help-0

[alpine sable]

Okay so I need help I can't manage to get the right result while solving this thing

If anyone could explain it to me step by step I would be so grateful

I'm practicing for an exam tomorrow by the way

@alpine sableok let's do it

when doing fractions the most important thing is the denominator

what do you notice about the denominators

Well I don't think I need to touch them except the first one

so I did 2(x-4)

the are all composed of x

and x-4

so we multiply them out

however it is under the assumption that they are nonzero

so we add the constraint that x does not equal to 0 and 4

okay

so what do we get

[thorn sundial]

can you guys help me??

[alpine sable]

we are busy

[thorn sundial]

ok

[alpine sable]

use another channel

I'm a bit lost sorry English is not my first language

So maybe give me a visual hint pretty please

ok

Ok I see

Kind of

But why these two multiplications have these results?

@alpine sable srry for ping if you are busy

[steep briar]

You mean why (x-4)(x-2)=x²-6x+8? and why (x-4)(3x+1)=3x²-11x-4?

[alpine sable]

Yes

[wary stream]

You use the FOIL method

First, Outer, Inner, Last

[alpine sable]

Ohh I see I'm dumb sorry

I understand now what I did wrong

Tysm all of u

Low-key very anxious about the exam and this helped

[foggy crypt]

If there is a gamble game like this
10 USD for a
1/20 chance of getting
One of these three outcomes. And when you hit that 1/20 every outcome has the same chance
-500 USD
-100 USD
-5 USD
how likely I am to get back more than i spend, it is worth trying?

[thorn sundial]

do you guys know this?

[tight locust]

W = Fdcos(theta)

[modern crystal]

is anyone available ?

[tight locust]

sure

[next hatch]

im confused as to how im supposed to do this

the condition's making me think that it's integration by parts but i tried that and got 0

idk if i did it wrong or something but

its confusing the fuck out of me

[prime mural]

idk man im in geometry

[modern crystal]

i’m super confused, i keep getting undefined but it’s not an option

am i doing it wrong ?

[tight locust]

note that 196 is a perfect square

[modern crystal]

mhm mhm

still confused 😩

[tight locust]

so the denominator can be factored as a difference of squares

[wary stream]

Factor

[gray isle]

consider (sqrt(x))^2 = x

[modern crystal]

i’m still getting undefined

[wary stream]

How would you factor x - 196?

[next hatch]

bruh my question

[west solstice]

can you even factor this?

[wary stream]

Yes

Using what ramonov stated

[modern crystal]

what are y’all getting ?

so i can work backwards cause

[wary stream]

Use difference of squares to factor x - 196

[sick frigate]

How to get good at math

[wary stream]

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

[tight locust]

a^2

not a^a

[ocean seal]

dldh06

[wary stream]

Good catch, thanks

What?

[tight locust]

no

[wary stream]

No

[tight locust]

let u^2 = x

[wary stream]

Also, stop trying to give answers

[tight locust]

then as x-> 196, u^2->196 meaning u->14

[west solstice]

rationalizing is considered factoring?

[solid blade]

@next hatch take the given equation as a function of alpha (say) and use Feynmans trick to differentiate under the integral sign but you have to differentiate it twice

[wary stream]

No, that's two difference concepts

You don't have to rationalize

x - 196 is factorable using difference of squares

[west solstice]

seems like thats what id do with this problem, then cancel out a part of the denominator

[next hatch]

the what

[wary stream]

No need, just factor

[next hatch]

its okay ill ask it another time theres already a question being asked rn

[solid blade]

Kk no worries you can dm for the solution if u want

[west solstice]

ok i see it now, yes factor the denominator, dont bother rationalizing

[gray isle]

if you're uncomfortable with factoring x - 196
you could always consider the conjugate of the numerator,
the principle of the difference of two squares will still be applied

[wary stream]

Why are you trying to give out answers?

You don't do that

[solid blade]

Sorry I'm new here

I didn't know that

[west solstice]

@modern crystal still with us?

[wary stream]

Read #rules and #❓how-to-get-help

[solid blade]

Yea I'm sorry

[modern crystal]

hows this looking

[rigid smelt]

Seems good

[modern crystal]

nice

having some troubles with this one too

might be right though

[rigid smelt]

Its wrong

Check A and C again

[modern crystal]

are they both 15?

[solid blade]

Check c

[modern crystal]

A and C ?

[solid blade]

If you figure the mistake in c all others are evident too

[modern crystal]

i’m guessing it’s that

but then again

wouldnt it be neither > or < if it’s just 0

[jovial knoll]

I heard math is applied philosophy. What philosophy book should I get started with to improve my math.

[buoyant kayak]

,rotate

[gray isle]

what have you tried?

[jovial knoll]

me?

[gray isle]

@jovial knoll try #book-recommendations

[cyan owl]

me? not much just stuff like 6= equation and replacing x with -3

[gray isle]

what did you do after that?

you'll have a linear equation that should be relatively simple to solve

[cyan owl]

oh ok wait nvm ty!!

[gray isle]

also -6 not 6

[warped phoenix]

I’m a little confused

When I substitute x for -8 in x^2, am I supposed to be putting -8 in parenthesis or not?

[kindred warren]

yes

[warped phoenix]

Oh ok, is that just a rule I should know?

[kindred warren]

because you are squaring 'x' and since 'x' is '-8' then you have to include the '-'

[placid zinc]

f(x) = x²
Is saying "take the input and square it"
f(-8) has an input of -8
So you square the entire input, not just the 8

[warped phoenix]

Ohhhh

Thank you both of you 🙏

Can someone double check my answer?? We are supposed to write our coordinates as an ordered pair

I got (-8, 88) for this one

[kindred warren]

yse thats correct

[warped phoenix]

Awesome

[kindred warren]

f(-8) = 88

[warped phoenix]

Ty!!!

[hushed marlin]

hello, I need help in the function decomposition of tan^2(3x) ?

[summer goblet]

You can use Moivre's formula.

Of complex numbers

By decomposition you mean find tan(x)?

[hushed marlin]

find f(x) and g(x)

[summer goblet]

What do you mean by decomposition?

Oh...

[hushed marlin]

Like split it into 2 functions, ya

[summer goblet]

Split into two...

[hushed marlin]

would it not be f(x) = x^2 and g(x) tan(3x) ?

[summer goblet]

You mean writing tan^2(3x) = f(x) + g(x)?

[hushed marlin]

ya kind of like that.

[summer goblet]

Moivre's formula.

[hushed marlin]

Not that.

[summer goblet]

Yes you can. Look.

It is hard to see at first.

[hushed marlin]

It's not the formula I need.

I just need to decompose the function tan^2(3x) into 2 separate functions if you understand me.

[summer goblet]

tan^2(3x) = sin^2(3x)/cos^2(3x)

[alpine sable]

sec^2(3x)-1

[hushed marlin]

nevermind.

I got it thanks.

[summer goblet]

Look

Moivre formula

[summer goblet]

With Moivre's formula

[hushed marlin]

ok

[summer goblet]

This formula

Ignore r

n will be equal to 2

What you have is sin^2(3x)/cos^2(3x)

You must develop the question for sin and for cos

[summer goblet]

So you you substitute this in moivre's formula.

You develop the real part and the imaginary part.

In the end you'll probabily find a value for sin^2(2x) and

[rigid smelt]

You do know Evan, was talking about function composition right? And it has nothing to do with de moirve's theorem

[summer goblet]

cos^2(3x)

Yes

It is function decomposition

Using complex numbers.

It is another perspective.

[summer goblet]

It terms of other components.

[rigid smelt]

I really really cant see how you wil bring de moirve's theorem into function composition

Or you just have no clue what composition of functions is

[summer goblet]

See there

If you solve the equation

[rigid smelt]

sigh

[summer goblet]

You'll have clearlly a decomposition for sin and cos.

Isolating Im and Re.

It can be used to decompose even sin(2453x) if you want.

[fiery walrus]

<@&286206848099549185>

https://media.discordapp.net/attachments/754860723321962628/881743935674921051/image0.jpg?width=1414&height=1061

can you help me solve the star wars one

[sinful geyser]

how is this written in interval notation ? <@&286206848099549185>

[rigid smelt]

Thats a graph of a function, you represent it with an equation

Or unless theres more context to this problem that you are deliberately opting to not show

Also ping helpers after a minimum of 15min

[next hatch]

i think they're trying to say how to describe the domain and range

[rigid smelt]

Look at the graph, the limit wont exist when there is a jump or an oscillation

Point out the spot where f(x) might have a jump

[sinful geyser]

(-inf,-1](-1,2](2,+inf) @rigid smelt was thinking something like this idk if this is the form theyre asking for

[rigid smelt]

Thats like saying a is in (-infty, infty) but you are try to look cool

[rigid smelt]

Try to answer this first

[sinful geyser]

im new to this haha i see it but am not sure how to put down in interval notation

[rigid smelt]

I know, but can you answer this?

[sinful geyser]

the jump seems to be from 2 to 1 when x is 2

[rigid smelt]

Yes, the jump is at x=2

Meaning a can not be 2

So there are many ways you can notate that

You can either write (-infty, 2)U(2, infty)

Or (-infty, infty){2}

[undone patio]

is this room in use?

or can i ask a question

[rigid smelt]

What do you think? Is it in use?

[undone patio]

well i think your done explaining but idk

[rigid smelt]

Are two people talking to each other seems like its not in use?

[undone patio]

i thought u were done lmao

[sinful geyser]

i got it thank you lots @rigid smelt

[rigid smelt]

Its free now

[undone patio]

ok so

i was wondering how i would go about doing this problem

[tight locust]

a1 = 1/k, a2 = 1/k^2
a_n = (1/k)^n

(1/k^m - 1/k^(m+1)) = (k-1)/(k^(m+1))

= ((k-1)/(k^(2)))^2 + ((k-1)/(k^(3)))^2 + ...

[undone patio]

ah ok i think i have an idea abt what i can do

thankss

[tight locust]

= (k-1)^2 * sum from m=1 to m=n of (1/k)^m

[proud swift]

??

[next hatch]

you don't square the square root

[tight locust]

the square root of a number squared is equal to the absolute value

[gray isle]

(a^m)^n = a^(mn) applies for a>0

and isn't necessarily true for other values of a

generally sqrt(x^2) = |x|
while (sqrt(x))^2 = x

[proud swift]

Oooo

[ripe mountain]

how do you do #16

iirc when u find the inverse function of something you swap the variables so it would look like x=y^5 + y^3 + y and then you solve for y, but u can't solve that, can you?

is there another way you're supposed to do it

oh wait do you do this with derivatives

[gray isle]

f^-1(3) is the value of x where f(x) = 3

and there is a trivial solution to
3 = x^5 + x^3 + x

[ripe mountain]

x=1 right

[gray isle]

yes

[ripe mountain]

ahh i see

you can't do that for the second part of it though can you?

[gray isle]

well for the second part, you can just apply the definition of the inverse

[ripe mountain]

what's that?

[gray isle]

exactly as what was just applied

[ripe mountain]

2= x^5 + x^3 + x?

[gray isle]

f^-1(3) is the value of x where f(x) = 3

similarly f^-1(2) is the value of x where f(x) = 2

[ripe mountain]

so would it just be f(2) then

[gray isle]

no

=f ( f of this gives 2)
= ?

[ripe mountain]

f(x^5+x^3+x)?

[gray isle]

no

don't overthink this

similarly f^-1(2) is the value of x where f(x) = 2
do you understand that?

(don't try and do any unnecessary solving)

[ripe mountain]

ehh

[ripe mountain]

i gues it makes sense its just foreign to me lol

[gray isle]

its pretty much applying the definition of an inverse function

[ashen dove]

can anyone help me with this :))

[gray isle]

$f( \underbrace{f^{-1}(2)}_{\text{$f$ of this value gives you 2}})$

[vale wigeon]

@ashen dove channel busy please move

[ocean seal]

ℝamonov

[ashen dove]

ah ok sorry

[ripe mountain]

oh okay

[vale wigeon]

f^-1(2) is the number that, when passed as input to f, gives 2

[ripe mountain]

i don't really see how that helps me other than 2=x^5+x^3+x

i guess i'm really overthinking it

idk

[gray isle]

you're overthinking it

[ripe mountain]

f(2)

[gray isle]

no

f^-1(2) is the number that, when passed as input to f, gives 2

f(f^-1(2)) is the expression that represents f^-1(2) being passed into f

[ripe mountain]

yeah

[vale wigeon]

what happens if you take the number that gives an output of 2 when plugged into f... and plug it into f?

[ripe mountain]

it gives an output of 2

[gray isle]

exactly

[ripe mountain]

LOL

[vale wigeon]

there we go

[ripe mountain]

okay i think i see

[rich basin]

Why is it inversely proportional when the d is increqased by 50 percent, the v is also increased by 1.5?

[olive forum]

correct one?

[pastel schooner]

What exactly is a limit? Is it the same value as f(x)?

For example as x goes to c the limit is 2.

Would f(x) = L as x goes to c?

This channel is occupied.

[ionic jewel]

you didn't pick one

[ionic jewel]

no it's as the function approaches that point

the value at that point is irrelevent

[pastel schooner]

So aproaching at a y point right?

So if limit is 2, then it is aproaching 2 but not on 2

with 2 being on the y-axis

[ionic jewel]

wait what

$\lim_{x\to2} f(x)$ is what f(x) approaches as x approaches 2

[ionic jewel]

not sure where your y-axis came from

[pastel schooner]

I mean that in terms of f(x) = y

[tight locust]

f(x) = y(x)

[pastel schooner]

For me its like learning a language and translating it in my old native language

if that makes sense lol

[tight locust]

y is something we call a dependent variable

[pastel schooner]

while y(x) is dependent on x

right?

[tight locust]

yes

[pastel schooner]

cooleo

[pastel schooner]

wait so if L = 2, then its actually talking in terms of as lim f(x) is approaching as x aproaches 2?

I thought it was as y aproaches 2

[tight locust]

x is the independent variable.

[ionic jewel]

you see how the thing under the limit is written as "x to 2"

[tight locust]

you use the value of x to determine what y does

not the other way around

[ionic jewel]

there are other things you can put under there, but in my example (and how you first learn limits) it's x approaching the number, not y

[tight locust]

lmao

[pastel schooner]

is this correct for the equation of the graph?

not up to scale lol

so L = 2

cause as x aproaches 1, f(x) aproaches 2

[tight locust]

remember that limits must go from both sides

[ionic jewel]

and also you wrote (x), not f(x)

[pastel schooner]

so this would satisfy that

oh whoops yea

[tight locust]

also what bunny said

[pastel schooner]

So would this new graph satisfy that for each side x - > 1 lim f(x) = 2?

[tight locust]

yep

[ionic jewel]

assuming f(x) is something like 2x, then yes

[tight locust]

good job

[pastel schooner]

Should that usually be stated with these graphs?

like f(x) = 2x

[ionic jewel]

it's probably good form, yes

[pastel schooner]

I see. Thank you guys.

So simple definition is "limit (or variable L) is the value of f(x) as x aproaches c" right?

for x -> c

[ionic jewel]

yes

[pastel schooner]

Fantastic.

[tight locust]

ask something more interesting now

[pastel schooner]

That solves my questions. I will soon lol.

[alpine sable]

hi! ive never learned this before so im not sure where to go about this, may i get help with how to solve this equation, please?

[jagged imp]

write both sides as powers of 6, so you have something like 6^a=6^b. Then, a=b (either by taking log base 6 of both sides or just assuming that it must be true. If you don't know what a log is, you're just going to have to take my word that if 6^a=6^b, then a=b)

[alpine sable]

Is Quadratic equations a part of which subset of algebra?

[tight locust]

how can the absolute value be negative

wtf

[tight locust]

pre

[alpine sable]

thank you sm! ill see if i can figure it out from there!

[alpine sable]

good question, ive been wondering the same thing

[tight locust]

it can't

so you rule out those options

[alpine sable]

i figured ye, i just cant remember the whole same base situation but ill try to figure it out

[tight locust]

(1/36) = 6^(z)

what is z

[jagged imp]

can you be more specific with what you mean here?

[alpine sable]

WAIT

DO YOU BRING THE DENOMINATOR UP N THEN LIKE UM

whats the word

why cant i think of it

square root to get base 6?

n then square 5x+2 in the exponent

[tight locust]

1/x = x^(-1)

[alpine sable]

okayokay, thats what i thought

was the square root part correct? or is there a different method

[heavy acorn]

Find Total Surface Area and the value of y.

please help

<@&286206848099549185>

[next hatch]

bruh wait 15 minutes before pinging

also someone else is answering a question

[tight locust]

(1/36^(5x+2)) = (1/36)^(5x+2) = (1/6^2)^(5x+2) = (6^(-2))^(5x+2) = 6^(-10x - 4)

[alpine sable]

Hi i am a 15 year old wanting to learn linear algebra. I do have basic understanding of high school algebra. Do ineed to learn more or is it enough

[heavy acorn]

I am in bit hurry so

[next hatch]

ask it in another channel, and wait

you're not an exception to the rules

[alpine sable]

Like there is linear algebra abstrat algebra etc.

[jagged imp]

elementary algebra

typically its just called algebra

abstract and linear are very different

[tight locust]

you have not even indicated what tsa is

lmao

[alpine sable]

Ok

[heavy acorn]

Total Surface Area

[alpine sable]

okayokay so i understood how to get base 6, but how come only the 2 became a negative when you move it to the numerator and not the 5x+3 too?

[olive forum]

Guys can anyone math the following with the correct answer. im too week for this..

[woeful briar]

btw guys

umm

x < 5y and 5y > x is the same right?

just making sure

[jagged imp]

yes :)

[heavy acorn]

help

[woeful briar]

ok thanks

[low topaz]

Is a parabolas height infinite

[tough hatch]

you can ask on a different (unoccupied) questions channel so as not to get interrupted and not to interrupt others

[tough hatch]

that question is ambigious

[low topaz]

Ok

If i graphed x^2, Would there be a point were the Parabola Stops going up on the y axis

[tough hatch]

yes

but that does not happen for all parabolas

the vertex of y = x^2 + 1 is not on the y-axis

[tough hatch]

i assume you are referring to the vertex of the parabola here

[pallid folio]

can someone help me with these questions?

(anyone of these)

[violet jetty]

Log laws

[steady jewel]

😩

[prisma glade]

Indices laws.

[violet jetty]

Ie in a you can take the log of both sides and bring down the x-1

[pallid folio]

ok thanks.

[violet jetty]

You find both roots and look at which one is positive @soft belfry

Did you get the roots?

Have you learned the quadratic formula?

[prisma glade]

For e) , you need to square both the sides so the base is same & then further substitute the value of x.

[pallid folio]

okey

thanks!!

[violet jetty]

You still need to know the quadratic formula to use the calculator

Like to solve for t

You use this formula

Oh

You use the third formula

You put a as the number that is before x^2

In this case 1

[soft belfry]

Because it’s t^2

[violet jetty]

So

Isnt t^2 = 1t^2

[sly mantle]

@soft belfry physics in #old-network

[soft belfry]

Ty

[pallid folio]

find the amount compounded annually on rs 9000 for two years if the rates of interest for two years are 8% and 10% respectively.

please help me once again guys

[alpine sable]

how do i do iv?

i did; 1 x 0 + 1 x3

it wasnt right

<@&286206848099549185>

[vale wigeon]

you tried to answer with a single number?

[alpine sable]

?

[vale wigeon]

you know the answer will be a 1×2 matrix, right?

not a single number as you tried to present just now with your 1*0 + 1*3

[alpine sable]

yes

so what do i do with these matrixes?

[vale wigeon]

you multiply them.

[alpine sable]

1 x 3

ok

[vale wigeon]

your book has no doubt explained how to multiply matrices.

if you must know, 1 * 0 + (-1) * 3 would have been the first entry in AD.

[alpine sable]

ok thanks

[warped jay]

x^(2)+5=0 identify the value of a b and c

help <@&286206848099549185>

[lone heart]

From

#❓how-to-get-help

Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[shell widget]

@warped jay I think u might be study quadratic equations(quadratic equations are of the form ax^2 + bx + c)

Compare ax^2 + bx + c to x^2 + 5, you'll easily find the values of a,b,c

[urban lily]

Can Someone explain how it got simplified from the first to the second and from the second to the last?

[frigid aspen]

The value of t =23????

Pls tell me i m waiting 😇😇😇

[fallow jasper]

👍

[frigid aspen]

😇😇

[shell widget]

@urban lily Multiply divide (y'/x) by xy^2, multiply divide (-y/x^2) by y^2, multiply divide (1/y) by x^2y, and multiply divide (-xy'/y^2) by x^2

This way, all terms have the same denominator, you can add them under one denominator, and then it's simple factorization

For the second to third step, the denominator cannot be 0, hence (y^2 - x^2)(xy' - y) must be 0, so either (y^2 - x^2) = 0 that implies y=+-sqrt(x) or xy' - y = 0 which implies y' = y/x

[vernal remnant]

Given the measure of an acute angle in a right triangle, we can tell the ratios of the lengths of the triangle's sides relative to that acute angle.
Here are the approximate ratios for angle measures 55\degree55°55, degree, 65\degree65°65, degree, and 75\degree75°75, degree.
Angle 55\degree55°55, degree 65\degree65°65, degree 75\degree75°75, degree
\dfrac{\text{adjacent leg length}}{\text{hypotenuse length}}
hypotenuse length
adjacent leg length
​
start fraction, start text, a, d, j, a, c, e, n, t, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, h, y, p, o, t, e, n, u, s, e, space, l, e, n, g, t, h, end text, end fraction 0.570.570, point, 57 0.420.420, point, 42 0.260.260, point, 26
\dfrac{\text{opposite leg length}}{\text{hypotenuse length}}
hypotenuse length
opposite leg length
​
start fraction, start text, o, p, p, o, s, i, t, e, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, h, y, p, o, t, e, n, u, s, e, space, l, e, n, g, t, h, end text, end fraction 0.820.820, point, 82 0.910.910, point, 91 0.970.970, point, 97
\dfrac{\text{opposite leg length}}{\text{adjacent leg length}}
adjacent leg length
opposite leg length
​
start fraction, start text, o, p, p, o, s, i, t, e, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, a, d, j, a, c, e, n, t, space, l, e, g, space, l, e, n, g, t, h, end text, end fraction 1.431.431, point, 43 2.142.142, point, 14 3.733.733, point, 73
Use the table to approximate ABABA, B in the triangle below.

[alpine sable]

<@&286206848099549185>

[shell widget]

@alpine sable Yes your answer is correct

[alpine sable]

ok thank you

[elder widget]

Hi, if lim x-> infinite of f(x) = 0

Can we say that lim x-> infinity of f'(x) = 0?

And what about if lim = constant?

[urban lily]

Righttt! didn't come across my mind, Now that's easy thank you so much :)) @shell widget

[urban lily]

correct answer

[shell widget]

@elder widget https://www.researchgate.net/post/If_a_functions_limit_is_zero_at_infinity_does_that_imply_its_derivative_has_same_limit_at_infinity

It seems that there are counter examples for the first one

For the second, no. Take y = e^x - 1. Then lim as x approaches 0 of f(x) is 0, but lim as x approaches 0 of f'(x) = e^x is 1

@soft belfry $\sqrt{9x^{\frac{2}{3}}} = (9x^{\frac{2}{3}})^{\frac{1}{2}} = (9^{\frac{1}{2}}) (x^{\frac{2}{3}})^{\frac{1}{2}} = 3 (x^{\frac{2}{3} \cdot \frac{1}{2}}) = 3 x^{\frac{1}{3}}$

[ocean seal]

Sup?

[shell widget]

remember ur power rules, (ab)^c = (a^c)(b^c) and (a^b)^c = a^(bc)

[elder widget]

ty

[rich basin]

why is it calculating the power for which it will decelerate to 85 to 65

and not when it will go from 85 to 75 km

So what i did was to calcualte the accelerating force to find the time for which it will go from 85 to 75 km per hour from the v =u + at

[alpine sable]

can anyone answer these before 6pm

i really need it fast

and also need the steps

pls

[alpine ledge]

Hi

Hello

Can anyone help in this

[alpine sable]

help on question 11

sorry my bad

ill move on

[shell widget]

@alpine ledge Which one?

[alpine ledge]

3rd and 4th

[shell widget]

@alpine sable Just do what it says, multiply and then equate

@alpine ledge I'll just show how one is done, the rest you can do yourself. (1/2)^n = 1^n / 2^n = 1 / 2^n = 2^-n

So you have 2^(-n) = 8

Recall that 8 = 2^3, so you have 2^(-n) = 2^(3).

Since bases are same, powers must be the same as well, and we get -n = 3, or n = -3

[alpine ledge]

Thanks bro

[shell widget]

$\int_{10}^{s} \dd{s} = \int_{10}^{s} 1 \dd{s} = s |_{10}^{s} = s - 10$

[ocean seal]

Sup?

[shell widget]

$\int_{4}^{t} 5 \dd{t} = 5t |_{4}^{t} = 5(t) - 5(4) = 5t - 20$

[ocean seal]

Sup?

[shell widget]

And so, you have s - 10 = 5t - 20

Which is just s = 5t - 10

@soft belfry

[soft belfry]

Ty

[dense panther]

when do use the open and closed circles when graphing functions?? plsss send help

[wary stream]

Open circle does not include that value while closed includes it

[dense panther]

yess i get that but like don't you use it on just inequalities or nah?

or is like for all functions?

[alpine sable]

theyre used for inequalities, yes!

[glass lichen]

You use hollow and filled circles to represent exclusion and inclusion respectively

[slim elbow]

What is the multiplicative inverse of -1 1/8?

[wary stream]

Is that a mixed fraction $-1 \frac{1}{8}$ or $\frac{-11}{8}$?

[ocean seal]

dldh06

[slim elbow]

It’s a mixed fraction

[quiet glade]

how do you know whats on top when you're doing systems of linear equations?

[slim elbow]

It’s a mixed fraction

[quiet glade]

like for c

when doing elimination, how do i know what goes on top

[gray isle]

first combine your mixed fraction into a single fraction

wdym what's on top?

[quiet glade]

when i’m subtracting the stuff

[gray isle]

it doesn't matter

[quiet glade]

really? because it’s fucking me up

this gets me 7y-7z=2

[gray isle]

as long as you're adding and subtraction properly, eliminating variables then it doesn't really make a difference

[quiet glade]

but it’s inverse gets me -7y+5y=-22

[gray isle]

how are you getting -7z

and how are you getting 2

[quiet glade]

deadbrain

i have brain lag

[wary stream]

Channel busy

[glossy current]

lmao noob @pine zealot

[quiet glade]

i’m good

[pine zealot]

what

smh

[finite scroll]

ok

need help with finding the internal angles on this trapezium

nvm

figured it ot

[neat merlin]

How to draw this in geogebra?

[clever plaza]

Hey so is the parallel chord method guaranteed to converge no matter the initial value?

[alpine sable]

am i tripping or the answer sheet is wrong

MADE PAINT ONE EASIER TO SEE

<@&286206848099549185>

<@&286206848099549185> is it row SPEAKS to coloumn?

i guess it is

oof

[bronze pelican]

Very nice

[alpine sable]

yes

[quiet glade]

for c again as an example, does it matter which equations replaces which?

like when i have the substituted value, does it matter where i put it?

[wary stream]

Nope, doesn't matter because at the end, you'll still end up with the same x, y, z values

[sage dune]

does anyone know how to solve this?

[iron loom]

am i right?

question is no 5 c

also i need help with 5 a and b

is 5 a and b the same as y-y1=m (x-x1)

[warped phoenix]

when do i distribute in a function?

if it says "apply a vertical stretch by a factor of 3 followed by a translation 3 units downwards to the parent function of f(x) = x", there is no distribution right?

so g(x) = 3x - 3

but if it told me to do the translation first and then the stretch, it'd be g(x) = 3x - 9?

[small bear]

Correct, what exactly is the question?

[warped phoenix]

Not exactly any question, it was just a concept I wanted to make sure I understood

Wait

What about this

Let’s say I have this equation

@small bear 4(2x – 3) + 2

Im told to apply a vertical shift downwards by 3 units and then a horizontal shift to the right by 1 unit

My new equation would just be 4(2x-4) - 1 right?

[shell widget]

integrate 12 - 3t^2, you get 12t - 3t^3 / 3 = 12t - t^3. Plug in the limits, you get (12t - t^3) - (12 - 1) = 12t - t^3 - 11

[light sleet]

how do i do the same thing for 6 = °75 when it comes to <1

[rigid island]

look at the properties of parallel lines with a transversal passing thru

there are certain rules ig

[alpine sable]

i forgot the term, but i think its supplementary angles. a supplementary angle is 180° so if you take 180-75, you would get 105. with that 105, you would use alternate angles to explain angle 1

not alterate

um whats the term called

[light sleet]

ah i see

[alpine sable]

I'm trying to find the radius between Q1 and point P and my triangle (first image) is wrong. My professor says it's "in the wrong plane" and should look like the second image but I'm not sure what he means by it being in the wrong plane.

[ancient saddle]

Hello, I think he wants you to find the angle Q1 at the triangle ∆Q1 P Q5

[livid storm]

Hola! quería preguntarles cómo hallarían una formula general para la relación entre el área de dos polígonos irregulares? Es decir, una fórmula que con sólo los datos del primer polígono, pueda calcular el área del proporcional...

[alpine sable]

hey I'm a bit confused on this considering ik where the speed goes but the other three confuse me I'm only in ninth grade and I'm a bit bad at math if anyone could just explain what each thing means it would mean the world

[orchid kayak]

Eyo is this channel free?

Bcuz if yes, I got a hw problem to do

that I didn't understand

someone help?

<@&286206848099549185>

This is the problem I got to do

[dense citrus]

what did you do so far. And don't tag so fast please

[orchid kayak]

Nothing yet, bcuz I didn't understand anything
Also sorry for tagging fast

[jagged ermine]

The question is volountarily tricky, it is just using synonims to confuse you.
volume is really length * length * length, which is m to the third power, also called cumic meters. The fact that it is using centimeter doesn't really matter from the point of view of measuring unit, it only changes the "amplitude" of a measure.
area is length * length, so meters to the power of two, also called square.
Speed is length / time, so meter per second.
Perimeter is a sum of lengths. When you sum measurements you are not changing the measurement unit, but just the value, so the unit remains meter.
length, distance, width, as I implied, are all the same.

[dense citrus]

how about you get rid of both fractions first?

[orchid kayak]

How do I do it?

[dense citrus]

how would you do it if you had only one?

[alpine sable]

OMG I UNDERSTAND NOW TYYY

[dense citrus]

$\frac{3}{x+1} = -1$

[orchid kayak]

I would multiply by x+1

[dense citrus]

how would you solve this?

[ocean seal]

lyinch

[dense citrus]

exactly

[alpine sable]

im gonna ace this math test >:D

[dense citrus]

do this, but this time for both fractions

[orchid kayak]

Mk

[dense citrus]

and then see what you get

[orchid kayak]

I multiply with x+1 or 1-x

[dense citrus]

both

because otherwise you can't get rid of both fractions

first with one, then with the other

[orchid kayak]

o alright

[alpine sable]

hey anyone know raitos that can help me

I need to know from the beginning

I would really appreciate it

[dense citrus]

don't expect a solution after multiplying. There's a little bit more work to do. But did you understand why we multiply with both?

[orchid kayak]

Yep

to delete the fractions

[dense citrus]

I hope that the next step now looks familiar to you

[orchid kayak]

It will be 3 + 4 = -3( x+1 )( 1-x )

is that correct?

@dense citrus Sorry for ping

[dense citrus]

no worries. let me check

[alpine sable]

Expand the brackets if it is ig

[dense citrus]

I have 7+x on the lhs

[orchid kayak]

lhs?

[dense citrus]

3(1-x)+4(x+1)

left hand side

[orchid kayak]

o

but what will happen to the other ''3''?

[dense citrus]

3(1-x)+4(x+1) = -3(x+1)(1-x)

[orchid kayak]

o

[dense citrus]

I only showed one side 🙂

[orchid kayak]

alright, so then it will be 3 + 4 = -3(x+1)(1-x)?

[dense citrus]

mmh you're still missing one x on the left

[orchid kayak]

wait where?

[dense citrus]

left side

[orchid kayak]

x + 3 + 4 = -3(x+1)(1-x)?

o wait

I think I got it

[dense citrus]

3(1-x)+4(x+1) = 3-3x+4x+4 = 7+x

that's your left side

so then you have 7+x = -3(x+1)(1-x)

and that's a normal equation. I guess you know how to solve it?

[orchid kayak]

lemme see

3x² - x - 10 = 0?

If yes, I think I can do the rest

[dense citrus]

I got something different

but you know what to do. Expand, bring it to the typical 2nd degree form and solve

note that you have a typical identity on the right

(a-b)(a+b)

[orchid kayak]

yeap

[dense citrus]

afterwards you can use wolframalpha to check the solution yourself

[fiery bronze]

I don't understand what the question is asking me to do here..

am i allowed to choose what to put in front of n^2?

@dense citrus I don't understand what you mean by that reaction lol

[dense citrus]

that I don't understand the question myself lol

[fiery bronze]

ohhh lol

nervermind then

[dense citrus]

it's strange haha

[fiery bronze]

it is ahah

i'll just put a 1 in front of n^2

[dense citrus]

yes, try that. Simplifies your life

[fiery bronze]

and square the original sequence

[dense citrus]

do you see the solution straight away? I'm curious what they actually want you to do

[fiery bronze]

it doesn't allow me to put more than two digits in the blank spaces

[dense citrus]

lol

[hushed pasture]

show the hole question

[glass lichen]

Then not really, cause you'd get $cx^TX^T$ just changing the scalar name

[ocean seal]

Mosh

[glass lichen]

unless you know X is say skew sym or sym, then X^T is just X^T

[thorny hound]

Doing sat practice and I forgot how to do this kind of problem and I just need some guidance on what to do

[topaz scaffold]

Find the slope of f(x)

Find the slope of a line perpendicular to that

Use point slope to find g(x)

Plug in -1

[remote heron]

its a really fundamental concept

starts with an e

well

idk if the name for c starts with an e

but the concept does

sounds german

i guess we dont have to play hot/cold

i think so

the idea of constant scaling is not uhh

not the key thing

[west bronze]

b is an eigenvector of A and c is an eigenvalue of A

[remote heron]

but its a big feature

just watch 3b1b linalg on 150% speed

youll be fine

itll come back

well mostly

i did the same thing 😄

ah lol

so were in the same boat almost

so just enough to scrape by

a true ml student

[glass lichen]

C) Yes, though I'd personally say non-invertible

cause Ax=0 has only a non-trivial solution iff A is invertible

[crisp comet]

Isometry I would guess

[remote heron]

o geez

i remember e

what the heck is it

thats something you see during diagonalization right

[crisp comet]

Pos def

I think

[glass lichen]

Yeah, I'd say Positive Definite

[remote heron]

err, decomposition

damn maybe i need to review too

[west bronze]

(a) symmetric
(b) eigenvector and eigenvalue
(c) non-invertible?
(d) orthogonal
(e) positive-definite

[misty moat]

any1 help?

[crisp comet]

None its inconsistent also should probably be on normal maths server

Nvm lmao

[remote heron]

are you in linear algebra?

or just normal algebra

you could get through this visually

[alpine sable]

@livid sail are you mongolian by any change?

chance*

[remote heron]

a good question is whats the most places a line can cross?

and can you find a place where these lines cross?

try setting them equal

[alpine sable]

yea idk the anglo spelling

[misty moat]

its fine i got it right anyways lmao

but what about this

isnt it infinite?

both the slope and y-intercept are equal so isnt that infinite @remote heron

[topaz scaffold]

The y-intercept isn't equal tho

[atomic blaze]

How would i simplify by combining like terms: x(x-y)+y(y-x)

[glass lichen]

what have you tried?

[atomic blaze]

i tried distributing and got 2x^2 -xy + y^2 - yx

[glass lichen]

where did 2x^2 come from?

[atomic blaze]

is it suppose to be x^2

?

[glass lichen]

yes...

[atomic blaze]

ahhh okok

[glass lichen]

How you did it both wrong for the xx and correct for the yy

No clue

However

yes $$=x^2-2xy+y^2$$

[ocean seal]

Mosh

[glass lichen]

which has a well known factorization

[atomic blaze]

so u just added the xy?

[glass lichen]

yes... -xy-xy=-2xy

[atomic blaze]

alr bet thanks

[alpine sable]

https://cdn.discordapp.com/attachments/269573202018041856/881991036082196510/image0.png

who can help me

how many bonus points do I get with 50%?

like 10,16,50,4 maybe

eii

@alpine sable here

yh i see it

ok

c:

what do u think

idk i am confused

chill

<@&286206848099549185>

help, plys

[next idol]

11/2 (D)

[alpine sable]

realy?

[next idol]

multiply second fraction by 4

your second fraction will become 12x-8

in result you'll have (8x-1-12x+8)/20 = -3/4

[alpine sable]

wow, thanks really

[next idol]

then you multiply -4x+7 by 4 and 20 by -3

[alpine sable]

could you help me with 2 more I'm bad at some

[next idol]

and solve the linear equation you've got

you should get 11/2

(actually i've just wrote your problem in mathway then came up with the solution but we'll drop that part)

[next idol]

i am bad as well but i could try to help you

[alpine sable]

thanks

I'll try to translate for you, because I'm from Brazil

[next idol]

por favor (no offense)

[bleak nacelle]

cool,i am brazilian too

[next idol]

but my wild guess is you need to find this figure's diagonales?

(i am russian and am not familliar with math terminology in english)

(so idk how is this figure called in english)

[alpine sable]

watch the diamond

Find the values ​​of angles x and y

[next idol]

oh angles actually?

[alpine sable]

massa

[next idol]

well Y is 25 and X is 55 i believe

wait no

i screwed up because things don't sum up

wtf is wrong with me, i mean, Y is absolutely 25 and

khm

X 65 and Y 25

[alpine sable]

thanks

I have 2 more

do you know a game called brain out?

[next idol]

Sorry, but no.

[next idol]

oh that one is easy

although i'll bring up libremath this time

[alpine sable]

Calculate x and y values ​​without parallelogram EFGH

gave a translated

ST is still there?

[next idol]

weird

i messed up somewhere

[alpine sable]

like this?

[next idol]

i constantly come to x = 55 y = 40 and idk why

my equation looks like this

x+2x = 3x
20-5 = 15
180 - 15 = 165
3x = 165, x = 55

y+2y = 3y
65-5 = 60
180 - 60 = 120
3y = 120, y = 40

either i don't know how to solve such problems or i suck at geometry

that's why i never visit these channels to help

well there is an other way

[alpine sable]

you tried at least

[next idol]

let me try something else

[alpine sable]

ok

[next idol]

nevermind i still got to the same conclusion

[alpine sable]

I think it contains obtuse angles there

[next idol]

i assumed that <E + <H = 180 and <F + <G = 180 (instead of my <H+<F = 180 and <E + <G = 180 thought)

[alpine sable]

these are the possible answers

esperi

wait i sent the wrong answers

[quaint trout]

@alpine sable opposite angles in a parallelogram are equal

Use that to set up your equations

[alpine sable]

okey

[dull musk]

so, this is my first time here

am i supposed to ask things here?

[next idol]

but that would mean that sum of opposite angles is 180 degrees?

i tried to solve the task based on that fact

and did not succeed

[quaint trout]

No

[next idol]

Wait it's not 180?

just equal?

[quaint trout]

5 = 5 but 5 + 5 ≠ 180

Why does being equal mean the sum is 180?

Totally different things

Yes, the sum if not 180, they're just equal (the opposite angles)

[next idol]

C (X 25 Y 70)

[quaint trout]

@next idol dont just give answers

Help people do it themselves, although it looks like they're gone now

[next idol]

alright

[hard compass]

How would I factor x^2+x-30?

[fossil nova]

do you want the answer or an explanation?

[hard compass]

an explanation

[fossil nova]

so to factor this, you need to break the 30 down to two numbers that can multiply to give you that 30 and add up to give you 1, due to the coefficient of x being 1

so when you can use 6x - 5x

this gives you x, and when multiplied, gives you 30

[hard compass]

oooooooooooooooooohhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

im stupid

[fossil nova]

you get it?

[hard compass]

yeah now I do

[fossil nova]

good good

good luck

[hard compass]

thank you for the assistance

[fossil nova]

no problem

[warped phoenix]

Let’s say I have this equation: 4(2x – 3) + 2, Im told to apply a vertical shrink by a factor of 2, and then a vertical shift downwards by 3 units, and a horizontal shift to the left by 2 units.

Would my new equation be: 2(2x - 5) + -2 ?

[rugged minnow]

help

[median tendon]

https://www.mathsisfun.com/data/least-squares-regression.html
This should help

[rugged minnow]

i dont understand

can u teach me the steps

[median tendon]

It literally has every step by step instruction on there, any particular steps you dobt understand?

[alpine sable]

How do I do this thing again can someone explain to me how to do it not the answer because I wanna figure it out

Can someone please explain the reasoning behind this? The answer is log1/2:

[median tendon]

1=log10

Then use logarithmic laws to combine

[misty moat]

someone tell me the answer please

[thorn vortex]

@misty moat When a system of equations has infinite solutions, what does that imply for their lanes

[misty moat]

the lines overlap at every point?

[thorn vortex]

Yes

What can you then deduce from that assertion

@misty moat

[misty moat]

@thorn vortex i dont know

just say it

[thorn vortex]

It means the lanes are the same

[wary stream]

Overlap means they’re the exact same line

[thorn vortex]

Then what does it means about their equations

(this question is easy)

[misty moat]

there equal

the lines are equal

[thorn vortex]

Yes their equations are equal

Now you can easily guess the answe

r

[misty moat]

both are equal?

slope and y intercept?

[thorn vortex]

Yes

You guessed right

[ancient saddle]

Hello, what have you tried so far?

[rugged minnow]

killing my seld

can u do it

for me

[wary stream]

No

[alpine sable]

Hi! Is this correct?

[hushed pasture]

yes

[alpine sable]

Ok, thanks

salah

how would I go about solving this?

[jade birch]

expand the binom

and some things cancel each other out

[tidal bane]

I apologize if I missed it but i have looked in a few of the other channels and can't seem to find it.

I'm looking for a solid textbooks on probability as well as statistics (not together though). Additionally it would be really great if people could refer a great online class. Ideally one that is designed for beginners, has lots of practice problems and is pretty rigorous in it's teachings.

[jade birch]

and when you get rid of the denominator, then substitute h=0

[alpine sable]

alright bet thank you

[jade birch]

have you tried #book-recommendations

[wary stream]

Ask in #book-recommendations

[jade birch]

np

[weak oasis]

i have a question,would h(-2) when h(x)=x^2+4x-7 be equal to -11 or -19?

[jade birch]

that would be -11

h(-2) when h(x)=x² is h(-2)=(-2)²

[weak oasis]

ok thanks

that’s what i thought

[jade birch]

Yes, you are correct

[weak oasis]

i was just checking because apparently i’ve been reading squares wrong my whole life

[jade birch]

The notation can be a little confusing but you'll get the hang of it with enough practice

[weak oasis]

i just learned yesterday that it’s read -(2)^2 without parenthesis present and: (-2)^2 when they are

[jade birch]

what do you mean by "read"?

[weak oasis]

i mean like when solving an equation e.g. -2^2 +5

[hollow beacon]

yes, if you put it into a calculator thats what it does

[weak oasis]

so that is right correct?

i mean it makes sense

[hollow beacon]

yea

[weak oasis]

0-2^2

order of operations

oh and which way do you think my math teacher would want me to answer? P(D)= 4D-20/3
or P(D)= 4/3 (D-5)

[jade birch]

ugh

those two aren't the same

do you mean

P(D) = (4D-20)/3?

[plush quest]

how do i solve for [1/5] to the 4th power

[jade birch]

$(\frac{a}{b}) ^n=\frac{a^n}{b^n}$

[jade birch]

You distribute the power to the numerator and denominator

[ocean seal]

.itsjustnai

[plush quest]

so 1/625?

💀

[jade birch]

yes

@plush quest

I was in a different channel

[patent hill]

🤓

[modern crystal]

anyone available?

[jade birch]

[warped phoenix]

Let’s say I have this equation: 4(2x – 3) + 2, Im told to apply a vertical shrink by a factor of 2, and then a vertical shift downwards by 3 units, and a horizontal shift to the left by 2 units.

Would my new equation be: 2(2x - 5) + -2 ?

[prime badge]

or 2(2x - 1) + -2

[gray isle]

those are expressions not equations

[modern crystal]

is this right ?

or would it be e

cause it’s not asking to completely simplify it if that makes sense

[jade birch]

I'm not sure what they mean by equivalent tbh

[icy dirge]

x = 9 - (-2) =22

[jade birch]

If you evaluate it you get +inf, but if you evaluate the last two they also give you +inf

[modern crystal]

this is the “practice shown” next to it

so that’s what they mean by equivalent

[jade birch]

well this is scenario 3

[jade birch]

and scenario 3 are also the last two limits here

[wary stream]

You take the leading coefficient terms from the numerator and denominator, then simplify

[wary stream]

Channel busy

[modern crystal]

if i’m not mistaken the leading term is x^2 and x right?

would it be the last answer choice then ?

[wary stream]

Which picture?

[wary stream]

Not the last choice

Close though

[modern crystal]

B?

[wary stream]

No

[modern crystal]

i don’t think it’s a c though

cause it’s asking for the equivalence not it simplified ?

[wary stream]

You "ignore" the limit part

[wild shard]

whats the best approach to fit a bezier curve?

specifically a cubic bezier

[modern crystal]

it was the last one 😃

[wary stream]

It was? Huh, interesting

[gray isle]

technically both the last two would be correct

as they ultimately have the same limit as x→inf

[alpine sable]

help

[modern crystal]

all good

[alpine sable]

help

pls

[gray isle]

what have you tried

[alpine sable]

yes

i dont get it

[gray isle]

is not a yes/no question

do you know what factors are

[alpine sable]

ik

umm

no

[gray isle]

that is a major issue

so if i were to ask you for the factors of 4, you won't know wtf i'm asking for?

[alpine sable]

um

idk

[gray isle]

i'd highly recommend you read up on factors of integers