help-23

[feral linden]

Then why do you ask

It’s a generator

[junior wagon]

well, I wasnt sure it prove the question

[feral linden]

Let V=
(0 0
1 0)

V^2=0

So( I+V)^n=C(n,0)I+C(n,1)V=I+nV=
(1 0
n 1) when n>=0

(I-nV)=(I+nV)^-1=(I+V)^-n

So as you said

I+V is a generator

[junior wagon]

hm ok

ty

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[wheat timber]

hello

[wheat timber]

im in need of help of 3 proof problems..

i hate proofs and im helping a friend, but i did this like 3 yrs ago and forgot everything

and i barely passed the unit tbh

anyone?

<@&286206848099549185>

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[safe radish]

Please don't occupy multiple help channels.

@spiral ivy Has your question been resolved?

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[mighty monolith]

hi, i have this inequality and i figured out i can get rid of x from right and 1 from the power on the left, but i have no idea how to proceed further

[quasi bison]

$x^{\log_4(x)} = 4^{\log_4(x) \cdot \log_4(x)}$

[flat frigate]

Ann

[mighty monolith]

it's not really clear to me the right side..

[quasi bison]

well you've already divided both sides by x (which is of course known to be positive), right

so you're looking at $x^{\log_4(x)} > 256$

[mighty monolith]

yeah

[flat frigate]

Ann

[quasi bison]

so now you have $4^{(\log_4(x))^2} > 256$

[flat frigate]

Ann

[mighty monolith]

how do you swap x with 4 like that?

[safe radish]

@mighty monolith Has your question been resolved?

[mighty monolith]

can you explain how did u do that?

[quasi bison]

i didn't swap anything

$x = 4^{\log_4(x)}$

[flat frigate]

Ann

[quasi bison]

so $x^{\log_4(x)} = (4^{\log_4(x)})^{\log_4(x)}$

[flat frigate]

Ann

[balmy sky]

@mighty monolith this is property of log

[mighty monolith]

wow I'm such smol brain..

[mighty monolith]

you're huge, thx 🙏

[balmy sky]

na @quasi bison is just big brain

[mighty monolith]

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[lone arch]

Using u, _ and the other symbols, express that from A and B, exactly one happens

[lone arch]

How do I do this

[tired imp]

???

is that the entire question?

[lone arch]

yes, why?

[tired imp]

what does it even mean??

[quasi bison]

so the entire paper is blank except for that one line written exactly as you typed it

is that what youre saying

[lone arch]

For example, you show that none of the things can happen by

But how do you show that exactly one of these things can happen

A or B

[lone arch]

It's either A or B

But not A and B

[quasi bison]

thank you for not answering my question

so what you meant to tell us is:

you're given two events A and B, and you need to express the event "exactly one of A and B happens" in terms of A, B and basic set theory operations (intersection, union, complement).

[lone arch]

you're given two events A and B, and you need to express the event "exactly one of A and B happens" in terms of A, B and basic set theory operations (intersection, union, complement).
yes

[quasi bison]

okay finally

now

do you know how to express "at least one of A and B happens"?

[lone arch]

hmm, is it not (A and B)

[quasi bison]

no

[lone arch]

oh, at least, so A or B

[quasi bison]

yes

and now can you express "A and B don't happen at the same time"?

[lone arch]

not (A or B)?

[quasi bison]

no

[lone arch]

not (A and B)

[quasi bison]

there we go

now can you express "at least one of A and B happens, but not both"?

[lone arch]

not (A and B) again?

[quasi bison]

no.........

[lone arch]

not (A or B)?

[quasi bison]

no!

[lone arch]

uh

[lone arch]

is there a way I can quickly come up with this?

[quasi bison]

i asked you for "at least one of A and B happens" and you correctly said A or B
i asked you for "they don't both happen" and you correctly said not(A and B)
now i ask you to take their intersection and you're unable to do that

[lone arch]

so A or B and not (A and B)?

[quasi bison]

yes!

[lone arch]

oh

so that's the answer

thx!

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[lone arch]

Btw, how would you know that "at most one of A and B happens" is not (A and B)?

[lone arch]

A and B means both happens, so not both happens = one happens?

[quasi bison]

since there are only two letters, "at most one" means "not both"

not both means at most one, i.e. one or none

[lone arch]

Thx

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[crude prism]

Sets can have other sets as their elements right? So can a set have the empty set as an element?

[feral linden]

Yeah

[crude prism]

okay thanks!

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[acoustic bluff]

Can someone explain what Im supposed to do here? (Red one is an example)

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@acoustic bluff Has your question been resolved?

[worn shadow]

Diemon, I suppose you put the value of 1 into x in the table, lets say we start with Green, then x=1, when x=1 then put it in the formula above. For this instance on the top table we have 7x+y=16. So put 1 into every x that is in the formula, 7(1)+y=16, then do simple algebra from there, meaning it will be 7+y=16, then move the positive 7 to the other side making it negative. y=16-7, and you get y=9

then since you put x=1 and you found y=9

it would look something like this

then try x=2

and so on

for every color above ^

to understand the red example, x+y = 2. if x = 1 then x+y=2 can be written as 1+y=2

y=2-1 making it y=1

or logically 1 plus what equals 2?

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[orchid crystal]

| z | of cosx+isinx-1 = 1. What is x

[acoustic bluff]

I see TYSM, this helped understand it much better than what my teacher explained!

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[worn shadow]

nws

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[ancient scroll]

I'm not sure how to do this question

cuz i think the eigenvalues and eigenvectors should be complex

[peak estuary]

start with lambda <x, x>

then use linearity, eigenvalue definition and def of A^T to get -conj(lambda) <x,x>

[ancient scroll]

Is A a skew-symmetric matrix?

[peak estuary]

skew-symmetric and anti-symmetric are the same thing

Yes

[ancient scroll]

for part b i got the case when n is off

odd*

but not sure about even

gimme a min ill send my working out

[peak estuary]

The det is the product of the eigenvalues. Note that complex eigenvalues always come in conjugated pairs and the product of those is nonnegative

So the only issue could be a real eigenvalue

[feral linden]

Eigenvalues of A are roots of the characteristics polynomial of A which is a real polynomial. so if bi is an eigenvalues , so is -bi. Their product =b^2>=0, so product of them are non-negative

[feral linden]

There isn’t. Any eigenvalue λ=a+bi of A, by λ=-(λ bar), a+bi=-a+bi, we have a=0, λ=bi

[peak estuary]

Well yes but I don't always want to tell the whole solution

[feral linden]

Oh sorry…

[ancient scroll]

thanks both of you

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[peak estuary]

Also just small note, 0 can still be a real eigenvalue

There just can't be nonzero real eigenvalues

[ancient scroll]

yeah tysm!!!

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[gaunt stag]

Calculate the volume created when the area between the two curves x=-y^2+10 and x=3 is rotated around the y-axis

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[gaunt stag]

No

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[safe radish]

Please don't occupy multiple help channels.

[hybrid flare]

please help

[queen parcel]

Don't create multiple channels - close this one.

[hybrid flare]

ok

.close

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[brisk coyote]

need some help on this question, the last of my homework: What value(s) of x would make the denominator of the fraction (x-4)/(x^2 - 9) equal to 0?

[brisk coyote]

I've tried plugging in 0 and stuff and im just really confused

[drowsy moss]

set the denominator equal to 0

[brisk coyote]

well yeah that's essentially rephrasing the question; but the denominators x^2-9 so how in the world would i get to make that a

0

[drowsy moss]

by setting it equal to 0 and solving for x

or factoring, if that's something you know to do

[brisk coyote]

yes i know how to factor

so itd be like

x^2 -9 = 0
add 9 to both sides
x^2 = 9

but thats kinda pointless

wait so what do i do to continue that

i have to divide something there

[drowsy moss]

how do you get rid of a square?

[brisk coyote]

isolate it to one side

of the equation

so is it x^2 = 9 divide by x on both sides? or divide by x^2

[drowsy moss]

if $x^2 = a$ then $x = \pm \sqrt a$

[flat frigate]

Zybikron

[drowsy moss]

basically, take the square root of each side.

[brisk coyote]

so going back to x^2 = 9

we say x = sqrt 9, x = -sqrt 9?

[drowsy moss]

yep

[brisk coyote]

and then sqrt9 = 3, -sqrt9 = -3

so 3, -3

[drowsy moss]

yes

[brisk coyote]

so 3, -3 would make the denominator equal to 0

[drowsy moss]

yes

[brisk coyote]

alrighty ty

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[pure spruce]

Im having trouble with finding the radius of this using disk method

wouldnt it be x^2-4

[lean otter]

Since you're revolving around y=4, the axis of rotation will be parallel to x-axis. This means that the radius will be perpendicular to x-axis, or in other words, changes with y.

[safe radish]

@pure spruce Has your question been resolved?

[pure spruce]

sorry new question

so here it's saying region bounded by the 4 curves

[lean otter]

what's your bounds, equation, general formula

Nah the question gave you limits

The area will revolve around a y-axis so your area will change with x. So use dx

And this is washer method

[pure spruce]

it's a vertical line so it would be dy

yah I found out it's washer

these two areas

I still can't find the area tho

[lean otter]

Oooo yea dy

[lean otter]

Divide you integral into 2 intervals

From 0 to 2, it is 2-1. And from 2 to 4, it is y-1

@pure spruce

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[stone slate]

slope = 0/0

?

intercept = (-7)

[potent roost]

slope isnt 0/0

how did you get that

y=mx+c
m is clearly 1

[stone slate]

what?

there isn't a slope value

[sacred stream]

1x=x

the 1 can be ignored

[stone slate]

oh ah i see

[potent roost]

0x = 0
1x = x

[sacred stream]

so its just 1x -7

so m = 1

[stone slate]

ok, thanks

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[safe radish]

@slate granite Has your question been resolved?

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[hoary token]

i think its better to start off with the definitions of echelon form and reduced row echelon form

row echelon:

1. non zero numbers go from left to right down every row
2. zero rows are at the bottom

reduced:

1. same idea but there should be 1s every time you go down each down

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[hoary token]

this would be correct since you cant have another row with 1 as your leading coeff in the same column!

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[hoary token]

this is also correct! because all your zeros are to to the left and any numbers you have are to the right

[hoary token]

oh boi the bot is dying

for b, let's think it through. you start off with a leading coefficient in your first row. check. you have zeros below and to the right also check. for your second row you it's 1) to the right of the 1 in the first row, has zeros above and below, so you're good. the third row would count as being in its row reduced form as well becuase it's to the right of the above

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.reopen

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✅

[hoary token]

hope that helped tho ^^

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[safe spindle]

is this correct?

sorry about the handwriting

I'm trying to differentiate the integral from 0 to x² of sin(sqrt(t))dt

i was wondering if you can do it like this

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[junior wagon]

$\langle a \rangle \cup \langle b \rangle \preceq \langle a \rangle$ and $\langle a \rangle \cup \langle b \rangle \preceq \langle b \rangle$. By Fundamental Theorem of Cyclic Groups, then $|\langle a \rangle \cup \langle b \rangle| | |\langle a \rangle| = 8$ and $|\langle a \rangle \cup \langle b \rangle| | |\langle b \rangle| = 19$

[flat frigate]

Kurama

[junior wagon]

So then $|\langle a \rangle \cup \langle b \rangle| | gcd(8,19) = 1$, meaning $|\langle a \rangle \cup \langle b \rangle|$ has order 1.

[flat frigate]

Kurama

[junior wagon]

Does this show $\langle a \rangle \cup \langle b \rangle = {e}$?

[flat frigate]

Kurama

[unique bison]

i think you mean $\cap$ rather than $\cup$

[flat frigate]

giannis_money

[junior wagon]

yes, my bad

[unique bison]

but yes, because a subset of G must contain the identity

[junior wagon]

ok

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[quiet plank]

What formula can I use to represent this relation between two variables x and y.
x = 1, y = 2

efficiency = 0.5
;
x = 2, y = 1
efficiency = 0.5

as you can see, I just want the ratio between the two, but x/y or y/x does not work as it will give "2" in one of the cases

[delicate aspen]

min(x,y)/max(x,y) would do it?

[quiet plank]

Oh, I forgot I can use those 2 functions, thanks

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[neon ember]

how would i go about doing this derivative?

[neon ember]

$$\frac{\sum^n\frac{1}{2}(\delta(M_2\cdot\delta(M_1\cdot x)) - y_a)^2}{n}$$

delta is a function and everything else is a variable

[flat frigate]

Leao

[neon ember]

could I divide both sides by the sum so itd be d/sum dx

?

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[cyan plaza]

x3+y3+z3=k

[hot oar]

Do they want you to simply

@cyan plaza

[cyan plaza]

yes

[hot oar]

Easy so can you identify like terms

[cyan plaza]

ok

[hot oar]

k

x
3
+
y
3
+
z
3

What happened

K=x^3 + y3

• z^3

I am making a mess sorry

[safe radish]

@cyan plaza Has your question been resolved?

[safe radish]

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[safe mural]

I need to know the formula

[knotty sigil]

a(r^n-1)/(r-1)

[safe mural]

a being and n being?

[knotty sigil]

a first term

n number of terms

r common ratio

[safe mural]

how do we get the number of terms isint it infinite ?

[lean otter]

it only wants the first 6 terms

[safe mural]

ah my bad thank you!

.close

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[gleaming anvil]

hi, im confused about b

[gleaming anvil]

i see that since $\mathrm{ord}(\sigma) = 20$ (found at a), that $\sigma^{-86421} = \sigma^{-1}$, but how do i find a negative power of a permutation?

fyi, the disjoint cycle is $\sigma = (1,7,12,10)(2,4,5,6,3)(8,11)(9,13)$.

[flat frigate]

Rœmer

Rœmer

[limber yoke]

if I have the cycle (1 2 3)
and i wish to compose it with something that gives me the identity permutation back, what might it look like
1 maps to 2, 2 maps to 3, 3 maps to 1
how do i undo those maps?

[gleaming anvil]

(1 3 2) right

so you're saying i should just find the inverse?

[limber yoke]

Yep

[safe radish]

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[safe radish]

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[frigid plinth]

Red is mine, pink is the answer key. What did I do wrong?

Why didn't she put it on parenthesis?

[safe radish]

@frigid plinth Has your question been resolved?

[regal girder]

the +3 is in exponent right?

[frigid plinth]

Yes

[regal girder]

$$x = 2^{y + 3}$$
$$x = 2^y2^3$$
$$2^y = 2^{-3} x$$
$$y = \log_2(2^{-3}x)$$
$$y = -3 + \log_2(x)$$

[flat frigate]

Doggo

[regal girder]

you wrote the exponent in wrong place in your answer

you can't subtract 3 like that

from both sides

[frigid plinth]

Where?

Oh

OH I SEE

My bad handwriting 💀 💀 💀

Got it

[regal girder]

our* bad handwriting because I can see that happening to me

[frigid plinth]

LOL

Ty for your help

Much appreciated

.close

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[lapis vapor]

This question came up in my textbook. "Find a vector of length 8 and of direction -i+3j"

[lapis vapor]

Im studying in french and length is called "norme". idk if its called the same in english

[regal girder]

are you referring to the $|v|$ thing?

[flat frigate]

Doggo

[lapis vapor]

yes

[regal girder]

that's called norm I think, similar to the french one

[lapis vapor]

then yea im referring to norm

of norm 8

[regal girder]

anyways $|v| = \sqrt{x^2 + y^2}$ on 2 dimensions, for the vector to be in the direction -i + 3j, it has to be a (positive?) constant multiple of it I think

[flat frigate]

Doggo

[regal girder]

so you really just want to solve $$\sqrt{(-k)^2 + (3k)^2} = 8$$ for k and multiply the direction by $k$

[flat frigate]

Doggo

[lapis vapor]

I overthought this question then

ty for help

[safe radish]

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[shrewd ginkgo]

hi

[shrewd ginkgo]

anyone there

<@&286206848099549185>

.close

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[lilac vector]

They are asking me to determine local min, local max, or neither from these statements

Then to explain how each classification would be correct

I don't know how I'd do this without being able to see the function

[thin bridge]

consider the given information about the slopes
before and after the specified locations

[lilac vector]

so test values? like 2 for the first one would work. but what function do I plug that into

[thin bridge]

no need to test values

you are explicitly given the signs of the slopes around x=3,5,7

[lilac vector]

x=3 has a negative slope

[thin bridge]

no

the slope at x=3 as 0

[lilac vector]

not <0?

[thin bridge]

f'(3) = 0

there is a stationary point at x=3

consider these common cases

[lilac vector]

oh is it talking intervals

like (-infinity, 3)

[thin bridge]

well yeh.

that's the interval where x is less than 3

[lilac vector]

I dont understand why they give 4 intervals

but i understand that image

the first graph is concave up meaning local min

[thin bridge]

my images are just common stationary points

for you to consider the slopes

consider the slope before and after the stationary point

[lilac vector]

all of them seem to give a positive value

[thin bridge]

wdym

[lilac vector]

all the intervals are greater than 0

besides the one we dont need

[thin bridge]

whut

i have no idea what you're on about atm

[lilac vector]

okay ill stop im trying to figure it out and failing haha

[thin bridge]

you are told the function has 3 stationary points

[lilac vector]

yes

[thin bridge]

and the info below that tells you the signs of the slopes before, between and after those locations

the signs can be used to determine the type of stationary point you have

consider the concave up parabola i made

what is the sign of the slope before (to the left) of that stationary point?

[lilac vector]

for x=3 it is +

[thin bridge]

no

[lilac vector]

0?

[thin bridge]

not waht i'm asking for

and no

to both

[lilac vector]

okay

[thin bridge]

draw a tangent line to a point somewhere of the left of the stationary point of that concave up parabola

[lilac vector]

it would be going down

[thin bridge]

and will the slope of that line be positive or negative?

[lilac vector]

negative because its slanting toward that point you made

[thin bridge]

yes.
and similarly consider a tangent line to the right of that stationary point

[lilac vector]

would increase

or slant away from the point

upwards

[thin bridge]

what will be the sign of the slope of that

[thin bridge]

yes

[lilac vector]

okay that visual makes more sense for sure

[thin bridge]

so if the slope to the left is negative and the slope of the right of the point is positive,
you'll have a local min

[lilac vector]

yes ahhhh wow

[thin bridge]

consider the same ideas for the others

tells you the signs of the slope before 3,
and a bit after 3

[lilac vector]

right okay I will try the answers and try and justify it, i'll get back to you

[thin bridge]

which you should now be able to use to determine what type of stationary point you have

[lilac vector]

because x was greater but also less than 5

it would just create a line

[lilac vector]

I think this is correct because x cannot go over 7 the slope would be negative

on the right side

of a congave down graph

[thin bridge]

they're all wrong

[lilac vector]

oh

[thin bridge]

consider the sign of the slope before and after the specified location (you could simple represent that with something like \ or / on your page)

[lilac vector]

yes I did exactly that i mustve done something wrong though

[thin bridge]

you'd end up with stuff like

/ \

/ /

\ \```
and 
it should be clear whether you have a local min/max or neither

[lilac vector]

I got / for the first one as well

V

thatd be a local min

[thin bridge]

how are you getting a V for the first one

$f'(x) > 0$ for $x<3$ \
what does that tell you about the slope to the left of 3? \
is it positive or negative?

[lilac vector]

i am looking at f'(x) > 0

[flat frigate]

ℝamonov

[lilac vector]

its positive

[thin bridge]

and which of these

/
best represents a line with positive slope

[lilac vector]

bottom

[thin bridge]

yes

so you'd start with
/ first NOT \

[lilac vector]

yeah thats good i dk why im still messing up

the derivative function for the next one is less than 0 initially

so im assuming its negative first then positive

between 3<x<5

"4"

[thin bridge]

wdym negative first then positive

[lilac vector]

a negative slope, then a positive slope, meaning local min for the second problem

[thin bridge]

yes

[lilac vector]

and the next one is two positives ... dk what to do about that

[thin bridge]

that would be neither local min/max

and you'd actually have what's called an inflection point

[lilac vector]

oh. inflection point is the next unit. i see the fourth is positive then positive again

so the last question is actually "neither"

[thin bridge]

yes

[lilac vector]

i will keep trying to understand it

thanks for the help

.close

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[gritty ice]

In implicit differentiation, when taking dx/dy can I say that d/dy(x) is the same as dx/dy?

[gritty ice]

,tex $\frac {dx}{dy}\left(a + b + c\frac{d}{dy}(x)\right)$

for example

Does it make sense at all

[flat frigate]

Jamestiago

[potent roost]

yes

btw you cant take dx/dy

it isn't an operation

d/dy would be

dx/dy is just a function, and what you have is the product of that function and the other function

[gritty ice]

So when implicitly differentiating an equation I could only use dx/dy at the end, to denote the answer

?

or would it be preferrable to use x'(y)

[potent roost]

either

works

its just notation

[gritty ice]

but only at the end, correct? like you said, dx/dy isn't an operator

[potent roost]

x' can be used anywhere inplace of dx/dy, but yes it isn't an operator

[gritty ice]

When I take d/dy(x^2) and it gives me 2x dx/dy is it the same as 2x d/dy(x)

[safe radish]

@gritty ice Has your question been resolved?

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[undone grail]

Ok so i have been doing quite a few practice tests for my uni entrance exam and at least 1 question like this (similar is not the same) keeps popping up but i always skip/dont know what to really do

[undone grail]

how would i go about figuring this out?

[safe radish]

@undone grail Has your question been resolved?

[undone grail]

<@&286206848099549185>

[safe radish]

@undone grail Has your question been resolved?

[undone grail]

anyone?

[undone grail]

.close

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[hushed cave]

the question is what is the minimum value of d

[safe radish]

Please don't occupy multiple help channels.

[shy temple]

multiply top/bottom by sqrt(x)+sqrt(y) to get |x-y|/[sqrt(x)+sqrt(y)]

[worthy hemlock]

Don't open multiple channels

[hushed cave]

different quesitions

[worthy hemlock]

You still don't used multiple channels, even if you have different questions

[safe radish]

@hushed cave Has your question been resolved?

[safe radish]

@hushed cave Has your question been resolved?

[plucky elk]

Stop opening multiply channels @hushed cave

[hushed cave]

You close them with no answer

[plucky elk]

Because you keep opening more than 1.

[safe radish]

@hushed cave Has your question been resolved?

[safe radish]

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[untold delta]

I tried using the A= P(1+i)^n formula but not sure what to put for i, do I write 0.09 or multiply 0.09x7?

[eager ravine]

simple interest

[untold delta]

we were told to use the Fv formula

[eager ravine]

that changes nothing

it’s still the future value of simple interest

[untold delta]

okay, what do I put for i

[eager ravine]

you are using the wrong formula

find a simple interest formula first

[untold delta]

the I = prt then?

[eager ravine]

yes interest is Prt

[untold delta]

I don't change the percentage then unless changing it into a decimal?

[eager ravine]

you mean 9% interest to r = 0.09

[untold delta]

yes

but how would I write that in the chat?

[eager ravine]

what

[untold delta]

how would I put the interest in this chart

[eager ravine]

you know P

you know r

and you can find t on the left column

[untold delta]

so for 3 years it would be I = 700 x 0.09 x 3?

correct?

[eager ravine]

yes

[untold delta]

okay, so how would I know when to use the I = prt and the fv one?

[eager ravine]

future value is the total amount

it doesn’t mean simple or compound

you find out which in the question

I = Prt is simple interest

[untold delta]

so when do I use it fv?

as in how would the question sound like

[eager ravine]

when you’re looking for future value

not for simple interest

the total amount column is the future value

[untold delta]

okay I think I get it

ty

!!!

.close

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[coarse birch]

<@&286206848099549185> I just got into this unit and Ik how hot solve for the function with the quadratic formula but I’m not able to solve for this with my work (not shown)

[winged timber]

@coarse birch what are your three points

[safe radish]

@coarse birch Has your question been resolved?

[safe radish]

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[coarse birch]

@winged timber

[radiant roost]

is this correct it’s the last question on a 9 question test on khan academy

[wild trench]

#❓how-to-get-help

[radiant roost]

oops wrong chat

[coarse birch]

ahh

<@&286206848099549185>

is what I got correct??

[wild trench]

Yes what's your question

[coarse birch]

And that’s my answer

[wild trench]

The first two are correct

[coarse birch]

What about the third?

[wild trench]

(4,6) is also correct

[coarse birch]

Alright

[wild trench]

Last one also good

[coarse birch]

I also got another question

[wild trench]

Yes

[coarse birch]

How do I solve this?

Without a calculator or anything

[wild trench]

With vertex form

[coarse birch]

Ohh

[wild trench]

f(x)=a(x-h)^2+k

You have the vertex and a point

[coarse birch]

Can you show me how it’s done?

[wild trench]

Ok

[coarse birch]

Step by step lmao sorry

[wild trench]

Alright no problem

So first you have the vertex formula : $$f(x)=a(x-h)^2+k$$ (Where h is the x coordinate of the vertex and k is the y coordinate)

[flat frigate]

Ze_Beeg_Almond

[coarse birch]

Alright

[wild trench]

Replace h and k in the formula with (4,3)

[coarse birch]

That’s all?

[wild trench]

$$f(x)=a(x-4)^2+3$$

[flat frigate]

Ze_Beeg_Almond

[wild trench]

almost... you're still missing the a value though

For that, use the additional point you're given (6,3)

replace f(x) by 3 and x by 6

$$3=a(6-4)^2+3$$

[flat frigate]

Ze_Beeg_Almond

[wild trench]

$$5=a(2)^2+3$$

[coarse birch]

Alright I’m gonna try it now

[wild trench]

Solve for a and you're done

[flat frigate]

Ze_Beeg_Almond

[coarse birch]

Do I have to solve for a?

@wild trench

Can I just leave it without solving for a?

[wild trench]

Yes you have to solve for a, for it is part of the question.

[worthy hemlock]

You have to solve for a

Because that equation is not the general equation for that quadratic

[coarse birch]

This is the quadratic formula

[worthy hemlock]

No it's not

[coarse birch]

Ohh

[worthy hemlock]

Quadratics are in the form of $f(x) = ax^2 + bx + c$

[flat frigate]

dldh06

[worthy hemlock]

Do you see an x^2?

[coarse birch]

A = 1 over 2

[wild trench]

Yes

[coarse birch]

So what would be my final answer be for that question

[wild trench]

You replace a in the equation by what you got (1/2).

[worthy hemlock]

Plug a into here

[coarse birch]

5 = 1 over 2

[wild trench]

No, just : $$f(x)=1/2(x-4)^2+3$$

[flat frigate]

Ze_Beeg_Almond

[wild trench]

And that's your final answer

[coarse birch]

Wait what???

[wild trench]

Yes

[coarse birch]

Alright lemme just look this over I’m confused

[worthy hemlock]

Literally this was the equation you had, you needed to find a. You found a, a = 1/2, plug in that value

[wild trench]

The question is just to determine the formula.

[coarse birch]

I got there

Than I solve for a

[wild trench]

Yes

[coarse birch]

And plug a into the equation

[wild trench]

plug a into the 2nd equation

[coarse birch]

Alright

All I gotta do now is plug it into the second equation

[worthy hemlock]

Plug that value of a, into the second equation, yes

[worthy hemlock]

Yes

Like that

[coarse birch]

Alright great

P(n

P(N) + -0.3n2 + 4n - 5

[worthy hemlock]

What is this suppose to mean?

[coarse birch]

wrong chat.

its the formual for my next question

[wild trench]

Ok no problem

[coarse birch]

im gonna solve it

and than see ur guys opinion

[wild trench]

You can still ask it here if you want ; it's your chat

[coarse birch]

How long will it be open for this chat?

I don't want you guys to go away ahahhh

[wild trench]

Until you're done with your problem

[coarse birch]

Alright ill be back in 5-10min

[wild trench]

Ok

[worthy hemlock]

Bot will ping you, asking if you're answer is answered or not, after some period of time

[coarse birch]

Ok.

[wild trench]

Same problem

[coarse birch]

Stuck

I solved for the function

I got (20/3, 25/3)

[wild trench]

Yes

[coarse birch]

So what would that be in word form?

3 being the amount of posters

[wild trench]

Question a?

[coarse birch]

And 20 being the profit

Yes

[safe radish]

@coarse birch Has your question been resolved?

[median cipher]

<@&286206848099549185>

[coarse birch]

<@&286206848099549185>

[winged timber]

what do you understand by far from question

[coarse birch]

Breaking even is Loss = Profit

Solving the function is (20/3, 25/3) ?

[winged timber]

yes so what is the equation that tells us profit

[coarse birch]

P(n) = -0.3n2 + 4n - 5

[winged timber]

since P(n) tells us about profit
what will be the value of P(n) if we break even

[coarse birch]

That is what I wanna figure out.

Honestly trying to figure out the whole question

at this point

[winged timber]

well if your loss = profit
then you don't gain any profit
so P(n) will be 0

[coarse birch]

? confused sorry

[winged timber]

break even is not actually loss = profit
its money exhausted = money gained

[coarse birch]

ohhhh

okay

[winged timber]

if your money exhausted < money gained
then you have profit otherwise loss

[coarse birch]

So the question is asking how much money is gained.

But how can I solve for how much money I gained?

[winged timber]

the question is asking that how many books you have to sell to gain 0 profit (break even)

[coarse birch]

ohhhhhhh.

I understand

Alright I understand what the question is asking now how can I solve for it what way?

[winged timber]

well you know that profit is calculated by P(n) = -0.3n2 + 4n - 5

you just have to substitute P(n) for 0

then solve it like simple quadratic equation and find the roots

the roots will tell you the no of books you need to sell

[coarse birch]

So I can't just solve for the function right wawy

awy

Alright.

[safe radish]

@coarse birch Has your question been resolved?

[coarse birch]

@winged timber

Don't know how to do it at all can you help step by step?

[coarse birch]

<@&286206848099549185>

is this CORRECT?

[queen parcel]

Idk what I'm looking at. Rewrite it more neatly

[coarse birch]

@queen parcel

[queen parcel]

Are you trying to solve the quadratic equation?

[dapper forum]

I got that.

[coarse birch]

Ye

This for b?

[dapper forum]

That's good.

[coarse birch]

What should I write down

for a written answer?

[dapper forum]

When I round up: -.3(4)^(2)+4(4)-5 =6.2

-.3(9)^(2)+4(9)-5 = 6.7

[safe radish]

@coarse birch Has your question been resolved?

[safe radish]

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[maiden mural]

how to integrate this with using trigonometry

[primal lark]

Use the double angle formula

[maiden mural]

what is that formula?

[primal lark]

You don't know?

[maiden mural]

well, maybe not the name ...

plz tell me what the formula is

[primal lark]

cos2x=1-sin²2x

[maiden mural]

alright, i know this formula , but not as "double angle formula"

but i am still confused

there is no cos 2x here

first we will have to simply the expression?

[primal lark]

It is the double angle formula you can write x as 2(x/2)

integral sin²(x/2)/cos²(x/2)dx is just
integral tan²(x/2)= integral sec²(x/2)-1 dx
2tan(x/2)-x+c

[safe radish]

@maiden mural Has your question been resolved?

[safe radish]

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[primal lark]

Is that the ceiling function? Or the floor function?

[buoyant shadow]

the ceiling

[chilly valve]

-0,3333333333333

[tiny igloo]

Need to solve this but dunno how. I solved it by ”my” way and got x=-0.4

But according to my teacher it was not the correct way to solve it. I should instead use:
X=n+r
0<=r<1

[glass lily]

Casework maybe?

[primal lark]

Graph them both if you have a good grasp on graphs

[tiny igloo]

Supposed to do it with algebra, hand in essay

[primal lark]

Ah i think you should consider x as I+f

I being the integer part

And f being the fractional part

[tiny igloo]

He gave me this help

[glass lily]

The round up is from real to integer?

So its not like rounded to the nearest multiple of 10?

[tiny igloo]

Please read up on ceiling functions before helping out 🙂 or it will become a chaos in here

[feral linden]

Clearly only one intersection point, when x is from (-1,0]

5x+6=4,x=-0.4

[soft fulcrum]

Yep

[tiny igloo]

Yes

I solved it that way as well,

Found range of x, and solved it from there, simple math in head

But he forces me to use the mentioned above :/

[feral linden]

Then why did you ask? To confirm your answer?

[tiny igloo]

I’m not supposed to “guess”

I’m supposed to solve it with

Method.

And algebra system

[feral linden]

At least I didn’t, I drew a diagram

[tiny igloo]

Same

Got this, not sure if it is correct tho

[soft fulcrum]

That's what I'm getting

What's the answer?

[tiny igloo]

-0.4

Dunno how to continue from there

[tiny igloo]

Hmm

U got -0.2?

[soft fulcrum]

Yea

[tiny igloo]

Let me check

[soft fulcrum]

What's the relation b/w floor and ceil functions?

[tiny igloo]

5*-0.2 + 6 = 5

-0.2 + 4 = ceiling(3.8) = 4

So thats not working

[tiny igloo]

Not sure, never done this before

[soft fulcrum]

Birre you know this? Maybe I related them wrong

[tiny igloo]

Let me send a link

https://brilliant.org/wiki/ceiling-function/

https://youtu.be/PMTY5XzcTV4

But i mean, those are not showing the full process of using x = n + r either

[soft fulcrum]

I understand the ceil function but not sure how its related to the floor function.

[tiny igloo]

https://en.m.wikipedia.org/wiki/Floor_and_ceiling_functions

I think I’m not supposed to use floor functions as he haven’t mentioned that

[soft fulcrum]

Oh ok

Let me think

[tiny igloo]

Yes, take your time

Got all day 🙂

I’ll try to figure out smth as well

<@&286206848099549185> maybe someone else has done this before and could help us 😉

[soft fulcrum]

Got it

I did the calculation wrong before

[tiny igloo]

Ooo

Looks promising

Do you mind writing it more clear step by step so i can understand the process?

[soft fulcrum]

Ceil x= floorx +1

Just used this

Then I put x=I+f

I being the integer part of the number x and f being the fractional part

fractional part must be b/w [0, 1)

So I did just that and wrote f in terms of I and made an inequality

Solved it to get two values of I

0,-1

That gives two values for f

One negative one positive

But we know f is b/w [0, 1)

So f is positive

Hence we take 1 case where f>0

As x=I+f

x=-1+0.6

0.4!

[tiny igloo]

One question

Here

Do you take 6-4-1?

Or how does the left side become +1

And what does right side say? I?

[soft fulcrum]

x=I+f

I just told you

[soft fulcrum]

Yes

Floor(x+integer) =floor(x) + integer

[tiny igloo]

Dont close it yet 🙂

[soft fulcrum]

[safe radish]

@tiny igloo Has your question been resolved?

[tiny igloo]

One more question

If X = f + i

On right side, why does it only become i and not i + f

@soft fulcrum

Here

[safe radish]

@tiny igloo Has your question been resolved?

[soft fulcrum]

Becoz floorx is just the integer part of x

[safe radish]

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[peak wraith]

how to explain (C) also part b is -7n+48 right?

[glacial fractal]

I suck at this but wouldnt it be that -7n+48=-201 where n is an integer?

[peak wraith]

eh idk

oh wait ye

nvm im stupid

.

but

like how to find interger?

or just guess

[glacial fractal]

do you know what an integer is?

[peak wraith]

whole number?

[glacial fractal]

yes

so solve for n

[peak wraith]

so like you +48

idk how to solve

acc

oof

[glacial fractal]

$-7n+48=-201$

[flat frigate]

.,..

[glacial fractal]

how do you get -7n alone

[peak wraith]

-48?

[glacial fractal]

from?

[peak wraith]

-201

[glacial fractal]

yes

[peak wraith]

after that

divide by 7?

[glacial fractal]

no

@7

-7

[peak wraith]

oh

-249 divide by _7?

-7*

[glacial fractal]

yes to get n

[peak wraith]

bt

but

it gives me

some random decimal place

[glacial fractal]

excactly

[peak wraith]

huh

oh wait thats why it is not...

rip

[glacial fractal]

yes

[peak wraith]

ooo

tks man:)

.close

[safe radish]

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[safe radish]

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[wraith coral]

since f(f^-1(x)) = x , would f(2*(f^-1(x)) = 2x ?

[nova creek]

Not in general. Consider x² and √x, which are inverses of each other (kinda). However, (2 √x)² = 4x ≠ 2x

[wraith coral]

ahh ok then how should I approach this question ?

[nova creek]

I would apply the trig identity for sin(2x)

You'll need to reason what cos(arcsin(3/5)) is, but that shouldn't be too bad

[wraith coral]

I tried using sin(2x) = 2sinxcosx

but I got stuck ;-;

[nova creek]

Stuck where?

[wraith coral]

Ahh wait I was stuck on how to find the exact value of arcsin 3/5 but I think I can figure it out

[nova creek]

You don't need the exact value of arcsin(3/5)

You only need the exact value of sin(arcsin(3/5)) and cos(arcsin(3/5))

[wraith coral]

o wait

sin(arcsin(3/5)) would just be 3/5 right

what about cos(arcsin3/5) tho

[nova creek]

Consider a right triangle

arcsin(3/5) = θ, so sin(θ) = 3/5

Using sohcahtoa, that's two sides down

Find the third and calculate cos(θ)

[wraith coral]

cos(arcsin(3/5)) = 4/5??

how does cosx=4/5 equal to cos(arcsin(3/5)) tho

[nova creek]

θ = arcsin(3/5), so cos(θ) = cos(arcsin(3/5))

[wraith coral]

o

OOO

AHHH I see now

thank you so much

I thinmk I got it this time for sure

tyty (the answer is 24/25) 😄 thank you again

.close

[safe radish]

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[safe radish]

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[dreamy marten]

Sets, introduction to combinatorics.

[dreamy marten]

Given sets A and B. Determine
A∩B
A∩B

,
A∪B
A∪B

and A \ B!

A = (-3; 6], B = [0; 8]; b) A = {a; d; k; t}, B = {d; m; t; v}

[split ether]

What are you having troubles with?

[dreamy marten]

solving it

i wasnt at school when we learnt this so im confused

[stoic dune]

Do you know what the symbols ∩ and U mean?

[dreamy marten]

nop

[analog flare]

I think