help-28

[cunning hatch]

like cos is negative?

[raven quail]

Yes

Cos is negative is π/2 to 3π/2

[cunning hatch]

but what do I do with the information

thats my question

[raven quail]

Use sin²x + cos²x = 1

You know sinx

[lone brook]

cou can find the value of cos

[raven quail]

Find cosx

[cunning hatch]

oh

thats so smart

[raven quail]

Or just make a triangle how everyone does and just add a minus sign

Because cos is negative in the given interval

[cunning hatch]

yeah got it

$\frac{-3√7}{8}$

[glossy valve]

Kap

[raven quail]

You should be getting -√7/4

Oh you talking about the final answer

Yeah that's correct

[cunning hatch]

thanks mate

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[twin wolf]

how do I do this?

[fallen bone]

What is an even function?

[twin wolf]

when f(-x) = f(x)

so i know it cant be A and B

C could be maybe

[fallen bone]

Why

[onyx glen]

using the name f is bad here

[twin wolf]

because 2 doesnt do anything

how

thats the definition of even

it uses f

[onyx glen]

the letter f as opposed to g or any other is NOT ESSENTIAL to the definition

[twin wolf]

well its still the right definitio

[fallen bone]

This is true, but why settle for intuitive argument when algebra works?

[onyx glen]

otherwise, you'd have to discount the following:

We say that a function h is even if h(-x) = h(x) for all x.

as invalid

[onyx glen]

yes but you're putting yourself through a clash of notation

[fallen bone]

Even for the correct answer here, you should have a proof based on properties of real numbers / related operations

It's not "choose one and it's right"

[twin wolf]

well if f(x) could be anything even without the 2 you can still have 2(f-x) = -2f(x) which isnt even

[fallen bone]

I think the lack of algebra is hindering your proof, which is why I'm asking you to increase your formalism

[twin wolf]

i dont know about f(f(x)) im just guessing for that but it justs sounds wrong

[fallen bone]

Can you write a short argument why any of the choices work/don't work

[twin wolf]

well f(x) is even if f(-x) = f(x)

a) 2f(x) if it is even then 2f(-x) = -2f(x) which is odd

b) i dont really know for that

c) wouldnt the square make anything positive

[fallen bone]

I'll do this one for you. Let f(x) = x. Then f(f(x))=f(x)=x. So f has domain of all real numbers, but is not even for -1 = f(-1) ne f(1) = 1

[fallen bone]

For C you should be thinking beyond polynomials

[twin wolf]

like what else?

[fallen bone]

There are a lot of functions with domain over all real numbers

Polynomials won't work

[twin wolf]

uh

logs? square roots? reciprocals?

that stuff?

[fallen bone]

Do logs have domain over all reals?

[twin wolf]

well if you add like

x∈R such that x >= 0 then I guess

as the domain^

would this work

[fallen bone]

I think the question is looking for functions which can properly be evaluated for any real input

[twin wolf]

so uh

how do we think about it ?

[fallen bone]

For C think into more kinds of functions. The example is not rare.
For D check algebra.

[twin wolf]

f(-x)f(-x) = f(x)^2

so that works

[fallen bone]

??????????????????

That is not how things work

[twin wolf]

💀

well negative times negative equal positive

and positive is even

[fallen bone]

f(-x)f(-x)=(f(-x))^2 and nothing more and nothing less.

Check your algebra.

[twin wolf]

if you have -a * -b

that becomes ab

which is even

[fallen bone]

I give up

[twin wolf]

lmfao

[white smelt]

it's not A or B

let's look at C and D

first try C

[twin wolf]

should I make up a function to test it

[white smelt]

sure

[twin wolf]

like how about f(x) = lnx does that work?

[white smelt]

lnx doesnt belong to all the reals

i mean the domain

[twin wolf]

oh

okayh so

f(x) = x^2

[white smelt]

sure

so that's your example if f(x) is an even function

if f is even, is (f(-x))^2 also even?

[twin wolf]

yep

[white smelt]

nice

now think of an odd function

[twin wolf]

x^3

[white smelt]

is f(-x)^2 even?

[twin wolf]

(-x^3)^2 = x^6

so yeah

[white smelt]

and last case

f being neither even nor odd

think of an example and tell me if f(-x)^2 is even

[twin wolf]

f(x) = 2x

so when (-2x)^2 = 4x^2

which is even

[white smelt]

are you sure 2x is neither even nor odd?

[twin wolf]

pretty sure

[white smelt]

f(-x) = 2(-x) = -2x = -f(x)

isnt it odd?

[twin wolf]

ohh

oops

i meant to say

somethng lik

e

e^x

[white smelt]

yeah let's work with that

(e^-x)^2

doesnt look even to me

[twin wolf]

i guess not because it still becomes e^-2x

[white smelt]

yep so the answer isnt C

now let's try D

[twin wolf]

so f(x)f(-x)

[white smelt]

go through the 3 cases again: even function, odd function, and neither

use the same 3 functions if you want, just for simplicity

[twin wolf]

x^2 * (-x)^2 which is even

x^3 * -x^3

hm

i think something is wrong?

(-x)^3 is still -x^3 which is odd

[white smelt]

yeah but it becomes -x^6 which is even

[twin wolf]

wait wut

ohhh

yeah

okay i see

[white smelt]

and lastly

e^x

[twin wolf]

e^x * (e^-x) = 1

so checks out

[white smelt]

yep, so the ans is D

[twin wolf]

oooh cool

i see how it works now

thank you

[white smelt]

yeah it's sort of a lengthy process but with more practice it becomes simpler

[white smelt]

np

[twin wolf]

yeah

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[errant abyss]

how do i define a ray if i have a point, a line and a relation "lie between" for 3 points?

[onyx glen]

call your line a and the point on it O

you could define a relation on a \ O which says A ~ B iff O doesn't lie between A and B.

this is an equivalence relation with 2 equivalence classes

each of which is a ray

[errant abyss]

What's a\O?

a without point O?

Oh makes sense, thanks a lot for your help

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[stuck island]

is the answer a

how about b

i need the answers please this is due in 5 min

[onyx glen]

no

[stuck island]

okay

for the first one

[onyx glen]

best way to guarantee ppl won't even want to help you

let alone give you answers

[stuck island]

ill explain my answer after

is the first one b?

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[willow wind]

<@&286206848099549185>

[ebon glacier]

move graph to the right by 3 points, so you get (x-3)^2, then shift it, you get -(x-3)^2, and finally at x= 3 you get y=1 so add 1, f(x) = -(x-3)^2 + 1

[willow wind]

im so behind on this class

whats best resource to learn

going to class is not helping i cant understand the teacher

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[green plank]

Hello

[green plank]

Question on this problem

https://i.imgur.com/EmOjlJe.png

How do i know if a set of ordered pairs make a function(s) of X?

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[reef karma]

Is that good enough answer? Can I say from inspection for that haha

That seems too easy so I’m wondering if I’ve done this completely wrong lol…

[fast peak]

no you cant plug A into that det(xI-A) definition

you are supposed to compute det(xI-A) first which gives a polynomial

then plug A into that

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@reef karma Has your question been resolved?

[reef karma]

When I computed it just gave 0, how do u get the polynomial out of it

[fast peak]

you should get something involving x

I am not sure how you are getting rid of x in any way

[reef karma]

Like this ?

[fast peak]

yes

[reef karma]

So now just expand brackets then sub in A for all the x values ?

[fast peak]

yes

[reef karma]

I don’t see how u could ever get 0 with this cus theres ad and -bc in it

Which I can’t put into the matrix

[fast peak]

you replace those by ad*I and bc*I

aka A^0 basically

[reef karma]

Oh thanks ye that works now ty

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[crystal cobalt]

https://cdn.discordapp.com/attachments/1164239660441161839/1164239720679755877/image.png?ex=65427dbb&is=653008bb&hm=f8435df470bcdfb6dde86e395319a2c8861933af285f5c437356232d7b544733&

[crystal cobalt]

How would i do this?

Answer is ||6/35|| i guess

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[stark locust]

I need help with question 3

[stark locust]

<@&286206848099549185>

[jade herald]

!15m

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[fathom saddle]

g(x) = f(f(x))
Can you differentiate and use the chain rule to get a form for g'(x)?

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[stark locust]

let me see

yeah idk my brain isnt working

let me show u an example i'm trying to use to understand this '

Look at question 5

[fathom saddle]

So you can take the derivative of h(g(x)), but not f(f(x))?

[stark locust]

I got that from the teacher I didn’t know how to do that either

Is the part where h(g(x)) g(x)= 1 always true ?

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[polar shell]

Simple question, how do we do the part in the blue?

Website wants me to pay to see 😭

[prisma flame]

use chat gpt

just ask it to simplify that

lim h->0 ((1/(sqrt(x+h) + 3)) - (1/(sqrt(x)+3)) )/(h)

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[polar shell]

Chatgpt is not helping

[thorny tendon]

did you try it at all?

what's your working so far?

[polar shell]

I was asking it the wrong thing

I was trying to get it to simplify to the specific expression on the blue line in the picture

[thorny tendon]

did you manage to do it?

[polar shell]

What is the explanation to get rid of the +3

.rtccw

[thorny tendon]

the explanation is 3-3=0

[polar shell]

Alright i think im good here thanks

[thorny tendon]

np

[polar shell]

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[thorn raptor]

Hi! Is it possible to solve this limit without using l'hopital or power series?

[torn jolt]

I’m pretty sure this is just asking what the derivative of 2h is

Graph it right hand and left hand

[thorn raptor]

I just want to know if is it possible to solve this limit without l'hopital or power series.

[torn jolt]

You can do what Magnesium Cheeson said

But tbh its just a waste of time actually solving it, so just knowing the question is asking what is f'(x) should be the way to solve this problem fast and easily

[thorn raptor]

I'm trying to find out, that's not an exam question, is just personal a doubt

[left bone]

Its probably possible, but everyone here would just default to lhopital

I cant see another way to do it off the top of my head but that doesnt mean it doesnt exist

[thorn raptor]

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[royal temple]

How do you solve this?

[gritty rose]

Do u sub

[royal temple]

What do I sub in?

[gritty rose]

Try something

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[drifting cargo]

"A balanced die is rolled and then a balanced coin is tossed the number of times that the die shows. Find the probability of obtaining exactly two heads."

[drifting cargo]

for the denominator im getting

2^1+2^2+2^3+2^4+2^5+2^6

for the numerator im getting 1+3C2+4C2+5C2+6C2

but apparently this is wrong

anybody know where im going wrong?

am i wronly assuming equiprobability?

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[tacit rapids]

Weirdest graph ever

Goofy aww graph

[narrow ermine]

HAHA VAVA

[tacit rapids]

But like

That graph doesn’t seem right to me

That is the answer key

[narrow ermine]

It looks alright

[tacit rapids]

Well i don’t like how they are going beyond their HA

Yeah nvm

It seems alright tho

Thanks

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[rough tundra]

.reopen

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✅

[rough tundra]

I would just like to add one thing if you don't mind @tacit rapids

a function can cross it's own HA just not a VA

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[tacit rapids]

.reopen

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✅

[tacit rapids]

Yeah actually you’re right

Ive seen some examples of that before

Thanks for reminding me

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[dark egret]

How do I do this question

I just started with dot product so I am still not too familar with it

[sullen mantle]

Remember that for any vector v, |v|^2 = v * v (where * is the dot operator)

and just like multiplication along the number line, the dot product is also distributive

[dark egret]

so |u-v|^2 would be uu-(vv)

is that correct

[dark egret]

going off of this ^

[sullen mantle]

Not exactly. Remember that when we FOIL everything out there should be some cross-terms

[dark egret]

oh right

[dark egret]

i mean just using foil it would be |u^2+v^2-2uv|

right

[sullen mantle]

Almost, it'd be |u|^2 + |v|^2 - 2u*v

[dark egret]

star is multiplication in this case right?

[sullen mantle]

Nope, it's still the dot product

[dark egret]

oh?

im slightly confused

how did foil end up with the dot product

[sullen mantle]

FOIL can be used when an operator is distributive. Since the dot product is defined as a distributive operator, we can use FOIL on the vectors it acts upon

[dark egret]

huh

interesting

so |u-v| |u-v| would become |u|^2 + |v|^2 - 2u*v

as you said above

with star being dot product

[sullen mantle]

Yes, $|\vec{u} - \vec{v}|^2 = |\vec{u}|^2 + |\vec{v}|^2 - 2\vec{u}\cdot \vec{v}$

[dark egret]

gotcha

[glossy valve]

thedude365

[dark egret]

question then asks to solve for u*v (dot)

is that just u1v1+u2v2+....

[sullen mantle]

The question writer wants you to solve for u*v in terms of the other terms in the equation we've found (|u-v|^2, |u|^2, |v|^2)

[dark egret]

hmm

how do I do that 😅

[sullen mantle]

You can reorganize this equation to get an expression for u*v

[dark egret]

oh gotcha

so would it become u*v = (|u|^2+|v|^2)/-2

using algebra

[sullen mantle]

Not exactly

[dark egret]

oh wow, im rly not getting this 😭

u*v = (-|u|^2-|v|^2)/-2

negatives instead

i think that was the missed part?

(hopefully)

[sullen mantle]

You're getting closer

[dark egret]

ive got no idea now 💀

since they are all negative it just becomes u*v = (|u|^2+|v|^2)/2?

[sullen mantle]

If you move all terms that don't include u*v to the left side, what does this equation become?

[dark egret]

,rotate

[dark egret]

Like this? ^

[sullen mantle]

Exactly

Except there shouldn't be a + on the |v|^2 term

[dark egret]

oh sorry

my bad

[dark egret]

so leading back to the original question, how does this determine that the dot product is determined by the length of vectors?

@sullen mantle

[sullen mantle]

For a given vector a, what does |a| represent?

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@dark egret Has your question been resolved?

[dark egret]

the magnitude of vector a

right

[sullen mantle]

Yes, which is the same as its length

So we've written u*v as the sum of the lengths of vectors

[dark egret]

oh

interesting

[dark egret]

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[nocturne trench]

$$ \text{Find and evaluate. }\lim_{u\to-2} \sqrt{9-u^3+2u^2} $$

[glossy valve]

Nerdy_Coder

[nocturne trench]

Uhh the problem is it seems the limit of u_3 doesn’t exist

Because like $$ \sqrt{(-2)^3} = \sqrt{-8} $$

[glossy valve]

Nerdy_Coder

[hybrid void]

Uhh

[hybrid void]

Doesn't it evaluate to sqrt(9-(-2)^3+2*(-2)^2)

Which is basically sqrt(25)

[nocturne trench]

What evidence?

Each term has it’s own limit

[hybrid void]

Evidence? You basically plug the limit of the variable in the expression

[nocturne trench]

I did

and uhh one of them is undefined

[hybrid void]

$$ \text{The question boils down to } \sqrt{\lim_{u\to-2} (9-u^3+2u^2) } $$

[glossy valve]

Ericsson

[nocturne trench]

Oh

Forogt that property of exponents

[nocturne trench]

Doesn’t the direct substitution property only apply to rational and polynomial functions?

[hybrid void]

Have you studied this property?
The limit of a composition is the composition of the limits, provided the outside function is continuous at the limit of the inside function

[nocturne trench]

It is?

Ph yea of course

[nocturne trench]

Wait there’s an exception to that?

[hybrid void]

In easy words $$lim_{x \to a} f(g(x)) = f(lim_{x \to a} g(x))$$

[nocturne trench]

Okay

[glossy valve]

Ericsson

[hybrid void]

Since f(x) here is sqrtx which is a continuous function

You can directly sub in the value of u

g(u) here is 9-u^2+2u^3 which is a polynomial functions

[nocturne trench]

Okay

[hybrid void]

The composition of these two functions is sqrt(9-u^2+u^3)

[nocturne trench]

Okay

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[sudden yew]

i am lost on how to answer this question

[stiff musk]

do you know what "unbiased" means

[sudden yew]

it produces parameter estimates that are correct

estaimator = true parameter

[fathom saddle]

What's the expected value of that estimator?

Remember, E() is linear

@sudden yew

[sudden yew]

5

is k 0.01?

[fathom saddle]

Yes

[sudden yew]

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[mighty bridge]

Hi guys can u help me please really urgent pls

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Please don't occupy multiple help channels.

[tacit siren]

ur own yer own m8

jk

[mighty bridge]

I didnt under can u repeat

[tacit siren]

actually nvm I hope somebody else can help, can't read text rn

[mighty bridge]

Oh ok

It is related to maths

Algebraic expressions

@tacit siren Can u just try to read it and help

i need it by 12pm ist

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[vast needle]

Two 4 digit number’s HCF is 200 and LCM is 18000, what are the two numbers?

[vast needle]

I have no idea the formula and how to calculate

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[vast needle]

<@&286206848099549185>

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[wicked aurora]

Try factoring 200 and 18000. Do you have any knowledge of how LCM and GCD can be expressed in terms of prime factorizations?

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[silk light]

The integral of a velocity time graph represents position and displacemnet; however, doesn't the integral of a displacement graph also represent position?

[pallid sorrel]

i think you can find the position from displacement

but not by itself i think

not 100% sure

[split swift]

the integral of displacement isn't position

it's a quantity you rarely use in practice

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[undone elbow]

what does it mean when I differentiation one variable in a two variable equation.
for example this equation.
$$ f(x)= \frac{(x-a)^2} {x^2+3} $$
I have to define a so that the function has a maximum at x=-1

[torn jolt]

then you would need to employ partial derivatives

[glossy valve]

N1x1T4

[torn jolt]

unless a is a constant

[undone elbow]

its a constant

[torn jolt]

then just differentiate normally

[undone elbow]

howp

do I first have to open the square numerator?

so that it becomes
$$ f(x) = \frac{x^2-2ax+a^2} {x^2+3} $$

[glossy valve]

N1x1T4

[torn jolt]

you can use quotient rule + chain rule

[torn jolt]

or just expand it instead of the chain rule lol

[undone elbow]

$$ f'(x)=\frac {(2x-2a) \cdot (x^2+3) - (x^2-2ax) \cdot 2x} {(x^2+3)^2} $$

[glossy valve]

N1x1T4

[undone elbow]

$$ f'(x) = \frac {2x^3+6x-2ax^2-6a-2x^3+4ax^2} {(x^2+3)^2} $$

[glossy valve]

N1x1T4

[undone elbow]

$$ f'(x) = \frac { 2ax^2+6x-6a } { (x^2+3)^2 } $$

[glossy valve]

N1x1T4

[undone elbow]

$$ f'(-1) = 0 $$

[glossy valve]

N1x1T4

[undone elbow]

$$ 2a(-1)^2+6(-1)-6a = 0 $$
$$ 2a-6-6a=0 $$
$$ -4a=6 $$
$$ a=-\frac{3}{2} $$

[glossy valve]

N1x1T4

[undone elbow]

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[spiral ledge]

Line Integrals Question, is there a better way to solve this?

[spiral ledge]

Also, the vector field is not conservative. Thus, you can't just find the scalar function and subtract one from the another

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[feral tundra]

I’m not sure how to do

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[strange wing]

hi, i need help with this question. I think we are finding the present value, but I'm not sure how to find it

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<@&286206848099549185>

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[tidal hedge]

how do i find the minimum without the original function

dont i need to plug in the critical points into the orignal function?

but it only gives me f'x

[umbral dome]

you can find the original function by taking the integral, they give you a point so you can solve for C

[tidal hedge]

i havent learned integrals yet

thats the next chapter 🥲

integrals**

[umbral dome]

wait you don't need the original function anyway

you can find the maxima/minima with first and second derivative test

not the f(x)-values, but the x-values where they happen

[tidal hedge]

i dont understand what you mean

[umbral dome]

it asks what values of x the minimum happens at. you can find whether a critical point is a maximum or a minimum by the second derivative test (if f''(x) > 0, it's a minimum, if f''(x) < 0, it's a maximum)

[tidal hedge]

ah ok

so i take the derivative of f' and plug in each of my critical points

one sec let me do it

ok i got it

2pi is the only critical point that gives me positive value

so that means its the minimum right

@umbral dome

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[wary jetty]

could anyone help me out with this? cause I had -4 / 2 / and 6 but is there something missing/wrong?

[buoyant wigeon]

why wouldnt -2 be a critical point ?

[wary jetty]

thats what I thought to but it marks it as wrong when I have -4 -2 2 and 6 selected

[buoyant wigeon]

Derivative seems to be zero at zero

[wary jetty]

ah I figured it out just now the other ones were 0 and 4

[buoyant wigeon]

ggs 👍🏻

[wary jetty]

hmm ok well now I need to find where the derivative equals zero

as well as undefined

[buoyant wigeon]

derivative is undefined when :

• Function is pointy
• Function is a single point
  derivative is zero when :
• Tangeant is horizontal

[wary jetty]

ah okay so 0 and 6 are zero and -4 -2 2 and 4 are undefined

[torn jolt]

yeah

[wary jetty]

ok it keeps asking more questions on the same thing - now its where f has a crit point but no local extremum

[buoyant wigeon]

local max (resp. min) is when there is an interval I such that for all x in I, f(x)<f(a) (resp. f(a)<f(x))

[wary jetty]

[buoyant wigeon]

or when f is defined on an interval it's when the derivative changes signs

For exemple [1,2] is an interval but [1,1.5[U]1.5,2] isn't

cuz it's not continuous

[wary jetty]

ok

[buoyant wigeon]

since your function is well defined on [-8,8] the answer are just the critical points where the derivative is undefined

mb

change signs

[wary jetty]

ok ty - also the last question that its asking here is inflection points is that just where the second derivative is changing in signs?

[buoyant wigeon]

yes

[wary jetty]

ok

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[rocky kettle]

Can someone please check my answer to q3

[mighty ridge]

they're asking for a probability, you didn't finish the question

also, it's easier to use binomial law here

[rocky kettle]

I’m not sure I’m allowed to use it here

Because they want me to use partitions

[mighty ridge]

1. how many ways are there to choose 10 people
2. how many to choose 7 red
3. how many to choose 3 blue
   using partitions, conclude

[rocky kettle]

Isn’t that what I wrote out

I just don’t know how to include the probability

I considered 20 choices for red person 1 and 19 for red person 2 etc

That’s where 20 x 19 etc.. came from

And there are 20 choose 7 for the red people

[mighty ridge]

I was hinting that you can just write the naive (20 choose 7)(10 choose 3)/(30 choose 10)

[rocky kettle]

Omg

Thanks

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[foggy trench]

how would i solve this? i tried solving it with the theory but it didnt work

[foggy trench]

it tells me that 11.66 is incorrect

[grim skiff]

Maybe it doesn't want decimal answers

So try converting 11.66666 to a fraction

[foggy trench]

im stupif how do i do that 😭

i never paid attention when they taught it

[scenic grove]

Mb

[wild sleet]

it would be 11.67

you could try 35/3 but i doubt it works

[foggy trench]

okay

WHAT THE HELL IS THIS SIGN

[grim skiff]

Which one?

The $\pm$?

[glossy valve]

CaptainNova22

[grim skiff]

Or $\sqrt{ }$?

[glossy valve]

CaptainNova22

[foggy trench]

this

😭😭

[foggy trench]

ohhhh okay

wouldnt this question be 75?

[undone vector]

You start with 1000. If you are gaining interest and go from 1000 to 75 I would be very not 🤑

[foggy trench]

OHHOOHOHOHH

I FORGOT

IDK MATH HELP

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[hasty bluff]

guys can anyone help me with discrete math?

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[torn jolt]

help

me plz

[full forum]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[torn jolt]

i did

oh thats a bot

no like- take a pic of the paper or screenshot

im on pc and its like paper

i cant

is it a test?

no

why cant you screen shot?

im on pc and i dont have a phone

well anyway- whats the question askin

find x

are you supposed to use a specifc method

uhh

no i dont think so

do you know the laws of angles?

yes

well corresponding angels will be useful to you

are the horizontal lines parallel?

yes

so what angel corresponds with the 35degree one?

the parallels are straght lines right? so you know x+the angel on the other side of the transveral = 180

sorry if i come off weird trying to explain it without out right giving the answer

I understand it now, thank you so much.

x = 131

i think

[torn jolt]

uh

[torn jolt]

oh it was 38 not 35

yeah

but uh how'd you get 131?

and that 97 is a 91

[torn jolt]

still not entirely sure how you got 131

[torn jolt]

here lemme show u

the horizontal lines are straight and parallel?

yes

so basically

each straight line = 180 degrees

and

if u subtract each exterior angle by 180

u get the interior angles

but for the bottom left corner

u do the opposite

and subtract the interior angle by 180

and get the exterior

thats how i got my answer

where did the 49 come from?

[torn jolt]

oh

yeah

1 quadrilateral = 360 degrees

and i added all the other interior angles besides the bottom left

and subtracted 360 by the sum of the interior angles

and got

49

then are the horizontal lines not parallel?

they are

the top and bottom are horizontal

and they do not intersect

[torn jolt]

does it state in your problem that they are parallel?

because if they are that angel couldnt be 49ᵒ

it would be 38ᵒ

[torn jolt]

no it doesnt

[torn jolt]

then you cant assume they are.
because anytime a transversal is through parallel lines, corresponding angels are equal.

131 is correct if those lines arent parallel.

which they cant be if thats a quadrilateral, which it is

lol, sorry i should have realized that since the coresponding angels created by the other tranversal arent equal

good job

thanks

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[oak berry]

is this answer correct

[oak berry]

shouldn't the roots be $e^\frac{\pm\pi}{3}$ and -1

[glossy valve]

undying

[spiral vigil]

we tend to prefer angles between 0 and 2pi

[oak berry]

oh

like the numbers i meant

isnt 60 degrees just pi/3

rather than 2pi/3

[fathom saddle]

You're right, they even drew π/3 and labeled it 2π/3

[oak berry]

ah okokok i was so confused lol

thanks 😄

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[fathom saddle]

They got confused between cube roots of -1, and cube roots of 1

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[swift fulcrum]

Hello

[swift fulcrum]

I understand I have to use potential energy formula to calculate for the first part

Not sure what to do next

I can't use mgh = 1/2mv^2 since there is height left, right?

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[glossy valve]

Ava

[solar flare]

Sqaure Root means power 1/2

Use that

Yes

(12a^6 b^3) ^ 1/2

Nah actually

√4 = (4)^1/2 = (2^2)^1/2 = 2^(2 × 1/2) = 2

So are u tyin to say

√2 = 2^2?

Thats what I wrote just now

According to ur view

[solar flare]

..

Thats when u remove sqaure and put that in exponent form

Do u know that
n th root of a = a to the power (1/n)?

nvm thats an exponent rule

Sqaure root of a means 2nd root of a

That means it would be a ^(?)

U can just write √12 = 2√3

Oh okay

[opaque harbor]

I usually do a factoring tree to solve it

[solar flare]

√ 12 = √(3×4)

= √(3×2^2)

[opaque harbor]

It's more easier

So the circled ones, we would put them inside the square root

The number that's alone or doesn't have a pair, would be placed outside

Using that, you can show that sqrt of 12 is 2√3

Just like what flamingo said, when we square root an exponent, multiply it by 1/2

So 6/1 * 1/2

Or 6/2, we would get 3

So sqrt of a^6 would become a^3

It's a rule from what I remember when square rooting

An exponent or radical rule, something along those lines

What my dance and math teacher said to me

Or if you want to make it more fun

factorization.

is another thing he told me

Oh wait, the rule was something else sorry.

a^3

We can't really give straight answers but help you out in solving it so you can learn it

But you can imagine it in this way, them having pairs.

Yes

[glossy valve]

Ava

[opaque harbor]

👍

You just completed the question, how'd I lie?

Even if you think so, what matters is you still got the concept down, it's your view and I can't change that.

[opaque harbor]

One way I primarily learned it is through factorization.

It's a fairly easy way to break it down, but feel free to use other methods, it's just a method I am most familiar with.

Can you elaborate more on 12 - 2?

What he's primarily doing is another way of factorization in a more of an expressive form.

Looking from what your teacher taught you, I believe you would disregard the first expression.

So, just disregard 12 - 2, and focus on the numbers that come after.

Like shown before, that way is essentially just plotting it like this.

However, I am unsure where you got the 1 from.

Since neither 3 or 2 can be factored any further with whole numbers.

Sure, I'll unsee it.

I mean, your teacher's way is still correct, however, just a bit confusing since I am not really familiar with that.

But if you'd like, you can use this method.

Mine is more of a visual type, takes a bit more room but lets you see much more.

So taking this, we factor it down from 12.

We would like to factor until we can't factor any of the numbers with whole numbers anymore.

Shown with the 12 and 6.

We want to identify the pairs, these pairs will go outside the square root.

So we would now have this: 2√

We want to fill inside of the square root, so we look for the numbers without pairs.

No, we don't add them.

We just take pairs.

And keep them as that number.

You can think in a sort of fun way where the mini 2 becomes a big whole 2.

Now, since we have 2√, we need to fill the inside of the square root, which we can find with this.

Since 3 has no pair, we'll just place that inside the square root.

We would then come out with ** 2√3**.

Hope that clarifies it up.

No, we factor the 6.

We want to take the results, or the answers that come out in the end after factorization is complete.

Numbers you factor ,you disregard them.

Why or what?

Do you mean what's inside the square root if it has no pair?

Or why inside the square root is the number with no pair?

It's essentially the concept when square rooting numbers, numbers with pairs are on the outside as ones with no pairs are inside.

However, you may have multiple pairs and no pairs.

Which you would multiply.

Sorry, I am not entirely understanding your question if I didn't answer it properly.

Sure, you can try 29.

Try factoring √29.

Or do you mean the ones with the variables as well?

I believe I have old notes on this, I'll see if I can find a sample question.

√8x^3y^4 is one I found if you wanna give it a go.

It's solvable.

You want me to break it down for you?

Let's try splitting them apart so we can break it down one-by-one.

√8 √x^3 √y^4

You wanna give it a go with √8?

[glossy valve]

Ava

[opaque harbor]

That's essentially it.

From my notebook, I have the same thing, so yes.

Now I gotta go do some work, hopefully this method can help you and your question was answered.

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[torn jolt]

this is the explanation for a)

what is this mysterious theorem 3

where does it come from

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@torn jolt Has your question been resolved?

[torn jolt]

b) 0 , -sin (0) + 3 = 3 , c ) https://www.youtube.com/watch?v=j3f88V9M0qM Steps for finding the inverse of a function f.
Replace f(x) by y in the equation describing the function.
Interchange x and y. In other words, replace every x by a y and vice versa.
Solve for y.
Replace y by f-1(x). , then get the derivative

[torn jolt]

its true actually but i dont remember the idea

[torn jolt]

have you tried solving for y after the interchange

cuz im not sure how to do tha

in this case

[torn jolt]

wait iam solving it

have fun

[torn jolt]

Sorry for my late my phone was uncharged and that what I get

I don't know if it's right btw but that what I remember when I talk inverse function

I hope that helped you

ty but i dont think you can just substitute the original function for y in line 4 cuz after you interchange y for x and vice versa, y becomes implicitly defined as the inverse of the original function

anyways its eepy time gn

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[torn jolt]

No If u get given that something is equal something it becomes equally

Even in any condition

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[gusty forge]

i know this is basic but i forgot how to derive 1/x

[gusty forge]

its suppose to be -1/x^2 but idk how

[onyx glen]

did you mean take the derivative

because in english we say "differentiate"

it's dumb but that's just what everybody says

[gusty forge]

yeah that

[onyx glen]

do you know the power rule

[gusty forge]

yes

it still confuses me

[hot herald]

do you know your exponent laws? \
are you able to express $\frac 1x$ in the form $x^n$?

[glossy valve]

ℝαμΩℕωⅤ

[gusty forge]

yeah, x^-1

[hot herald]

and can you apply power rule to differentiate that?

[gusty forge]

sooo -x^-2

[hot herald]

yes

[gusty forge]

okay i get it now thanks!

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[torn jolt]

Plzz solve this

[full forum]

What step are you on?
1. I don't know where to begin.
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

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Show your work, and if possible, explain where you are stuck.

[torn jolt]

i don;t know how to solve

[ornate bobcat]

So you are at step 1?

@torn jolt ?

[elfin stream]

@torn jolt

DONT cheat

[ornate bobcat]

Yeah he seams very busy solving the other questions

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[undone pendant]

Does anyone know if I am supposed to use a calculator or not for this question?

[fathom lotus]

No, you use google to factcheck /j

jkjk

There probably is a way to solve this by using calculus

[summer echo]

Write out all of them in decimal form

[summer echo]

They already assume archimedes was correct

[fathom lotus]

Is this your hw?

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[pallid sorrel]

what an interesting question

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[remote root]

I'm having a difficult time trying to make sense of De Morgan's law in boolean algebra\newline\newline

Let R = it will rain tomorrow\newline
Let S = it will snow tomorrow\newline\newline

What's the intuition behind\newline

\begin{equation}
\neg (R \land S) = \neg R \lor \neg S
\end{equation}

[glossy valve]

ZOOP

[remote root]

Like this is how i read the first formula: "It will not be the case that it will both rain and snow tomorrow"

And I read the second formula as follows: "It will not rain or it will not snow tomorrow",

I know the "or" in math is inclusive, but how can it grammatically make sense in english

like the first one reads for me like: R and S cannot both happen

the second one reads for me like: R or S cannot happen, or they both can't happen

so i guess the question is how does the first formula also say that either one can't happen and not only that they both cannot happen.

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@remote root Has your question been resolved?

[jade herald]

The logic is basically, if it is not true that it will rain AND snow tomorrow, that means it must false that either, it will snow, it will rain or both. The fact that both aren't true means that at least one or both is false

If they can't both be true, at least one must be false basically

In a truth table, NOT (A AND B) basically says "every other pairing than A=1 and B=1 are valid"

At which point the only combinations left are A=0, B=0, or A=1, B=0, or A=0, B=1. Which can be described by NOT A or NOT B

[remote root]

this makes sense to me

[remote root]

what do you exactly mean by "valid", how can a pair be unvalid?

[jade herald]

Well it's not that it "isn't valid", but it doesn't satisfy the criteria laid out by the statement NOT (A AND B)

[remote root]

as in if the truth value of the whole formula [not (a & b)] is 0

?

[jade herald]

In the case of A=1 and B=1 yes

With the not A or not B included

[remote root]

Yeah I see, the "If A & B can't both be true, at least one must be false" clicked

Thanks a lot

[jade herald]

Np, it's a confusing subject, I solved a bunch of tasks before getting it

[remote root]

Ok that makes me feel a little better haha

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[tepid glen]

X is random variable, its expected value is E(X) = 24.4, and its variance is VAR(X) = 25.
A = 4X, find the E(A) and VAR(A)
I multiplied E(A) by 4 to get 97.6. For VAR(X) I tried 25 * sqrt(4) and 25 * 4 but neither of them were right.
How do I solve for VAR(A)?

[vital ermine]

helloguys any one tell me a cube plus b cube formula please

[jade herald]

!occupied

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[vagrant tangle]

Can someone help me understand the difference between the sum of f(x) where i=1 and n=5, and the sum of f(x) where i=2 and n=6?

[vagrant tangle]

I'm little bit confused about exactly what i is

[glacial pasture]

the sum of (i assume you mean) f(i) from i=1 to 5 is
f(1)+f(2)+f(3)+f(4)+f(5)
the sum of f(i) from i=2 to 6 is
f(2)+f(3)+f(4)+f(5)+f(6)

can you see why those arent necessarily the same thing?

[vagrant tangle]

Ok so the full question is "suppose f is a continuous, positive, decreasing function for x>/=1 and an=f(n). By drawing a picture, rank the following three quantities in order: the integral from 1 to 6 of f(x), the sum of ai from i=1 to (I believe) five repetitions? But maybe it's to 5. And then the sum of ai from i=2 to 6.

Question 2 there

[glacial pasture]

ah i see, may help to note that
if $\sum_{i=2}^{6}a_i=\sum_{i=1}^{6}a_i-\sum_{i=1}^{1}a_i$

[glossy valve]

AℤØ

[glacial pasture]

that last sum is just a_1

what kind of pictures are you drawing for comparison

[vagrant tangle]

Does this seem right?

I'm not sure how to directly compare the integral with the sum to 6

Obviously the sum to 5 will be greater, I know they aren't reimann sums but they function as reimann sums since the interval is one so the area is equal to the y value

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[wicked cliff]

RB is 8 + y or 8-y?

[blazing nest]

I believe RB = y

if ur talking CB then it'd be 8-y

[wicked cliff]

why 8-y and not 8 + y ?

[blazing nest]

oh sry CB is actually just 8, CR is 8-y

8 is the total length of the CB side and CR is a portion of the CB side

[wicked cliff]

why cr is 8- y and not 8 + y?

[blazing nest]

Think of it as CR + RB = CB

we know CB = 8, RB = y

giving CR + y = 8

solving for CR we get CR = 8-y

[wicked cliff]

ohhh i see tgx

thx

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[static mesa]

How do I draw the secent lines and how I get the slope?

[flat mesa]

why did you draw the lines the way you did

[static mesa]

Tbh I do not remember

[flat mesa]

do you know what a secant line is

[static mesa]

Yes

[flat mesa]

what is it

[static mesa]

isn't it just a line hitting two points

[flat mesa]

can you be more specific

[static mesa]

not really?

[static mesa]

it has to touch the curve?

[flat mesa]

this line is indeed a secant line, but that's not what the question wanted

it wanted a line that goes through the points specified in part a

and the slope

[static mesa]

so -2

and f(-2)?

[flat mesa]

no

(-2,f(-2)) is a point on the curve

[static mesa]

yeah I'm confused about that

[flat mesa]

your teacher has highlighted (-2,f(-2)) on the correction