and 3>x correct?

[modest mango]

I would check the X values for your anser first

then check your Y values for the answers that fufilled the requirements for the X values

For example check to see what answers, have a value < 2 in the x position

Does that make sense?

[stark zodiac]

Yes

C and d match

[modest mango]

double check

for your X values yes

now check the y values for C and D since you can elimate A and B

[stark zodiac]

How do I set up the equation for y though?

[modest mango]

you have two y values you are checking now correct?

what are they

[stark zodiac]

1 and -2

[modest mango]

and y need to be > -1

[stark zodiac]

So just remove the x?

[modest mango]

you already took care of the x

[stark zodiac]

Oh

[modest mango]

which eliminated A and B

which left you with C or D

[stark zodiac]

So the answer is c ?

1>-1

[modest mango]

yes

this is all process of elimination

[stark zodiac]

ty

[modest mango]

np

[stark zodiac]

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[upbeat sage]

i have dy/dx = 1/2y

so perpendicular line would be -2y

[midnight plank]

@upbeat sage Has your question been resolved?

[upbeat sage]

would i replace x and y with like (x^2, x) because those would be points on the graph

i end up with x = sqrt(a+(y/-2))

idk where to go from here

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[steep helm]

someone teach me the pythagorean theorem

[steep helm]

i'm learning it at school tmrw

but i wanna learn ahead of time

[blissful trench]

watch a video

[steep helm]

k

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[blissful trench]

don't "k" at me next time

[steel trench]

LMFAO

[hearty rune]

[steep helm]

i'm just confirming what you said

i don't understand what i did wrong

[blissful trench]

saying by "k" to me seems rude

just don't

[steep helm]

ok

[steel trench]

do u know algebraic topology

[blissful trench]

no

[steel trench]

cries

[blissful trench]

im only in hs lmfao

[steel trench]

Oh

Sorry

[steep helm]

oh shoot didnt even have to watch a video

pythagorean theorem is startlingly easy

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[misty wagon]

how do i solve it ?

[hearty rune]

youre not solving anything

its asking you to graph

have you done that?

[midnight plank]

@misty wagon Has your question been resolved?

[misty wagon]

no

[wary thorn]

Why not?

[midnight plank]

@misty wagon Has your question been resolved?

[midnight plank]

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[floral plinth]

here is a rather pedestrian proof in my book

[floral plinth]

but im wondering why it's true

because what if the matrix was

\begin{bmatrix}
a_{11} & -a_{11} & 0 & \dots \\
& & * & 
\end{bmatrix}

[grand pond]

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

[floral plinth]

and if we look at just the first row, then $\lambda_1 a_11 - \lambda_1 a_11 = 0$ and $\lambda_1$ could be anything, not necessarily zero

[grand pond]

omgatriple

[nova yoke]

and what does that prove?

[floral plinth]

it doesn't show lambda_1 to be 0, which doesn't show this row to be independent

oh mb

[nova yoke]

any single row is independent unless it's all zeros

[floral plinth]

yes, a single row is independent

but, it says a constant times a single row equalling zero must mean the constant is zero, since there is some nonzero term in the row

[nova yoke]

yes

[floral plinth]

but if the row consists of the nonzero term and the negative of the nonzero term, then the product could equal zero even if the constant was some real number != 0

[nova yoke]

what product?

lambda times that row?

i'm not sure what you're calculating here:

if you have a row like [1, -1, 0, 0, 0] then lambda times that is just [lambda, -lambda, 0, 0, 0]

which is zero if and only if lambda is zero

[floral plinth]

oh crap im mistaking what it means to multiply a row

i see, that makes sense now

[nova yoke]

yea it just means multiply each element of the row by the same scalar

[floral plinth]

i see, ok thanks

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[elder ivy]

Not too sure how I forgot but how would I graph the line x + 2

[elder ivy]

I'm graphing like slanted asymtotes but Idk how to graph that line

[dull yoke]

y = x + 2

Plug in a value for x

Then get the point and plot

[flat spire]

Or set the x and y = 0 and go from there

[elder ivy]

That doesn't work let me just show what i am doing

This is what I graphed (ik the VA is wrong) how do I find that slope there I just copied my teacher and the points aren't really correct

Just substituting random points in won't work

I know for a fact my math is fine for the 3 points just not fir the slope itself

[elder ivy]

Yea already found the intercepts

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[spare condor]

While doing partial fraction decomp would the s not disaphere from e^s? Im really struggling with understanding why it is sitll there

[midnight plank]

@spare condor Has your question been resolved?

[fallow scarab]

nope

just add the 4 fractions together and you'll get your starting one

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[cedar vortex]

What’s an function T: V to V that’s injective but not surjective (V is not a finite dimensional space, bc injectivity would imply subjectivity)

[cedar vortex]

Uh

Ig the infinite dimension spaces that come to mind is P and C^{\infinity}

[jagged saffron]

take any space with an infinite countable basis v_i, and define T(v_i) = v_(i+1)

[cedar vortex]

Okay ty

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[stark wedge]

How is this true

[halcyon trellis]

Because 1000 divides 9-9

a is congruent to itself in any mod

[stark wedge]

explain

[main current]

Note the 9 does not belong to the (mod 1000), but the entire equation does

And you'd never disagree that 9 = 9

[halcyon trellis]

Nothing to explain this is just definition of mod

a congruent to b mod n means n divides b - a

[stark wedge]

what

[surreal moon]

where did I lose you?

[stark wedge]

here

i thought it was

1000/9

[surreal moon]

What you're thinking is 1000 divided by 9. When we say 1000 divides 9-9, we are saying that there is some integer k such that 1000k=9-9

In general, we say "a divides b" when there is an integer k satisfying ak=b

[simple olive]

That can also be written as 9 (mod 1000) = 9 ( mod 1000)

I believe

[midnight plank]

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[midnight plank]

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[dull yoke]

how do i do this, not sure where to start

[dull yoke]

A bucket contains 30 red balls and 50 white balls. Sam and Jane
take turns drawing balls until all the balls are drawn. Sam goes first. Let N be
the number of times that Jane draws a ball that matches the color of the ball
that Sam drew on the turn before. Calculate the expectation of N.

[midnight plank]

@dull yoke Has your question been resolved?

[next rover]

calculate the probability that it happens on turn 1 and multiply by 40

[dull yoke]

Like this?

@next rover

[next rover]

that's right

[dull yoke]

hmm

whats the logic behind that? like why am i just able to multiply by 40 if the trials are not independent

[next rover]

i don't know how it's proved that it happens on turn 30 with the same probability

it does, it's the same on every turn

[dull yoke]

i see

[next rover]

like, no, it's not independent

just not dependent on the turn number

once you've established that, linearity of expectation says you can add it up

[dull yoke]

ah yea i think i remember this concept. its called exchangeability right

[next rover]

probably 🤷‍♂️

so imagine 100000 experiments, and you've showed that in 52.53% of them turn 20 is a match

and same proprtion has match on turn 12

so you have 0.5253 × 100000 × 40 / 100000

[dull yoke]

how come ur multiplying by 100000

[next rover]

i'm counting total matches to divide by number of experiments

0.5253 × 100000 matches on turn 15
0.5253 × 100000 matches on turn 16
0.5253 × 100000 matches on turn 17...

[dull yoke]

interesting

yea i remember we did an example on this in class

deal 5 cards from a 52 card deck without replacement. X = number of aces dealt. We found P(draw 'k' is an ace) is just 4/52, meaning every draw had the same probability of being an ace

[next rover]

that's interchangeability

i'm talking about linearity

you do both, just i'm skipping the interchangeability

or exchangeability you said

[dull yoke]

alright

[next rover]

40 is the numebr of turns

[dull yoke]

yep

i think im starting to understand this stuff

thank you

[midnight plank]

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[midnight plank]

@fickle oriole Has your question been resolved?

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[zealous spire]

is someone avaliable to help me with geometry

[midnight plank]

Please don't occupy multiple help channels.

[junior flower]

[zealous spire]

how do i solve for the ranges?

.close

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[formal raptor]

help

pls

[midnight plank]

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[noble jay]

Computer the magnitude, the dot product, and the angle between: A = [2, -3, 1] * B = [-4, -3, 2]. [x, y, z] if it's not obvious (I've never studied vectors, so I'm not sure if it's implied).

So, the magnitude is easy enough. 2(-4) + -3(-3) + 1(2).

I'm not sure I understand the angle part. Like I said, this is my first introduction to vectors.

I tried thinking about unit circle, but I didn't know where to put the arms of the vectors. I know the magnitude of each one, but I'm not sure if I get how to connect them. Third page of vectors and I'm already a bit confused lol.

[noble jay]

sup sup

I'm missing an inside joke, aren't I

[fresh sparrow]

there's a useful formula

. is dot product (weird notation)

so the angle is arccos of the thing on the right

[noble jay]

Ahhhh, okay, that makes sense. It didn't occur to me that we could divide by the multiplication of their absolute values. Figured vectors might be different.

Thank you. 🙂

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[last slate]

What do I set f(x) to

[rose kayak]

we're looking for what values for when f(x) = 0 for x intercepts.

If you're looking for x intercepts, set f(x) (or y whichever one is defined) to 0. If you're looking for your y intercept, you set x = 0

[last slate]

Ohh

That was such a stupid question

[last slate]

Did I get the possible rational roots right?

[rose kayak]

no stupid questions my dude

you're learning

[last slate]

I got like 20 possible rational roots

[rose kayak]

you cut them off but the pattern looks good so far

60 is a very divisible number lol

[last slate]

If I’m not able to use my calculator on the upcoming test I swear 💀

[rose kayak]

well the good news is the fact that your q is 1

so it makes your roots integers

which is very easy to check with synthetic division

if you get a remainder of 0, then you know you have a root!

it's a lot to check

but like it's really really nice that we have this tool.

[last slate]

.close

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[wraith hamlet]

hi

[wraith hamlet]

$f(x) = (x+7)^2 + 4$

[grand pond]

Courtesy

[wraith hamlet]

The function f is defined by the given equation

For what value of x does f(x) reach

it's minium

idk what the question is asking

so pls help

[blissful pier]

the minimum of a quadratic that opens down is just the vertex :)

[wraith hamlet]

well

how do I caluclate it

[blissful pier]

your quadratic is in vertex form

$f(x)=a(x-k)^2+h$ where $(k,h)$ is the vertex

[grand pond]

PajamaMamaLlama

[wraith hamlet]

so

(7,4)?

[blissful pier]

close

x-k not x+k

[wraith hamlet]

so

(-7,4)?

[blissful pier]

see, super easy!

[wraith hamlet]

k

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[inner glacier]

Trying to solve this with the binomial theory

i know 72p^3q and 1458pq^3 are wrong but im not entirely sure why

i think it has something to do with the pryamid thing and i got the wrong numbers there?

it should be
4!/1!4! right? which would just be 1?

or wait no

its 4!/1!3!

yep thats all lol

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[potent halo]

Im unsure what the square on the log affects

[wraith hamlet]

hey

[potent halo]

hi

[wraith hamlet]

uhm

can you help me uh

it's basically easy tbh

[potent halo]

?

[wraith hamlet]

actually nvm

[potent halo]

<@&286206848099549185>

🙏

[fervent echo]

it's basically $(\log (5 + 7x))^2$

[grand pond]

nalin

[potent halo]

that makes a lot more sense

so i do it normally and square the final function?

[fervent echo]

no, you use chain rule

[potent halo]

cahain

i just realized

alr

tyyyy

[fervent echo]

np

[potent halo]

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[naive flint]

wat mistake i made ;

😦

maybe i am not supposed to re-write it like how i did?

,rotate

[naive flint]

the re write version is allowed?

[velvet oar]

These are not the same

circled in red, those aren't the same

The first one is the log times -4, and the second one is the log minus 4

you accidentally changed multiplication into addition/subtraction

@naive flint

Your asymptote is correct. Don't rewrite it like that and try plugging in your values for x again using the original version

[midnight plank]

@naive flint Has your question been resolved?

[naive flint]

Ohhh

Ok so never r e rwrite like that ok

Thnxs

[midnight plank]

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[flat spire]

am i correct in thinking its option B?

[flat spire]

ok yes it is

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[rose kayak]

you need to use the product rule for the numerator

[leaden matrix]

ah

I completely forgot that existed

lmao

[rose kayak]

no worries!

[leaden matrix]

lemme retry

is it negative infinity?

since you get -1/4 * 1 ^-3/2 all divided by 0

<@&286206848099549185>

[midnight plank]

@leaden matrix Has your question been resolved?

[leaden matrix]

<@&286206848099549185>

[wheat mesa]

damn your on your own for this one buddy

[midnight plank]

@leaden matrix Has your question been resolved?

[leaden matrix]

<@&286206848099549185>

[dense idol]

you only use lhopitals when the limit is indeterminate
you can limit to 0+ in the second line

[leaden matrix]

Ah so its just infinity then?

[dense idol]

oh nvm $$\lim_{x\to0^+}\frac{\sqrt x\cos x}{2x}=\lim_{x\to0^+}\frac{\cos x}{2\sqrt x}$$ which you can evaluate directly

[grand pond]

chlamydia

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@leaden matrix Has your question been resolved?

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[midnight plank]

Please don't occupy multiple help channels.

[coral mortar]

^^^

.close

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[vapid loom]

@gray widget

[vapid loom]

help solve the limit using only 1 and 2 wonderful limits

<@&286206848099549185>

[soft token]

!status

[midnight plank]

What step are you on?
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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@vapid loom Has your question been resolved?

[midnight plank]

@vapid loom Has your question been resolved?

[midnight plank]

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[heady lodge]

i got dy/dx in terms of t

how do i manipulate to put in terms of x and y?

[fallow scarab]

Show all your work

[heady lodge]

the top left is my dy/dx

then i was just pondering at the bottom

and am now stuck

[fallow scarab]

You can try writing cosh and sinh as a linear combination of x and y

[heady lodge]

okay

[fallow scarab]

Then plug that in for cosh and sinh in the top left

[heady lodge]

i see ill try after my dinner

[fallow scarab]

Can you close and reopen later then

There's almost no more help channels

[heady lodge]

sure

.close

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[ionic lance]

Coth(0.75x) = p. Solve for x in the form x = aln(k) where k is a function of p

[ionic lance]

<@&286206848099549185>

anyone?

[last slate]

What's the question

[jagged saffron]

!15m

[midnight plank]

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

[jagged saffron]

also you have work you just deleted, show it

[last slate]

yeah

[ionic lance]

It was compiled wrong

???

I deleted it I don't have it

I know that x = Arcoth(4p/3)

But I can't use Arcoth in the question apparently

[jagged saffron]

figure out how to show your work properly so people can tell you what to do next and not tell you things you already know

[ionic lance]

I can't use this latex shit

[jagged saffron]

then write on paper and take a pic

[ionic lance]

Okay what from here

[jagged saffron]

multiply everything by $e^{\frac34 x}$ and you'll have a quadratic in disguise

[grand pond]

ΣΑC

[ionic lance]

Okay so (P-1)a² - (p+1) = 0

Where a = e^0.75x

@jagged saffron

[jagged saffron]

(P-1)^2?

[ionic lance]

Not the (p-1)

That isn't squared

[jagged saffron]

then yeah now just solve for x

[ionic lance]

$$ a^2 = \frac{P+1}{P-1}$$

[grand pond]

Josh ♘

[ionic lance]

How do you write square roots with this latex crap

[jagged saffron]

\sqrt{}

[ionic lance]

$$e^x = \sqrt{\frac{P+1}{P-1}}$$

[grand pond]

Josh ♘

[ionic lance]

$$ x = 0.5ln(\frac{P+1}{P-1})$$

[grand pond]

Josh ♘

[jagged saffron]

where did the 3/4 in the exp go

[ionic lance]

Oh yh

[midnight plank]

@ionic lance Has your question been resolved?

[midnight plank]

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[last slate]

I do i find the change of base matrix

[last slate]

forgot to add:
find the change of base matrix "P" for changing B' to B

[grizzled blade]

Write a basis element as a linear combination of the basis elememts of the other basis

[last slate]

dont know what that means rly

but can i not use B = B'*P

then find the inverse of B'

[grizzled blade]

You are finding P

Do u know what linear combination is

[last slate]

if you can scarlar mult and scaled vectors are added together?

[last slate]

yeah but P will be equal to B*B'^-1

also im not quite sure what that way the books has written it means

is that the same matrix?

or can one matrix be mutiple matrices?

@grizzled blade

.close

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[last slate]

Can you simplify exponents

[mortal sleet]

For example?

[last slate]

I'm given the identity cos^4 x - sin^4 x = 1 - 2sin^2 x
which I determined (by working on right side)
was cos^2 x -sin^2 x

$\cos^4x - \sin^4x = \cos^2x -\sin^2x?$

[grand pond]

mj

[mortal sleet]

Yea what do you want know?

[last slate]

are they equal

is there anything I can do to the right

other than what I did

[mortal sleet]

Its true i think

[shell wigeon]

$a^4 - b^4 = (a^2-b^2)(a^2+b^2)$

[grand pond]

Nel

[mortal sleet]

Yea its difference of squaref

[last slate]

how though

[mortal sleet]

Split powers

Into 2 and 2

And sin^2 + cos^2 is 1

[tribal temple]

possibly double angle, if you're thinking of that? nvm seen you wanted to prove the identity they gave

[shell wigeon]

Take $A = a^2$ and $B = b^2$: $A^2 - B^2 = (A-B)(A+B)$

[grand pond]

Nel

[shell wigeon]

Exactly the same thing as this

[last slate]

$\cos ^2x-\sin ^2x = (\cos x\cos x+\sin x\sin x)\cdot(\sin x\cos x-\cos x\sin x)$

[mortal sleet]

$Let …sin^2(x) = a ..and.. cos^2(x) = b$

[grand pond]

𝓡𝓮𝔁𝓸

mj

[last slate]

is this correct?

[mortal sleet]

Want me to write down?

[shell wigeon]

No

[last slate]

yeah if possible

[last slate]

are you supposed to just do difference of squares

[shell wigeon]

Yes

[last slate]

$\cos ^2x-\sin ^2x = (\cos x+\sin x)\cdot(\cos x-\sin x)$

[last slate]

this better?

[shell wigeon]

Not really

[grand pond]

mj

[shell wigeon]

I kinda gave you the answer

[mortal sleet]

Like this perhaps

[last slate]

wait but your simplifying other side then

[shell wigeon]

Yeah?

[last slate]

so just squares on all of em

[last slate]

my teacher told me to not touch the other side

but I guess that'd help a lot then

[mortal sleet]

Sin^4 is just (sin^2)^2

[shell wigeon]

I mean if you're given the identity then why would you not?

[last slate]

$(\cos ^2x+\sin ^2x)\cdot(\cos ^2x-\sin ^2x)= \cos^2x -\sin^2x$

[shell wigeon]

In a proof you can go straight from one side to the other but to actually find the steps in between you can do whatever you need

[grand pond]

mj

[last slate]

but then how would this be equal?

bit new to trig if you can't tell lol

x*x isn't equal to x

so logically wouldn't make sense

[shell wigeon]

How did you go from 1 - 2sin^2 x to cos^2 x - sin^2 x?

[last slate]

unless x=1

[shell wigeon]

Where do you see x*x here?

[last slate]

because 1-2sin^2x= cos2x

[last slate]

left side

[last slate]

cos2x= cos^2 x-sin^2 x

[shell wigeon]

Put your glasses on

So you did 1 - 2sin^2 x = cos 2x = cos^2 x - sin^2 x?

[last slate]

yes

[last slate]

It's left for me idk if your facing a different way

[shell wigeon]

You might have forgotten the most basic trig identity:
sin^2 x + cos^2 x = 1

[last slate]

but whichever way <-- is

[shell wigeon]

Yeah, I don't see x*x on the left side of that equation

[last slate]

I do

but theoretically whatever way you go

using different identities

you should arrive at the same answer

hence why it's equal

[shell wigeon]

Sure, but one way is more obvious

[last slate]

how would you use this

$1-2\sin^2x$

[grand pond]

mj

[last slate]

factor out a 2?

[shell wigeon]

$1 - 2sin^2 x = sin^2 x + cos^2 x - 2sin^2 x = cos^2 x - sin^2 x$

[grand pond]

Nel

[last slate]

or is it $\cos^2x + \sin ^2 x$

[last slate]

I don't get the middle part

1-sin^2x = cos^2x

we still have a sin^2 x left over

so cos^2x + sin^2x

[shell wigeon]

??

[grand pond]

mj

[last slate]

$1-sin^2x = cos^2x$

[grand pond]

mj

[shell wigeon]

I'm just replacing the 1 by sin^2 x + cos^2 x, following the identity

[last slate]

$1-2sin^2x = cos^2x + sin^2x$

[grand pond]

mj

[shell wigeon]

You subtracted on one side and added on the other

[last slate]

yeah but in the middle you still have -2sin2x for some reason

[last slate]

so -ve sign?

[shell wigeon]

... yeah, because I only replaced the 1

[last slate]

ohhh

okay sorry

so $cos^2x+sin^2x-2sin^2x$

[grand pond]

mj

[last slate]

so $cos^2x+sin^2x-2sin^2x$

[grand pond]

mj

[last slate]

wait we got the same answers

yours was just more complex to get

[shell wigeon]

Was it?

[last slate]

regardless though

actually mines was

but anyways

that is still

$\cos^2x-\sin^2x=(\cos ^2x+\sin ^2x)\cdot(\cos ^2x-\sin ^2x)$

[grand pond]

mj

[last slate]

which means we still have some way to go

[shell wigeon]

.

[last slate]

but it isn't plus

it's -

[shell wigeon]

I see a + in there

[last slate]

ohhhh

you're really on top of your stuff

yeah and that way we have LS=RS

thanks

.close

[midnight plank]

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[graceful pebble]

Hey all, working through this I end with the equation

V = integral[0,2] x^2 dy

not sure what to do from here

I get there because the cross sections are squares so the area = (side length)^2

and the length of the square side between the curves = 2x - x = x

so the area is x^2 for each square cross section

and the sections go from y=0 to y=2

but obviously you can't solve that integral and get a numerical volume

so any help would be appreciated

[midnight plank]

@graceful pebble Has your question been resolved?

[graceful pebble]

<@&286206848099549185>

.close

[midnight plank]

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[last slate]

How would you get $cos^2x cos^2y + sin^2x sin^2y$ with the cosine formula?

[grand pond]

mj

[last slate]

$\cos^2x \cos^2y + \sin^2x \sin^2y$

[grand pond]

mj

[last slate]

I know the cosine formula is cos(x-y), but how would you get the power 2 exponents

$cos(x-y)^2, cos^2(x-y), cos(x^2-y^2)$ all don't work

[grand pond]

mj

[midnight plank]

@last slate Has your question been resolved?

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[honest kelp]

it rather should look in such way:

[honest kelp]

$cos\left( x-y \right)\cdot cos\left( x+y \right)=\\\left( cosxcosy+sinxsiny \right)\left( cosxcosy-sinxsiny \right)=\\=cos^{2}xcos^{2}y-sin^{2}xsin^{2}y$

[grand pond]

Joanna Angel

[proud island]

do u need help or?

[honest kelp]

.reopen

[proud island]

.

[honest kelp]

.close

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[haughty cloud]

help explain stretches and shrinks transformatikns

[blazing shard]

hi

[haughty cloud]

How do u do transformations dude

[blazing shard]

i can help

[haughty cloud]

stretches and shrinks

[blazing shard]

what you need help with

[haughty cloud]

idk how to do them

i have a quiz tmw

[blazing shard]

ok

send a problem

and i’ll work you threw it

[haughty cloud]

nvm ig .close

.close

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[blazing shard]

dude

[hearty rune]

[blazing shard]

@haughty cloud i can help

[tacit rose]

Google videos

[blazing shard]

i just need a problem 💀💀

[midnight plank]

Available help channel!

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[violet carbon]

how do i find cos pie/2

[violet carbon]

without just subbing into calculator

[blissful pier]

do you know your unit circle?

[violet carbon]

yes

so do i say because its over teo

two

[blissful pier]

at theta=pi/2 the triangle is just a straight line up and down, right? :)

[violet carbon]

i can split the circle into 4

[violet carbon]

yes

like i need to explain it

not just look at unit circle

and move on yk

why do they tell u to split the unit circle x2 of den

?

[blissful pier]

idk what your teachers are telling but all I'm saying is $\cos\left(\frac{\pi}{2}\right)$ is the value for which the length of the base of the triangle on the unit circle is 0

[grand pond]

PajamaMamaLlama

[violet carbon]

yea

[midnight plank]

@violet carbon Has your question been resolved?

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[errant forge]

help!

[errant forge]

<@&286206848099549185>

[wary thorn]

!15mins

[midnight plank]

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

[errant forge]

i js forgot how to do this

[wary thorn]

Don't immediately tag the helprs, you hadn't even posted a question yet.

[errant forge]

iv been on this for 15

and yea i js posted it

[wary thorn]

Exactly. Don't tag helpers until after you have waited 15 minutes

[errant forge]

bro what?

what is ur problem

[wary thorn]

No problem. Just explaining that you're not supposed to tag the helpers until after 15 minutes.

[errant forge]

iv been stuck for 15 min tho D:

[wary thorn]

You did not post the problem for 15 minutes and wait

that was the point

[errant forge]

bluddddddddddddddddddddddddddddddddddddd

[tacit rose]

What Austin means is, you post your question first, and if you have not gotten a response after 15 minutes, you can ping helpers, but you don't ping helpers before asking your question even if you attempted it 15 minutes prior

That is how the server operates

[errant forge]

😭

ight cya in like 9 mins

[wary thorn]

You can only ping them once

and you already did

So you can still get help, without pinging them again

just wait patiently like everyone else

[errant forge]

its been 15

[wary thorn]

It has been 7 minutes... and as I said, you don't need to ping them again (and you shouldn't)

[errant forge]

i didnt ping tho

also did u fr start a timer orr?

[wary thorn]

No? I can see the timestamps on the old messages

[errant forge]

ok welp 5 more mins

[wary thorn]

I don't understand what you are waiting for

You can only ping them once anyways and you already did. Feel free to do your question at any time

[errant forge]

oh wait wut

mb

im just confused

on where to even start

[wary thorn]

Did you select those blue points?

[errant forge]

nah

its pre selected

it wants an equation for the graph

[wary thorn]

I don't even see a graph

I see a number line

with two points selected

[errant forge]

well it calls it a graph : /

but yea its absolute value

[wary thorn]

Have you clicked the video where it says, "need help with this?"

[errant forge]

its not a vid

its a weird "hint"

[wary thorn]

Okay

Well

The question is sort of unclear to me atleast at first, maybe not to you if you have done similar ones

but it wants you to express using absolute value, an inequality that describes the region in between the two points

so the region [3,5]

[errant forge]

mhm

[wary thorn]

Or actually

is it the region?

Or just the points?

I can't really tell

[errant forge]

idk 😭

[wary thorn]

Have you done any similar problems

where it was shaded in perhaps

[errant forge]

umm no

[wary thorn]

Okay weir

weird

[errant forge]

ima js get it wrong and let it explain

[wary thorn]

Well

we can try something first if you'd like

Absolute value is useful to talk about the distance between two points

right?

[errant forge]

😭

[wary thorn]

Okay, so it only wanted the points, and not the region in between

Can I explain?

[wary thorn]

Lets say you wanted to know the distance between the points -5 and -3

what would you do?

and my hint to you is to use absolute value

[errant forge]

so x-2=2?

[wary thorn]

No

you didn't use absolute value

it is |-5-(-3)| or |-3-(-5)|

either way, you get the result is 2

which is what makes sense right?

take the difference between the two points

this is what we would do if we wanted the distance between positive numbers

like 7 and 5

we would do, 7-5=2

[errant forge]

!close

.close

[midnight plank]

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[midnight plank]

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[viscid quartz]

to find the derivative of x^3 - 3/x

[viscid quartz]

we can just use power rule for the first one

but for the second term do we have to use quotient rule

or is there a faster/different way

[runic hamlet]

3/x = 3x^(-1)

[viscid quartz]

OK THANKS

.close

[midnight plank]

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[midnight plank]

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[last slate]

When it asks to describe the direction

What does it mean?

[maiden forum]

displacement basically means how far it is from the original point (can be on a single axis measurement)
here its a horizontal line, so a positive displacement means your displacement is to the right. and if its negative, then left

[lime matrix]

• the direction

[last slate]

I mean the direction, brother

[last slate]

Is the direction and displacement 2 different things?

[maiden forum]

no

displacement means direction

and how far you went in that direction

[last slate]

So you find the area beneath the graph too?

[keen plank]

you see the graph decreasing, it means the particle or body is moving at the opposite direction

[last slate]

Ik brother

[last slate]

Am I meant to?

[lime matrix]

basically, if displacement is positive, then the object is in the positive direction. if it's negative, then it's in the negative direction

[lime matrix]

since you have the graph of x vs. t, you don't need to

[last slate]

I agree with you

[last slate]

Can displacement be negative

Wait displacement can be negative

However distance can’t

[lime matrix]

yes

[last slate]

How do I find the velocity?

2<t<4

[last slate]

Part b

[lime matrix]

you know that velocity is the derivative of displacement right?

[last slate]

No?

I’m not into that hard stuff yet

We haven’t done differentiation or integration in mechanics

We’ve done it in core maths tho

Acceleration is velocity

So I can do displacement/time

ms^-2

[lime matrix]

acceleration is the rate of change in velocity

[last slate]

Or m/s^2

[last slate]

What’s velocity?

[lime matrix]

the speed with direction

[last slate]

Speed and direction

Okay

[last slate]

Would this be right?

[lime matrix]

yes, change in displacement/change in time

[last slate]

What if the change goes from positive to negative