help-23

[short topaz]

i'll msg u l8r

[modern bloom]

Ok!

[fathom jewel]

Ok!

[modern bloom]

I'll close this for now?

[fathom jewel]

prob

[modern bloom]

.close

[safe radish]

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[visual pond]

Ok so

Division rule

I get

$\frac{(x^2-7)(1)-(x)(2x)}{(x^2-7)^2}$

[flat frigate]

smeagol

[visual pond]

Which is

$\frac{-x^2-7}{(x^2-7)^2}$

[flat frigate]

smeagol

[visual pond]

So where did I go wrong cause the answer was denied

[cedar void]

numerator is -(x^2 + 7)

can't cancel out like that

[visual pond]

oooh

ok

Got part 1 ty

ok now part 2 i messed up

[visual pond]

so I need to find the derivative of this

$\frac{(x^4-14x^2+49)(-2x)-(-x^2-7)(4x^3-28x)}{(x^2-7)^4}$

@cedar void could you check this for me?

[cedar void]

what's the first derivative?

okay nvm

[visual pond]

this is

[cedar void]

how did you got -28x?

[visual pond]

14*2

(x^2-7)*(x^2-7)

Expands to (x^4-14x^2+49

[flat frigate]

smeagol

[cedar void]

okok

[visual pond]

I made a typo sorry

[cedar void]

seems alright now

[visual pond]

$\frac{(-2x^5+28x^3-98x)+14x^5+28x^3-28x^3-196x}{(x^2-7)^4}$

[flat frigate]

smeagol

[cedar void]

14x^5?

[visual pond]

ooh

it;s positive 4x^5

my whiteboard was messy 😅

got it now

tysm!!

[cedar void]

nice

but i didn't do anything

[visual pond]

you read my work and saw the typo

very appreciated

[cedar void]

np

[visual pond]

.close

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[compact raft]

!help

[safe radish]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[fickle monolith]

recall the properties of secant

or maybe cos can help

[unborn flare]

just convert it into cos

[compact raft]

As in the domain restraints?

[fickle monolith]

more like range

[unborn flare]

and you will see that cos does not care about negative inputs

[fickle monolith]

range and domain wil both help

[unborn flare]

cos( -x) =cos x

[fickle monolith]

and that is the same for sec

[compact raft]

Okay so what about sin?

[unborn flare]

yes

[fickle monolith]

you do not need sin

[unborn flare]

sin does care about inputs but you don't need any sin here

[fickle monolith]

but just for info sin(-x) = -sinx

[compact raft]

I’m asking if the same question were asked about sin and its inverse

[unborn flare]

just for reference sin(-x)= -sinx

[compact raft]

Okay

[unborn flare]

yea then you have to see how sin works in this condition as we said

[compact raft]

So the answer to the original question is square root 2?

[unborn flare]

stop?

yes

it's the same

root 2

[compact raft]

Okay cool

!close

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[lean otter]

hiii i need help understanding how to do these equations 😓 im very weak at math but i want to try

[unborn flare]

open the brackets in the first question

there is a plus sign infront of that bracket in the first question

so it will open normally without changing any sign of the things inside the bracket

4x^2+5x+3+2x^2+7x+1

like this

then you can just add them

[lean otter]

ohh thank you!!! what about the second question?

[leaden lily]

multiply the first term in the first bracket by both the terms in the second brackets and then take the 2nd term in first bracket and do same as before

so it will be
2x^2 + 8x + 3x + 12

[fickle monolith]

for reference, use this
(a+b)(c+d) = ac+ad+bc+bd

[unborn flare]

start with the first term and multiply it with 2 terms inside the bracket with appropriate signs and do the same for the second term

then you can just add them

[lean otter]

thank you guys

.close

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[harsh bloom]

Voyager 1 moves with 17 km/s closest star is 4.3 lightyears away how long would it take for voyager 1 to reach it

[safe radish]

@harsh bloom Has your question been resolved?

[plucky elk]

translate lightyear to distance im kilometers

[harsh bloom]

how would i do that with the information given

[plucky elk]

do you know speed of light

[harsh bloom]

yeah thats given

299792458

[plucky elk]

units are important

[harsh bloom]

sorry

m/s

[plucky elk]

do you know how many seconds are in a year

[harsh bloom]

yeah uh in the question it was 3.2 x 10^7

[plucky elk]

in words, 1 light year = how long it would take light to travel in one year

now you have enough information to find light year in distance

[harsh bloom]

how so

how do u do it

[plucky elk]

answer this with numbers

[harsh bloom]

3.2 x 10^7 = 3x 10^8 like what

[plucky elk]

what are you doing here?

those are two different numbers but you're setting them equal?

[harsh bloom]

o shit yh

got conufsed

1 light year = 3.2 x 10^7 x 3 x 10^8

not rlly sure wht to do

[plucky elk]

.

[harsh bloom]

1 light year = 3.2 x 10^7s x 3 x 10^8m/s

like that

?

[plucky elk]

now you know speed (in km /s) and distance (in meters). find time

either convert distance to kilometers or speed to meters / second

[harsh bloom]

17 000 m/s

[plucky elk]

use distance = speed * time

[harsh bloom]

where would i get time from?

[plucky elk]

did you read this

[plucky elk]

use this to solve for time on one side of the equation

[harsh bloom]

3.2 x 10^7s x 3 x 10^8m/s = 17 000m/s * X

do i js solve this equation?

[plucky elk]

yes and this again

[harsh bloom]

5.65 x 10^11?

[plucky elk]

.

[harsh bloom]

alright thank you

solved it

.close

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[ruby axle]

Ben and his mother, Jenny, were both born on January 1. in 2002, ben was x years old and jenny was (2x²+11x) years old. in 2007, Jenny was 5 times older than Ben. a) form and solve a quadratic equation to find x. b) find jen's age when ben was born.

[ruby axle]

Helppp

[fathom jewel]

The first sentence sounds weird

[ruby axle]

No

They were just both born on jan1

[fathom jewel]

yea Ben and his mother

[severe pond]

we can read yes

[fathom jewel]

anyway

[ruby axle]

Yes

[severe pond]

what have you tried

[ruby axle]

Okay soo

2002 to 2007 is 5 years so , ben will be x +5

[severe pond]

indeed

[ruby axle]

And jenny sill be 2x²+11x ) +5

[severe pond]

indeed

what else

[ruby axle]

Also

[severe pond]

"in 2007 jenny was 5 times older than ben"

[ruby axle]

Yes

[severe pond]

mathematically what does that mean

[ruby axle]

Itll be jennys age in 2007 = bens age x5

[severe pond]

"mathematically"

using x

[severe pond]

^

[severe pond]

^

[ruby axle]

Idk

Tell me

[severe pond]

ben’s age in 5 years is x+5

jenny’s age is 2x^2 + 11x + 5 which is 5 times ben’s age

thus

2x^2 + 11x + 5 = 5(x+5)

[ruby axle]

I js saidddd that

[severe pond]

did you say this though

no

[ruby axle]

I was too lazy to write it mathematically

🙄

[severe pond]

whatever you say

[solar hazel]

you are so pretty

[severe pond]

thanks

[ruby axle]

Omg tysm😭💗💗💗

[ruby axle]

FOCUS

Omg

[severe pond]

^

move all terms to one side

[ruby axle]

Lemme solve it

2x²+6x-20=0

[severe pond]

divide that by 2

then factor

[ruby axle]

Ok

[severe pond]

and

what did you get

[ruby axle]

X=2

X=-5

[severe pond]

yes

[ruby axle]

But since age cant be negative

Its js 2

Okay and b) its just replacing so jts easy

Ok i got another one

😊

[severe pond]

what did you get for that one btw

it says

[ruby axle]

28

[severe pond]

"when ben was born"

yes

you had to subtract 2

👍🏻

[ruby axle]

a piece of wire is bent to form a rectangle with an area of ​​85 cm². the total perimeter is 60cm and the length of the rectangle is x². a) form an expression on the surface of the rectangle. b) replace x² with z and form a quadratic equation depending on z c) find all possible values ​​of x

[severe pond]

length of the rectangle?

length of one side? sum of the lengths of all the sides as in the perimeter?

anyways what’s the area of a rectangle?

and what’s the perimeter

in terms of variables

[ruby axle]

Yes?

[severe pond]

what does that mean

[ruby axle]

U got length and width

[severe pond]

^

was that the question verbatim?

do they mean the diagonal?

[ruby axle]

No

Wait

[severe pond]

then the length of what lol

"length of rectangle" has no meaning

unless it is to be interpreted as perimeter

but they explicitly mentioned that the perimeter was 60

so i doubt that’s what they meant

i think it’s length of diagonal

because diagonals are congruent

in a rectangle

[ruby axle]

I see length as the blue sides

does that make sense?

[severe pond]

ok we can interpret it that way

[ruby axle]

cus thats what it says length

yea

[severe pond]

and the other sides are the width

[ruby axle]

exactly

[severe pond]

then what can you say about the area

also

define the width

with some variable

it wasn’t given

[ruby axle]

lets just use w

so area will be x2 x w=85

[severe pond]

x^2 w

[ruby axle]

yes

what about b)

[severe pond]

what’s the perimeter

[ruby axle]

p=2(x^2 + w)

[severe pond]

yup and p=60

so 2(x^2 + w) = 60

and x^2 w = 85

[ruby axle]

yes im solving it

30=x^2+w

[severe pond]

they want you to substitute z = x^2

[ruby axle]

yes

w= 30-x^2

[severe pond]

you can do it that way yes

go on

[ruby axle]

and we can use that in the area formule so x^2 x (30-x^2)=85

what about now

oh wait

simplify

[severe pond]

yes

you’re solving for x

[ruby axle]

i gotta fjnd the

posibble values of x

[severe pond]

,rotate

[ruby axle]

😭

[severe pond]

it’s a quadratic in terms of x^2

it’s clear if you let x^2 = z

[ruby axle]

ohhhhh

rightttt

[severe pond]

z^2 - 30z + 85 = 0

[ruby axle]

?

.close

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[tawdry marten]

help

[stoic bramble]

grade 11 physic?

[tawdry marten]

idk tbh

im in grade 9

[stoic bramble]

oh mb 💀

[tawdry marten]

all g

im just not sure where to start

[stoic bramble]

so is mutiple choice?

[tawdry marten]

ye

its a b c or d

the questions are 1. 2. 3. and 4

[stoic bramble]

well first you need to convert them to same unit

[tawdry marten]

that would be 42188 meters in 2h 30min and 12s

[stoic bramble]

time as well

[tawdry marten]

ight mb

5412 s

[stoic bramble]

then use the percentage formula for a and b

[tawdry marten]

25/42188 *100?

[stoic bramble]

yea

[tawdry marten]

0.059 about

[stoic bramble]

same for b as well

[tawdry marten]

1/5412 * 100 = 0.018 about

my physics teacher didnt even teach this XD

[stoic bramble]

bruh

[tawdry marten]

he just assigned us this

[stoic bramble]

also for c and d use the velocity formula:
Velocity =Distance/Time

you need to watch out for the units btw

[tawdry marten]

ah i see

everything coming together

[stoic bramble]

good

[tawdry marten]

42188/5412 gives us the meters per second

wait i did something wrong

[stoic bramble]

i think you calculate the time wrong

[tawdry marten]

oh yeah

im selling

its 42188/9012

which is 4.681 which is a possible answer

[stoic bramble]

yea

[tawdry marten]

i dont even need to calulate the 4th one but how would i do it?

[stoic bramble]

hmm

[tawdry marten]

if your not sure then it is ok

[stoic bramble]

na i wont let grade 9 science take over me

[tawdry marten]

alr

😀

hey are u here rn?

[stoic bramble]

yea

you got an idea?

[tawdry marten]

can u dm me how to solve it

whenever u get a chance

cause i got dinner

[stoic bramble]

ok

.close

[tawdry marten]

.close

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[distant barn]

How would I solve 2x^2 + 2 = x using the quadratic formula?

I have tried moving the x over with subtraction to get 2x^2 - x + 2 = 0 and it doesn't give me a nice answer at all.

[sick scarab]

how dare you call complex roots ugly :d

[fading solar]

wym they are 💀

super annoying too

[fading solar]

ngl your answer prob isnt gonna be nice

especilly when quadratic formula is used

[distant barn]

the only thing is that with what's given, it seriously won't work

at least not in my mind

because my b value is negative

and my c value is positive

so i'm not sure if i'm missing a step or forgetting something

what's under my root in the formula itself comes out to an imaginary number

and i don't think that's how it should be

[sick scarab]

show the entire problem, maybe that'll help

[distant barn]

my work is a nightmare

i have schizophrenic visions when i work on math

[sick scarab]

lol

[distant barn]

Here is what I have though

my initial problem being in the top left

everything working your way down is to the same problem

wait i lied

the initial problem is

2x^2 + 2 = x

[sick scarab]

i mean what led you to this equation?

[distant barn]

It is the equation given on the study guide I'm doing

[sick scarab]

oh, so its not in the middle of some exercise

youre simply asked to solve it

[distant barn]

yes exactly

[sick scarab]

then thats right

roots wont be cute

[distant barn]

But normally they're so adorable

I always get whole numbers :(

[sick scarab]

the discriminant = b² - 4ac

when this is negative

youll always get cmplx roots

[distant barn]

welp

i need to find out how to drop this class

lol

[sick scarab]

ive been there lol

but youll get used to them

[distant barn]

i thought i was done with math

i've done all of this before i'm just frustrated that i can't remember it all

[sick scarab]

,w 2x²-x+2=0

[flat frigate]

Results provided by WolframAlpha

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Requested by its.emily.official

[distant barn]

THAt

is what i got

im not stupid i'm just hopeless

[sick scarab]

so its correct

[distant barn]

thank you

.close

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[agile vigil]

does anybody know how i would state the intervals of increase and decrease for the sin and cosine function

[agile vigil]

welllllllllllll how would i state it then

[severe pond]

guess

[agile vigil]

say less

wellllllll

now what

and it repeats every 2 pi

[hasty wagon]

are you allowed to use calculus, or just plain old graph reading?

[agile vigil]

no calc yet 😦

[hasty wagon]

no problem

lemme draw on your graph, brb

[hasty wagon]

first of all, let's look at the values of sin(x) x=0 to π

as we can see, the yellow arrow the values are going up and up, but gradually slower and slower

[hasty wagon]

what can you tell about this?

[agile vigil]

rate of change is getting lower and lower right

unless im missing something

[hasty wagon]

yep, so we can see that
its value is "increasing", but the rate of change is "decreasing"

is that what you need?

[agile vigil]

i just needed to see how you would state it cus i feel life if i write is as (-pi/2,pi/2) and repeats every 2pi she wouldnt like that answer

with interval notation

[hasty wagon]

oh i see what you mean

lemme draw with the picture again

[hasty wagon]

is that correct?

[agile vigil]

yeah

[hasty wagon]

so, to generalize the notation, we shall look intofirst few intervals

(-5π/2,-3π/2),(-π/2,π/2), (3π/2,5π/2)

can you see a pattern

[agile vigil]

factoring im guessing?

they increase by pi everytime

[hasty wagon]

so we can write it as:
$$\bigcup_{n\in\mathbb{N}}\left(\frac{-\pi}{2}+n\pi,\frac{\pi}{2}+n\pi\right)$$

[agile vigil]

ahhhh

this is genius

[hasty wagon]

that's how we write repeated values for natural numbers n

[agile vigil]

yeah i get the n is an element of all natural numbers part

alright i understand it

ty

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[flat frigate]

Biscuity

[safe radish]

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[buoyant ridge]

can I just get help calculating the cpc

[buoyant ridge]

The 2.66 and 3.33 are wrong and my next best guesses are 1.33 and .67

still looking for help

[safe radish]

@buoyant ridge Has your question been resolved?

[safe radish]

@buoyant ridge Has your question been resolved?

[safe radish]

@buoyant ridge Has your question been resolved?

[safe radish]

@buoyant ridge Has your question been resolved?

[safe radish]

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[eternal carbon]

any progress?

[devout shale]

🔠

[eternal carbon]

true

[rapid egret]

I saw a substitution of U=tan(x) but I did not understand how that is feasible I know of Weierstrass substitution which is U=tan(x/2)

<@&286206848099549185>

[devout shale]

!15mins

[safe radish]

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

[eternal carbon]

first rewrite this in terms of sin() and cos()

[rapid egret]

I have done that

[eternal carbon]

ok i go read what u have done

[rapid egret]

This one is more explanatory

[eternal carbon]

ic yes this page is better

ok this is good

from here, create different integral with substitution u = pi/2 - x

you will have much easier time integrating

[rapid egret]

🤔🤔
Gimme a sec lemme check it out

I don’t seem to understand the aim could you help me put it to paper

[eternal carbon]

can you show me what you get

[rapid egret]

I didn’t understand it’s a double angle so it would sin2(pi-X)is not equal to cos2x

[eternal carbon]

very true

[safe radish]

@rapid egret Has your question been resolved?

[eternal carbon]

bro

[eternal carbon]

so wt do u get

[rapid egret]

I’m guessing Probably the initial substitution of U=tanx would do the trick cause now it’s already getting unnecessarily over complicated when I try to sub U= tan(x/2)

But I need a proper reason as to why we sub U= tanx

[eternal carbon]

tht does not explain what u got

[eternal carbon]

the proper reason will be easily seen when you take this and do u = pi/2 - x

[rapid egret]

When I sub U= pi/2 -X what am I meant to look out for…, will the cos and sin switch form…?

[eternal carbon]

no,

sin(2x) = sin(2(pi/2 - x))

so that stays the same

[eternal carbon]

no

[rapid egret]

Wait I got an idea I seem to know what you’re getting at

I didn’t get anywhere

[eternal carbon]

what is cos(2(pi/2 - x))

[rapid egret]

-cos2x

[eternal carbon]

there is no minus here

[rapid egret]

Ohh that brings back to the first equation I ran from

I wasn’t able to integrate this that’s why I scrapped the idea

[eternal carbon]

factor denominator and use partial fraction decomposition

[safe radish]

@rapid egret Has your question been resolved?

[rapid egret]

Alright I’d check it out now

[rapid egret]

🤦‍♂️🤦‍♂️I got pi/4 as an answer

Which is incorrect

[safe radish]

@rapid egret Has your question been resolved?

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[cold crescent]

Can I ask how to solve rational equations?

I'm dumb

[simple gazelle]

did you put in some effort to get the answer

[cold crescent]

idk where to start TT

[wraith swift]

take lcm

or take common and see if it works out

[mossy lotus]

This is equivalent to calculating the LCM of numbers. Can you tell the steps if the denominator were numbers?

[cold crescent]

I see thx

[safe radish]

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[chrome saffron]

An ultracentrifuge accelerates from rest to 100,000 rpm in 1.50 min.
What is the radial acceleration in m/s2 and multiples of g of this point at full rpm? (i literally have no idea how to get this nor what multiples of g means)

An archer shoots an arrow at a 72.0 m distant target; the bull's-eye of the target is at same height as the release height of the arrow. At what angle in degrees must the arrow be released to hit the bull's-eye if its initial speed is 31.0 m/s?

[pine horizon]

for the second one, you know the projectile's range and initial speed

so use formula of range

$R = \frac{u^2\sin(2\theta)}{g}$

[flat frigate]

Astar777

[chrome saffron]

what is u

i assume its just v0^2 but why u?

[pine horizon]

idk

[chrome saffron]

so would i rearrange the equation to solve for theta?

[pine horizon]

yes

[chrome saffron]

wait can u check if i rearranged correctly

1/2(sin^-1(Rg/v0^2)) = theta

idk how to use the texit thing so its kinda hard to read

[pine horizon]

yes

$\theta = \frac{1}{2}\arcsin{(\frac{Rg}{v_o^2})}$

[flat frigate]

Astar777

[smoky nacelle]

$\theta = \frac{1}{2} \arcsin\left({\frac{Rg}{v_o^2}\right)}$

[flat frigate]

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

[smoky nacelle]

oh you got there first lmao

[pine horizon]

[chrome saffron]

wait am i donig something wrong

cuz im getting undefined in myu calculatro

[pine horizon]

yes

[chrome saffron]

oh im an idiot i forgot to do v0^2

[pine horizon]

,calc (arcsin((729.8)/(3131)))/2

[flat frigate]

The following error occured while calculating:
Error: Undefined function arcsin

[chrome saffron]

no i got it its fine

23.62

thanks

.close

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[weary stream]

Line a is parallel to line b, and line c intersects both of them. Prove that all three lines lie in the same plane

[atomic geode]

well for line A and B to be parallel they need to lie on the same plane

As for line C

it passes through 2 points

one is on A

other is on B

2 points are enough to define a line

and the 2 points are lying in the plane of A and B

so C must be also in their [plane

[weary stream]

why*

i cant prove that

cos two planes can have 1 intersaction point and it can A s point and other two of B and other point of A can be on another plane

its an Axiom

[lean otter]

,iamnotstudying

[flat frigate]

Removed the studying! role from you.

[atomic geode]

we can think of A and B as vectors, as they are parallel, then they must be collinear vectors
any 2 collinear vectors lie in the same plane

+i think i should add i have not formally studied 3d yet, im just speculating using logic

[weary stream]

yh

3D started when someone said that a point outside the line would draw many parallel lines

so

[weary stream]

idk baut this

[safe radish]

@weary stream Has your question been resolved?

[weary stream]

<@&286206848099549185>

[glacial ferry]

sup?

[hardy river]

WTF

[glacial ferry]

whats ur issue?

[safe radish]

@weary stream Has your question been resolved?

[safe radish]

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[lean otter]

hi how the flip do i find a percentage on excel

[pine horizon]

the same way you find percentage on paper

[lean otter]

idk how

..

[pine horizon]

💀

[lean otter]

LMAOOO

[pine horizon]

(part/whole)*100

[lean otter]

THANK U

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[chrome delta]

its my second week learning math in eglish and i wanted to ask what would the difference be between find and solve

[thin bridge]

solve usually involves manipulating an equation(s) to find the value of a specific variable

or ordered list

[pine horizon]

^ and "Find the solutions of <equation>" and "Solve <equation>" mean the same thing

[thin bridge]

how "find" is being used here is more of an instruction to simplify an expression

[chrome delta]

so i just have to simplify both a and b?

math in english is gonna be my death

[pine horizon]

for a. you just write what f(g(x)) would be and simplify it

[pine horizon]

for b, you take this simplified form and equate it with f(x+3), then find the solutions

[chrome delta]

ohhhhh

thank youu

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[white spire]

I have no clue how to solve this is there any way someone could help me? Please I’m desperate

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@white spire Has your question been resolved?

[white spire]

<@&286206848099549185>

[stiff vault]

whats your question?

@white spire

[white spire]

The second part on the first pic is where I’m rly stuck

Can someone help me please😭

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[fair goblet]

Number 8 correct?

[low canyon]

Yes

[fair goblet]

Thank you

How would I differentiate

11

Am I able to split it up

Like two cos

Or no

Cause I would be take the differentiable or whatever of it if I took it in two poeces

Nvm

I’m not able to do that

Can someone help

🙏

[low canyon]

You have two choices

1. cos^2(t) = cos(t) * cos(t) and you use the product rule

Or

2. cos^2(t) = (cos(t))^2, and you use the chain rule

[fair goblet]

I thought I couldn’t do that

[low canyon]

Why not?

[fair goblet]

Also chain rule we learn that after this section

We haven’t touched on that yet

[low canyon]

Ok, then go for the product rule

[fair goblet]

I thought you could do that if it’s 2cos^t

[low canyon]

What do you mean by 2cos^t ?

2cos(t) ?

[fair goblet]

Yes

[low canyon]

No, 2cos(t) = cos(t) + cos(t)

[fair goblet]

Oh

Right

[low canyon]

cos^2(t) = cos(t) * cos(t)

[fair goblet]

☠️

[low canyon]

!

[fair goblet]

.close

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[fair goblet]

.reopen

[safe radish]

✅

[fair goblet]

Did I do this right?

[plucky elk]

no

[safe radish]

@fair goblet Has your question been resolved?

[fair goblet]

Can I ask what is 1-sinx? Maybe I’m blind but I couldn’t find it here

[plucky elk]

there's no simplifying it. you just use quotient rule to find y'

$\frac{d}{dx} (1 - sin(x)) = \frac{d}{dx} 1 - \frac{d}{dx} sin(x) = ?$

[flat frigate]

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[fair goblet]

Thanks

[safe radish]

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[mighty haven]

Hey, i just want to know how to write solutions for an equation for infinite solutions like my solutions are for n = 6q+5

S(n) = {6q+5} with q € N

Is it the right way ?

[tepid summit]

Yeah, normally that would work

is it just naturals?

[mighty haven]

Yeah i think

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[tawny steppe]

hi, I am working on linear algebra problems and I ended up with this equation:

4a-6ab+6b-4

I need to know which values of a and b gives 0 and I don't know how to factor the equation

looking up for the answer I find that factoring it results in:

2(1-a)(2-3b)

the question is: how should I procceed to factor 4a-6ab+6b-4 into 2(1-a)(2-3b) ?

[latent raptor]

the proper factor is 2(2-3b) x (a-1). how did u get 2(1-a)(2-3b)

[tawny steppe]

I've spelt it wrong , i wanted to write exactly what you have written: 2(2-3b) x (a-1)

[latent raptor]

do you know how to factor?

[tawny steppe]

only when there is one unknown, when there are 2 unknowns then I don't know

[latent raptor]

to factor you have to find the GCF

and see whats the most you can take out

for 4a-6ab+6b-4, you gotta see whats the most you can take out of the equation

and remmeber

always group it into 2 groups

so (4a-6ab) (6b-4)

the most you can take out of group 1 is 2 and the letter a

and so on

[tawny steppe]

thank you I think i can base on this and understand it, thank you!

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[crystal palm]

!status

[safe radish]

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

[vestal hearth]

wrote down the common differences

thent he common differences of the common differences

but they werent equal

so it can't be parabola or linear so idk wht t do

[crystal palm]

parabola definitely works

you can see in the data that it is symmetrical around x=3

you can start with the general parabola

f(x)=ax^2+bx+c

we know:
f(0)=6=c
f(2)=22=4a+2b+c
f(4)=22=16a+4b+c
f(6)=6=36a+6b+c

so we have 4 equations with 3 unknowns

so it is likely solvable (it is)

[safe radish]

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[feral knoll]

Why is the vector r considered the "vector of the line" here?

[feral knoll]

shouldn't the vector equation of the line be the blue line, not the green line?

r = r0+tv only gives the vector form of the vector r, how does this equation also give the vector form of the blue line, which i assume is the line we're trying to find

[somber merlin]

its a similar case with y=mx+c except theyre vectors

here r is the y where its a single point on the line

but all instances of r forms the blue line

if you see it more as a position than a line vector

[feral knoll]

great, thanks!

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[silver axle]

Do I js do tan(64)=18/x

And then tan(64)/18

[wispy monolith]

Yeah you can do that

[silver axle]

I got 0.1cm

But it says it's wrong

[wispy monolith]

Yeah it's saying find it in 10th of a meter

[silver axle]

It's supposed to be 8.8

I mean I got .1m

[wispy monolith]

Oh well

Tan(64) =18/x
So x = 18/tan(64)

[silver axle]

Wait huh

So you divided both sides by 18

So wouldn't that make it tan(64)/18

[wispy monolith]

But then x will be in denominator

[wispy monolith]

we multiply both side by x first

Do this first ^

[silver axle]

Zo that becomes

Tan(64)*x=18

[wispy monolith]

Yes

Now divide tan(64) both side

[silver axle]

X=18tan(64)

[wispy monolith]

Divide

x = 18 / tan(64)

[silver axle]

Ohhhh

I seee

Thabks so much

[wispy monolith]

No problem

[silver axle]

.close

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[warped yoke]

$xy' + y(1 + \ln(xy)) = 0$

[flat frigate]

syecko

[warped yoke]

i tried u = xy

u' = xy' + y

u' + yln(u) = 0

how would i continue

oh

$\frac{u'}{\ln(u)} = -y$

[flat frigate]

syecko

[warped yoke]

hmm y = u/x

$\frac{u'}{uln(u)} = \frac{-1}{x}$

[flat frigate]

syecko

[warped yoke]

$\frac{1}{2}(ln|u|)^2 = -\ln|x|$

[flat frigate]

syecko

[covert yoke]

From here just integrate with respect to y.

[warped yoke]

i can?

but how would i integrate 1/ln(u)

i think i got it now

i just missed separation of variables

[covert yoke]

The integral of 1/ln(x) dx is li(x) + C, which is the log-integral function.

So it's probably not that

[warped yoke]

now clue

no

1/uln(u) i can integrate

[covert yoke]

If you made a mistake leading up to it then that's understandable.

[warped yoke]

what

did i?

[covert yoke]

I don't know! I just glanced

But if you have 1/u ln(u)

Then that's manageable

[warped yoke]

yup

[covert yoke]

And now I see where you got it

[warped yoke]

ok thank you

.close

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[coral dagger]

Someone please explain

I have ((-1)^2)^m+1. Idk where to go from here

[hard crest]

doesn't seem right

[coral dagger]

Okay so we start off with (-1)^2m+1

[hard crest]

(-1)^(2m+1) yes

[coral dagger]

Dude that +1 is throwing me off hard

Can I do associativity with all those terms?

Can I seperate (-1^2m) and (-1)^1?

[hard crest]

,tex .exp rules

[flat frigate]

hayley is not layla

[coral dagger]

Ok so yes

Right I see

ty

/solve

solved

@safe radish solved

https://tenor.com/view/crying-black-guy-meme50fps-interpolated-interpolated-crying-black-guy-crying-crying-black-guy-gif-23747218

[hard crest]

.close

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[past birch]

when finding angle between plane and line

[past birch]

must i use the most simplified normal vector of the plane

like if n=(-4,2,-8) must i make it (-2,1,-4) before doing cos theta = a.b/|a||b|

[sour herald]

It shouldn't matter I believe

I might be wrong

[past birch]

but when i didn't simplify it, my angle is wrong 😭

[sour herald]

Oh really?

[past birch]

yeah

[sour herald]

My fault then

[past birch]

since im prelearning this i just wanna know if its like a rule or something

[hardy lion]

show your work please

[past birch]

ok

b. should be wrong ( answer is 27.6)

[hardy lion]

it shouldnt matter because by dividing by 2, a.b becomes a.b/2 and |a||b| becomes |a||b/2|

when you divide, the /2 should cancel

[sour herald]

Yes

[past birch]

what did i do wrong then?

[hardy lion]

your angle should be between 0 and 90 degrees

do you know what the 118 degrees signifies?

[past birch]

uhh

Not really sorry

[hardy lion]

remember that <-4,2,-8> is your normal vector

so that means it forms what angle to the plane?

[past birch]

huh? what does this mean 😭

[hardy lion]

what is normal vector?

[past birch]

vector perpendicular to 2 other vectors?

[hardy lion]

those two vectors lie on a plane yeah?

specifically plane Pi

[past birch]

ye

[hardy lion]

since the normal vector is perpendicular, what angle does it make with the plane

[past birch]

90 degrees

right angle

?

[hardy lion]

yup

[past birch]

o

and why -90? i cant find the connection yet sorry

[hardy lion]

whats the angle with the plane?

[past birch]

ohhhhhh

i get it now

thanks mate

[hardy lion]

youre welcome

[past birch]

.close

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[covert talon]

is the answer to this 8 square root 8

[versed wave]

sounds wrong

show your work?

[covert talon]

oh shit nvm

i get what i did wrong

sorry

.close

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[covert talon]

m

[covert talon]

um

this again

i got 11 sqr root 2..

[fathom adder]

So 2sqrt2 + 3*4sqrt(2) = ?

Sqrt(32) = sqrt(16*2) = 4sqrt(2)

[covert talon]

14?

[fathom adder]

Indeed

[covert talon]

But where did 3 come from

[fathom adder]

It multiply with the 4sqrt(2) which is 12sqrt(2)

Like 3sqrt(32) = 3sqrt(16* 2) = 3 *4sqrt(2)

You see ?

[old wedge]

so 3 plus 3 is 6?

[covert talon]

AUR

AUR AUR

Yeah now i get it

thus 3 rught

[fathom adder]

Yes it still mutliply while the whole simplify of the sqrt

[safe radish]

@covert talon Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

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• Show your work, and if possible, explain where you are stuck.
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[woven zodiac]

How'd I turn this to standard form
y=(x+4)(x+1)(x-1)²

[woven zodiac]

Please help

[astral goblet]

standard form of what?

[woven zodiac]

Polynomial

[astral goblet]

multiply the terms

what do u get

[woven zodiac]

I start with (x-1)² right?

[astral goblet]

yes

[woven zodiac]

(x²-1)?

[astral goblet]

no

[woven zodiac]

Is that correct

Oh

[astral goblet]

its of the form (a-b)^2

so use the identity

[woven zodiac]

This?

[astral goblet]

thats (a+b)^2

[woven zodiac]

Oh

Is this it?

[astral goblet]

yes

[woven zodiac]

(x-1)²=x²-2x+1?

[astral goblet]

correct

multiply this with the others

[woven zodiac]

How?

[astral goblet]

(x²-2x+1?)(x+1)

then multiply that with x+4

[astral goblet]

multiply the terms one by one

[woven zodiac]

x³-2x+1?

[astral goblet]

nope

multiply it one by one

[woven zodiac]

x³+x²-2x²-2x+x+1

???

[astral goblet]

there you go

correct

[woven zodiac]

Then 4x?

x+4?

[astral goblet]

now simplify that

[woven zodiac]

Oh

[astral goblet]

add the terms with the same degree

[lean otter]

hey is there any trick to factorize very quickly?

[astral goblet]

this isnt factorization

[lean otter]

I just wanted to know

please help me

[astral goblet]

yes there are many tricks, if you have a specific question please open a new help ticket

[astral goblet]

simplify this

[woven zodiac]

x³-x²-x+1

[astral goblet]

yes

[woven zodiac]

Ohh

Then we multiply with x+4?

[astral goblet]

yes

same method

one by one

[woven zodiac]

(x⁴-x³-x²+x)(4x³-4x²-4x+4)

Am i still on the right track?

[astral goblet]

????

what did you just do

[woven zodiac]

Oh

[astral goblet]

(x³-x²-x+1)(x+4) you should multiply this

[woven zodiac]

x⁴-x³-x²+x+4x³-4x²-4x+4

Then simplify?

[astral goblet]

correct

simplify, and then arrange in descending order of degree

i.e power 4 first, all the way to constant

[woven zodiac]

x⁴-3x³-5x²-5x+4

Is this it?

[astral goblet]

+3x³ this

not -

also -3x not -5x

[woven zodiac]

Ohh

I see

Thats the only error?

[astral goblet]

.

[woven zodiac]

Ohh

x⁴+3x³-5x²-3x+4

So this is the final answer?

[astral goblet]

yes

[woven zodiac]

Ohh I see it thanks

Tysm

.close

[safe radish]

Channel closed

Closed by @woven zodiac

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[junior sundial]

How does this became 1. I tried to rationalize but it got nowhere

[terse lichen]

did you just try to use difference of two squares on a cube root

[craggy sedge]

*hint: $\lim_{x \to 0}\frac{\sqrt[3]{1+3x}-1}{x}=\frac{3(\sqrt[3]{1+3x}-1)}{(1+3x)-1}$

[flat frigate]

convergence

[junior sundial]

I can't find any resources online on how do you rationalize cube roots lol

[craggy sedge]

hmm do you know that $\lim_{x \to a}\frac{x^n-a^n}{x-a}=na^{n-1}$?

[flat frigate]

convergence

[junior sundial]

wat

[craggy sedge]

?

[junior sundial]

I don't get what am I suppose to do with that info

na^n-1?