help-0

[winter light]

Yeah

So $x^2 - 8x + 7 = (x - 1)(x - 7)$, right?

[ocean seal]

Alberto Z.

[muted breach]

yeah

[winter light]

Nice

Now do the same for the other two denominators

[muted breach]

ok

[winter light]

Note that for x² - 1 you should not need to solve a quadratic equation, it's factorizable in a quick way

[muted breach]

So $7- x² +6x = -( x² -6x-7x)=-(x-1)(x+7)$, right?

[ocean seal]

tal

[winter light]

No, it is $-(x + 1)(x - 7)$

[ocean seal]

Alberto Z.

[winter light]

In general, if you aren't sure about your result, just multiply out what you got and see if that matches the original expression

[muted breach]

like it would be just

$(x-1)(x+1)$

[ocean seal]

tal

[winter light]

Yep

Now you need to check if there are some forbidden values of x

In other words find the domain of that equation

[muted breach]

I got

3 4
------ + --------- =x-9
x+7 -(x+7)

[winter light]

Nope

[muted breach]

so where did I got wrong?

[winter light]

What's the answer to this?

[muted breach]

oh

x=1,x=-7,x=-1

[winter light]

And 7 as well

But yes

So now you are allowed to multiply both sides of the equations by the lcd

Supposing you know what the lcd (least common denominator) is in this case

[muted breach]

isnt it like this?

if you understood what i tried to say

[winter light]

No, I asked you for the lcd (least common DENOMINATOR)

[muted breach]

oh

how to do it

[winter light]

Multiply all the distinct factors appearing in the denominators

[muted breach]

but there is plus beetwen

why should I Multiply

[lone heart]

@muted breach Has your question been resolved?

[winter light]

What's the problem of the minus??

[winter light]

Let me change the question...

[lone heart]

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[winter light]

$\frac{2}{x - 3} - \frac{x}{2 - x} = 0$

[ocean seal]

Alberto Z.

[winter light]

Do you know how to solve this? @muted breach

[lone heart]

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[vapid steppe]

yo

[real gazelle]

yo

[vapid steppe]

when you use trig sub for $\int{(\frac{x^4}{1+x^6})^2 dx$

[ocean seal]

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

[vapid steppe]

if u let x^3=tan(theta)

then u will eventually get the integral as $1/6\theta-1/6sin(\theta)cos(\theta)$

[ocean seal]

Jash

[vapid steppe]

for the first term you need theta in terms of x

[vapid steppe]

so if u take inverse tangent of this arent you restricting the range

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[alpine sable]

Anyone knows where I went wrong ?

The answer is supposed to be

[grave quartz]

well the integral of sin(2x) not -2cos(2x)

so...

[alpine sable]

Oh yeah i mixed it with derivative notation

[grave quartz]

ye lol

happens no worries

[alpine sable]

Still getting the wrong answer

[tacit arch]

You still haven't fixed this

Use chain rule to check your work

[alpine sable]

Ok i see it's divided

By the number inside the sin

I almost had it this time

Except I have 2 instead of an 8 in the second fraction

Hold up

It worked

Thanks

.close

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[lapis zephyr]

what does it mean to rewrite something "in terms of" sin and cos? Like idk what kind of answer that would give, is it two answers? Example: rewrite sin(x+pi/6) in terms of sin x and cos x. i haven't got a clue what this means, but it's coming up in my classes and we never covered it lol

[paper mango]

sounds kind of like an arbitrary task

I presume the context is trigsum?

[lapis zephyr]

yeah

[paper mango]

trigonometric sum properties

k

sin(a+b) =

[tardy stag]

generally this means to write it terms of $\sin(x)$ and $\cos(x)$ specifically (edit: nvm you said that already hehe)

[paper mango]

sin(a)*cos(b) + sin(b)*cos(a)

@lapis zephyr is it clear now?

[lapis zephyr]

so the example of sin(x + pi/6) would just be rewritten as sin(x)*cos(pi/6) + sin(pi/6)*cos(x)?

[paper mango]

yop

[lapis zephyr]

ohhh

yeah, that does seem kinda pointless lol. okay, thanks

[paper mango]

well you can calc cos(pi/6) & sin(pi/6)

but otherwise yes

[lapis zephyr]

gotcha. thanks

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[azure remnant]

How should I approach the optimization

?

I figured to use a cube

but the volume isn't a perfect cube root

so it ends up being close to 5

but not 5 exactly

I think it's wrong but are the dimensions approximately 4.93 x 4.93 x 4.93

so just a cube with side length 4.93?

.close

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[azure remnant]

.reopen

[lone heart]

✅

[lone heart]

@azure remnant Has your question been resolved?

[paper mango]

few sec, 'll be here

@azure remnant k

you're at a) right

I'm confused due to your cube, since it mentions the prism shape

@azure remnant are you still present

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[vivid heath]

how do i calculate how to pick up an object?

[vivid heath]

i know that w = m*g

and force = ma

i know that theres normal force opposing the object

but i dont believe that matters when picking up an object

is it just F = m*a-g?

[lunar ravine]

ma = the resultant force which is F - mg

[vivid heath]

so it wouldnt be F = m*g

[lunar ravine]

No, it will be if the body didn't move like if the acting force was less than or equal to the force of weight

So the resultant force or (ma) will be zero

[vivid heath]

so if this is a straight lift it would be F = -mg?

[lunar ravine]

Straight lift as in it moved but in a straight line? If that's what you meant then it depends whether the body moved with or without acceleration, the general law is that ma= resultant force, the resultant force here is F - mg, so if the body accelerated F won't be equal to mg, if it didn't and it moved with uniform velocity then yes F=mg, F is the lifting force

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[solar tartan]

yo

[solar tartan]

I wanted to call someone to help me with some basic geometry hw

[wary stream]

Just post your question and whoever can help, will come and help you

[solar tartan]

@wary stream

[fossil pecan]

where are you stuck?

[lone heart]

@solar tartan Has your question been resolved?

[fossil pecan]

what do you know about transversals?

[lone heart]

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[haughty gulch]

how is the controlled variable the material and absorption rate, but not pressure????

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[lime sluice]

Why this is wrong
Question: there are 5 horses we need to pick 2
What is the probability of choosing the winning horse?

[lime sluice]

But if i see directly we know that 5c2 total outcomes

Suppose 1 horse wins 2nd loses and 1 loses 2nd wins so 2 outcomes probablity will be 2/10 which is 1/5

[old heath]

the second horse can lose in 4 ways tho

5c2 total outcomes yeah

lets see favourable outcomes

so one of them has to win

in 5c2 how many times does a particular horse appear?

go from here

[lime sluice]

See

[old heath]

this

doesnt count

how many ways

[lime sluice]

Total 10

[old heath]

the horse can win

[lime sluice]

2 favourable

[old heath]

its not 2 favourable

[lime sluice]

Then?

[old heath]

try this

[lime sluice]

1 wins 2nd loses
1 loses 2nd wins

[old heath]

ok

but the second horse has 4 choices

in both cases

[lime sluice]

How? Elaborate

[old heath]

the losing horse

ok so first horse wins

second horse loses

the losing horse

can be any of the other 4

yes?

[lime sluice]

You meant 1 wins 2 lose, 1 wins 2nd lose ?

Like this

Ohh yes same

[old heath]

no im taking your cases

you selected 2

the first one wins

second loses

[lime sluice]

I meant like that

[old heath]

the winning one is fixed

however

the losing one has 4 favourable outcomes

[lime sluice]

W1 L2
W1 L3
W1 L4
W1 L5

[old heath]

yea

like that

[lime sluice]

L1 W2
L3 W2
L4 W2
L5 W2

[old heath]

no now youre repeating

yeah

so 8

out of 20

[lime sluice]

Yes

[old heath]

20. because

youre takiing first and second

[lime sluice]

8/20 =2/5

[old heath]

so choose and arrange

yes

[lime sluice]

So both of my answers were incorrect

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[cursive sluice]

can somene explain what nmumber 2 is asking me

rational function is quotient right

how does thaat even

[young finch]

rational function means it can be represented as a fraction of two integers

independent variable is the one you change dependent variable is the one changed by the independent variable

well you wouldn't be changing it

so I guess x would be indepdnent y would be dependent thinking of a normal function like y=mx+b

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[cursive sluice]

What kind of variation is this?

what is a variation

never even heard of this

[cursive sluice]

ty

[young finch]

not really sure

[hushed locust]

that's a rational number. a rational function is a fraction of two polynomials

[cursive sluice]

yeah

This is an Inversely Proportional relationship or an Inverse Variation.

thats whats the answer is

what is variation tho if anyone knows

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[long topaz]

,rotate

[long topaz]

is my working correct?

[near apex]

What's the formula for average velocity?

Part 1 is correct.

[tardy tapir]

server's really getting occupied by physics lol

[long topaz]

displacement/elapsed time?

[near apex]

What's the total displacement of the boat?

[long topaz]

sorryyyy idk where can i get help😭

[long topaz]

ohno is it 0?

[near apex]

Yes

[long topaz]

but is it logical for the average velocity to be 0?

[tardy tapir]

yeah

not for speed tho

[long topaz]

i see

[near apex]

Yes. For velocity.

[long topaz]

but what about the direction?

or it dne?

[near apex]

Direction of what?

A zero vector doesn't have a direction.

[long topaz]

a velocity must have a direction right?

[near apex]

.

[long topaz]

ahh ure right

[near apex]

In general, it should. For zero, it doesn't.

[long topaz]

i see, thanksss

.close

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[teal ore]

Can someone pls help with c

[minor needle]

,rccw

[tardy tapir]

write x in terms of y

[minor needle]

multiply by x, then collect by terms and take out x

[teal ore]

If I times by x does the numerator also disappear?

[minor needle]

no

just the denominator on the RHS cancels out

[teal ore]

Okayy

So rn I have

xy=2x-2a

[minor needle]

yup

move the terms containing "x" to the one side

[teal ore]

xy-2x=-2a

That right?

[minor needle]

factor common term on the LHS

which is x

[teal ore]

Lhs?

[minor needle]

Left Hand Side

[teal ore]

So divide by 2

?

I mean y

[minor needle]

no, take out "x", like ab + ac = a(b+c)

[teal ore]

How do I do that

??

[left isle]

you have an x in both of the terms on the LHS, right?

xy-2x

[teal ore]

Yess

[left isle]

now place it in parentheses so you have (xy-2x)

now place the x on the outside of the parentheses and remove the x's from the inside of the parentheses.

what do you get

[teal ore]

x(y-2)

[left isle]

perfect. you've just factored out x.

[teal ore]

No I divide by x(2-y)?

[left isle]

you now have x(y-2) = -2a

and you want x to be by itself

so what should you divide both sides by to get x by itself

[teal ore]

(2-y) i mean

[left isle]

(y-2)

but yes

so divide both sides by (y-2)

now what is x

[teal ore]

X=-2a / y-2

[left isle]

great!

[teal ore]

Can you help me with another one?

[left isle]

sure!

[left isle]

so x^2-36 looks really nice. do you think you can separate it into two factors? something like (x-a)(x+b)?

[teal ore]

Yes

[left isle]

okay so what does your denominator look like now

[teal ore]

I’m quickly working on it

[left isle]

yea no rush

[teal ore]

(X+6)(X-6)?

[left isle]

yep!

it's a difference of squares

okay so now, take what we learned before and factor an x out of the numerator

[teal ore]

Okayy

So numerator is just x?

[left isle]

no. factor an x out of x^2-6x

[teal ore]

X-6?

[left isle]

you have (x^2-6x), and factor out the x

so you'd end up with x(x-6)

[teal ore]

I thought we’re on the denominator?

[left isle]

no you finished the denominator with (x+6)(x-6)

[teal ore]

Okayyy

[left isle]

i then asked for you to factor an x out of the numerator

[teal ore]

Ohhhhhh

Okayyy I get it

It’s x(x-6) like you said

[left isle]

right. okay and the denominator is
(x+6)(x-6). is there anything we can simplify from here?

[teal ore]

We can take away (x-6) on top and bottom

So it’s then

[left isle]

right

[teal ore]

X/x+6

[left isle]

yep!

[teal ore]

Ahhh I seee thanksss

[left isle]

no problem

[teal ore]

.close

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[shy grove]

Hello,everyone!

[left isle]

Did you have a question?

[wild trail]

[shy grove]

Why i can't send it?

[weary wyvern]

l'hopital

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@shy grove Has your question been resolved?

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[mint oxide]

Can someone please explain to me the difference between "one-to-many” and “many-to-many” relations? I am a bit confused because they are both considered as a function and many-to-many has alot of it's domains paired to similar ranges and vice versa? And as far as I know it is not considered a function when domains share similar ranges and vice versa...

I just need an explaination and clarification because it is genuinely confusing for me.

[mint oxide]

.close

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[simple saddle]

min value of quadratic equation can be found from -D/4a is it also used for finding max value too? (parabola down facing)

[wise dirge]

what is -D/4a?

[echo socket]

-D/4a is either the max/min value depending on the sign of a

[simple saddle]

ok understood

[echo socket]

D = b^2 - 4ac and a, b, c are the coefficients of x^2, x and 1 respectively

[simple saddle]

like in this quest they were asking

its will be zero right

@echo socket

[echo socket]

Yeah, the minimum value of x^2 - 16x + 64 is 0

[simple saddle]

thanks

.close

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[worn lark]

how do i add a number below the bracket $\underbrace{abc}$

[ocean seal]

Kaiyan

[junior idol]

use underscore

$\underbrace{abc}_{=def}$

[ocean seal]

DAILI

[worn lark]

oh

thanks

.close

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[azure tapir]

hi

[azure tapir]

$\left(\frac{2x^2-x^3}{\sqrt{x}}\right)$

[ocean seal]

Sunset

[azure tapir]

can i get some help with dy/dx this problem

[vale wigeon]

is there meant to be anything outside the ()?

anyway simplify that fraction before differentiating

[azure tapir]

no

is just

$\frac{2x^2-x^3}{\sqrt{x}}$

[ocean seal]

Sunset

[vale wigeon]

anyway simplify that fraction before differentiating

[azure tapir]

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

[ocean seal]

Sunset

[azure tapir]

done

[vale wigeon]

this is half halfway to the simplification i had in mind and half not

would have been simpler to just write this thing as $2x^{3/2} - x^{5/2}$

[ocean seal]

Ann

[azure tapir]

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

[ocean seal]

Sunset

[azure tapir]

$2x^2-x^3 = 2x^{\frac{3}{2}}$

[ocean seal]

Sunset

[azure tapir]

?

can you help example how you simplify

[iron sinew]

you can separate the fraction

[azure tapir]

lets go

[iron sinew]

and attempt to simplify each one first

[azure tapir]

oh\

i see

ann left me

lol

[iron sinew]

2(x^2)/sqrt(x) -x^3/sqrt(x)

[azure tapir]

$\frac{2x^2}{\sqrt{x}}\cdot \frac{x^3}{\sqrt{x}}$

[ocean seal]

Sunset

[azure tapir]

like this

[iron sinew]

yeah

wair not multiplication

substraction

[azure tapir]

yes i see

[iron sinew]

anyways the first expression

2(x^2)/sqrt(x)

can you think of any way of getting rid of the denominator

[azure tapir]

$2x^2\cdot x^{-\frac{1}{2}}:-x^3\cdot :x^{-\frac{1}{2}}$

[ocean seal]

Sunset

[azure tapir]

is this correct way of simplifying it

[iron sinew]

you can simplify further

in both expressions you have the same base

what does that mean for the exponents?

[azure tapir]

add

[iron sinew]

yes

[azure tapir]

$2x^{1.5}:-x^{2.5}$

[ocean seal]

Sunset

[iron sinew]

Correct!

[azure tapir]

now we dy dx

[iron sinew]

yes i assume you know the power rule

[azure tapir]

$3x^0.5 -2.5x^1.5$

[ocean seal]

Sunset

[azure tapir]

that printed out wrong

$3x^(0.5) -2.5x^(1.5)$

[ocean seal]

Sunset

[iron sinew]

yeah but i see what you were trying to type

[azure tapir]

thats good

[iron sinew]

$3(x)^(1/2)-2.5(x)^(3/2)$

[ocean seal]

lotus man

[iron sinew]

this bot is useless lol

regardless its correct

[azure tapir]

lol

i got another one

i feel like is the same

$\frac{3}{4x^2}$

[ocean seal]

Sunset

[iron sinew]

hm

have you tried to do it

[azure tapir]

i will try now and tell my answer

[iron sinew]

once you're done make sure to show ur work

[azure tapir]

okey

i got this

$\frac{3}{4}\cdot \frac{3}{x^2}$

[ocean seal]

Sunset

[iron sinew]

hm

how did you go about doing it

[azure tapir]

$\frac{3}{4}\cdot 3\cdot x^{-2}$

[ocean seal]

Sunset

[wary stream]

Btw you need curly brackets for exponents

[azure tapir]

thx

[iron sinew]

where did u get the 2nd 3 from

[azure tapir]

?

oh

well

i split like the one before

$\frac{3}{4}\cdot \frac{1}{x^2}$

[ocean seal]

Sunset

[azure tapir]

should it be like this

[iron sinew]

we split the last one because it made it easier and we could; in this example there is only one term and therefore no reason to attempt to separate the fraction

yep; now you can apply the power rule

[azure tapir]

already?

dont i need to simplify more

[iron sinew]

you can if you want to

just rewrite (1/x)^2 in terms of x

[azure tapir]

$\frac{-6x^{-3}}{4}$

[ocean seal]

Sunset

[azure tapir]

i will filp to make the top positive

$-\frac{2}{3x^3}$

[ocean seal]

Sunset

[iron sinew]

correct

[azure tapir]

lets go

thank you for the help i really appricate it

https://tenor.com/view/hollow-knight-gif-26279280

i will close now

.close

[lone heart]

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[granite rapids]

Daniel takes out a loan of $30,000 to renovate his house. The loan has an annual interest rate of 7%, compounded half-yearly. He plans to make fixed monthly payments of $600. Calculate the remaining amount due on the loan after 5 years.

[granite rapids]

the answer is 3231.43, however, i am getting 6886.47

could someone help?

[latent dawn]

Hi I need help with logarithms

[tired bone]

Hi i need help with 0+1

i think its 2

out of 0+1

[lone heart]

Please read #❓how-to-get-help

[lone heart]

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

@granite rapids Has your question been resolved?

[lone heart]

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[steep pike]

Can someone explain whats happening here?

[steep pike]

Is the 'dagger' simply the complex conjugate?

[tiny cipher]

transposed conjugate

[steep pike]

Ok, so i transpose the matrix

And then swap the signs in front of the i's?

[tiny cipher]

yes

[steep pike]

Ok thanks @tiny cipher

.close

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[zinc portal]

Hello looking to voice call someone

[zinc portal]

i am very funny

but i need help with math

D:

[mossy siren]

yh sure where is ur question

[zinc portal]

Do you wanna call because im losing my mind but i can type if not

[mossy siren]

sure

bro was just rambling on, didn;t even have a question?

[zinc portal]

no i do

i need to know what the 23.78 infers about randomness

chatgpt said it does but swear it doesnt

actually maybe it just doesnt

[mossy siren]

No It doesn't mean has nothing to do with randomness

hope that helps

[zinc portal]

but does median because its the middle of the dataset

0- 5 is 2.5 median

random

[wary stream]

Don't use chatgpt to do math

[zinc portal]

idk im literally innumerate dropped it in yr 10 and got straight Ds was panicked

thought it could probs do numbers

glorrified calculator

[wary stream]

Chatgpt is trash with math

[zinc portal]

u think with the knowledge of the universe or whatever it wouldnt be so shit lol

[wary stream]

I never said it was trash at everything, I said it was trash at math

[zinc portal]

ya ik but its still poor on its behalf

ok byebye

[wary stream]

Did you have a math problem, if so post it

[mossy siren]

no bro this guy just talks

I was on a call with him for 15min and he didn;t even ask a question

[lone heart]

@zinc portal Has your question been resolved?

[lone heart]

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[long panther]

Some clarification on trigonometric graphs

If x = 30, you would move 30 along the x axis and look to the y value that corresponds to that x, and that would be the value of sin(x)

Then when you have a question of sinx = a you are looking for all the values of x which give a y value of a?

So if I knew what a was and I drew it, I would be looking for all the x values that intersect with the line a

[lone heart]

@long panther Has your question been resolved?

[rustic coral]

Yeah, you're looking for the intersections of the graphs of y=sin(x) and y=a

[lone heart]

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[long panther]

is sin(x-90) the same as -sin(90-x)

[iron sinew]

yes

[long panther]

ok thanks

.close

[lone heart]

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[long panther]

does that also apply to cos

.reopen

[iron sinew]

no

[lone heart]

✅

[long panther]

hmm howcome

oh beacuse

cos x = cos-x

[iron sinew]

yes

[safe spindle]

Draw unit circle

Helps

[long panther]

.close

[lone heart]

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[dawn crest]

hello, how can i see if this succession has maximum or minimum? I know that in theory, when it converges and it exists a result of it bigger/smaller than the one it converges to it has maximum/minimum, but i dont know how to apply it in practice

[open warren]

first of all, is it monotonic? if yes decide whether it gets bigger or smaller with n -> inf. Only then you can try find limit

Simply enough you can do in other direction if n -> 0 in which you get infinity

[lone heart]

@dawn crest Has your question been resolved?

[dawn crest]

got it, but once i find out its monotony how do i understand if it has a maximum or a minimum?

[open warren]

if it is monotonically decreases then for x<y => f(x)>f(y). If you find that for infinity it gets to that value then it's the minimum

[dawn crest]

youre right, i didnt think of that :) thank you sm!

.close

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[slender sun]

what is a theorem from algebra who converse is not valid

[iron sinew]

what do you mean by converse?

[echo socket]

Converse of p -> q is q -> p

[iron sinew]

first thing that comes to mind is derivability and continuity

[echo socket]

Not sure if that's meant under 'algebra' though

[slender sun]

I don't think I learned that yet

[iron sinew]

oh alright

[last ether]

The opposite

[modern sedge]

if a = b and c = d then a+c = b+d

[last ether]

So basically "if then A then B" is valid but "if B then A" isn't

[golden canyon]

I mean, x > 2 implies x > 0, not sure if it is a theorem

[last ether]

Pretty that's just set stuff

[iron sinew]

x>0 implies x^2>0

[last ether]

They want a theorem though

[iron sinew]

the other way doesn't always work

[last ether]

I know one

Wait nvm

I stupid

[modern sedge]

well fundamental theorem of algebra works too, if f(x) is a polynomial then it has at least one complex root

the converse, if f(x) has at least one complex root then f(x) is a polynomial wouldnt be true

[last ether]

Well actually

[iron sinew]

they said they haven't learned continuity and derivability

[last ether]

Geometry is filled with such things

[iron sinew]

i doubt they know this theorem

[slender sun]

I know this one

thank you!

[iron sinew]

i stand corrected lol

[last ether]

But if a shape is a rhombus then the diagonals are perpendicular, but perpendicular diagonals themselves do not mean that the shape is a rhombus

A square has all right interior angles but right interior angles themselves do not mean the shape is a square

[slender sun]

thank youuu

.close

[lone heart]

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[last ether]

Just google a bunch of geometry theorems lol

[lone heart]

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[crimson basin]

this is literally algebra 1 or smth but I need help with it 😭

[rose sigil]

mixed numbers ☠️

[crimson basin]

💀

[dense bridge]

As I prepare to enter grade 10, I'm determined to elevate my math skills to new heights. While I currently don't feel entirely confident in my math abilities, I'm eager to change that. My aim is to become adept at mental math, tackle challenging problems well above my current level, and build a solid foundation for advanced learning.

I'm reaching out to this community for guides, resources, and tips that can help me achieve my goal. I'm particularly interested in eventually delving into calculus ahead of schedule. If you have any recommendations – whether it's strategies for enhancing mental math, book suggestions, online courses, or other resources – I'd be grateful for your insights.

My aspiration is to not just catch up but to forge ahead, and excel in math beyond what's expected at my level. Thank you for your time and any support you can provide. I'm excited to learn from your experiences and knowledge as I work towards my goal.

[crimson basin]

.

[undone ledge]

wrong channel.

[tacit arch]

are you chat gpt

[undone ledge]

wrong server .

[modern sedge]

try #chill or #discussion

[crimson basin]

can anyone help tho

please .-.

[undone ledge]

try using elemination method

to find x and y

[crimson basin]

I tried that x-x

[undone ledge]

which method have you overlooked

lemme check brb

[lone heart]

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

[undone ledge]

share your work perhaps

ah

.

[crimson basin]

it would be -x-4y=-5 after you eliminate

what do you do next tho

[undone ledge]

??

[crimson basin]

how do I isolate one letter or the other

[undone ledge]

elimination reffers to eleminating one whole term

be it x or y

completely

to do that try to see what you can perhaps multiply or devide to get result matching the expectations of elimination method

i.e. one term

*divide

[crimson basin]

is this wrong

I thought that was the first step

[undone ledge]

its not wrong, but it wont help in the solution

[crimson basin]

.

idk what I'm doing

[undone ledge]

hm lets see

can you see what i did here

(random equation to explain not yours)

[crimson basin]

uhm

[rose sigil]

graphing the lines like it seems to want you to would also work if you have never seen what weirdo is doing

[ruby seal]

It's convenient to know the rules of elimination

Do you know the rules of elimination?

[undone ledge]

you should revise linear equation in two variables as a topic

[crimson basin]

I know how to eliminate when both equations of variables are isolated

if that makes sense

[undone ledge]

you wanan try with graph?

or you can try substitution

substitution would be easier to understand, but once you are thorough with elimination method , you can do these questions much easily

[ruby seal]

One tip is to more about thinking on which equation to multiply and by what to multiply so that once equations are added one variable will eliminate allowing to easily find what one of the variables should be

[crimson basin]

oh wait .-.

I could try that

tbh

[ruby seal]

To me substitution is harder

[ruby seal]

Take a look at the coefficients of your two equations

[undone ledge]

yeah it is lenghthy but is generally easier to impliment and get a solution

wrong chat mb

[crimson basin]

yes I see

[ruby seal]

Anyway i'm bad at teaching people so maybe listening to weirdo is better

All i can do now is show you directly how to solve it

[undone ledge]

na na go on

[ruby seal]

Or should i say how i solved it*

[undone ledge]

i kinda have to go rn

[ruby seal]

Wait

[undone ledge]

i need to do calculus worksheet...

[ruby seal]

I need help too

[undone ledge]

oh sup

[ruby seal]

I got a question

I concluded that if the quotient of two real sequences is convergent, then their product is also convergent

I'm not sure whenever that is true

But what i want to know is if whenever lim(x_n/y_n) exists then does that imply the existence of lim(y_n) ?

[undone ledge]

i havent studied sequence and series yet, but i dont think the conclusion is right.

[ruby seal]

Yeah

Seems sketchy

But the manipulations on inequalities show otherwise

And if it ends up being true i can propose a solution to a much harder problem

[undone ledge]

tbh idk

[ruby seal]

I can show you how i got there

It's quite easy

[undone ledge]

in my cource would be studying series and sequence in phase 3 ( 3-4 months)

really dont know what you are talking about

[ruby seal]

Oh

Alright

[undone ledge]

yeah sorry about that

[ruby seal]

Well im not gonna take more of your time

Cya and gl

[undone ledge]

na its alright

[ruby seal]

I will handle the rest

[undone ledge]

thanks

[ruby seal]

Got it now?

[undone ledge]

gl

[crimson basin]

yeah

[undone ledge]

w

[crimson basin]

tyty

how do I close this .-.

oh I see

.close

[lone heart]

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[halcyon grove]

how would i simplifiy x^-3/4

[ebon sparrow]

using the negative exponent rule

[halcyon grove]

and after that?

[ebon sparrow]

thats it

[lone heart]

@halcyon grove Has your question been resolved?

[halcyon grove]

it wont get more simplified?

after 1/x^3/4

[ebon sparrow]

ye

,w simplifiy x^{-3/4}

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by kensukeken

[ebon sparrow]

@halcyon grove

[halcyon grove]

will 1/x^3/4 not be = (x^3) / 4

[lone heart]

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[native cloud]

$\frac{ax-1}{1-bx}=\frac{a\left(x-\frac{1}{a}\right)+k}{-b\left(x-\frac{1}{b}\right)}$

[ocean seal]

LE SSERAFIM

[native cloud]

How do I find the value for k?

[tacit arch]

algebra?

the equation is of the form
$\frac{p}{q} = \frac{r + k}{s}$

[ocean seal]

riemann

[tacit arch]

multiply both sides by s, subtract r

[native cloud]

I'm dumb

Sorry, I still don't understand

<@&286206848099549185>

[clear hollow]

Ok, I can see the simplified problem

First what u do is multiply both sides by s, so you dont get a fraction

[native cloud]

s?

What's s in my equation?

[clear hollow]

p/q = r+k/s

Right?

Wait I can only see the one that riemann sent

[native cloud]

...?

[clear hollow]

Which equation

[native cloud]

^

[clear hollow]

Sorry this will take me time to figure out

[exotic belfry]

resolve the brackets in -b(x-1/b). what do you get?

[native cloud]

1-bx..?

[exotic belfry]

yes, isnt it the same as on the left side?

[native cloud]

Yes

[exotic belfry]

can we then ignore it?

[native cloud]

Ignore? wdym?

[exotic belfry]

x/b = y/b -> what does this mean for x and y?

[native cloud]

Common denominator

[exotic belfry]

yes, but what can you say about x and y then?

[native cloud]

idk tbh

[exotic belfry]

if x/b = y/b, multiply both by b so you get x = y.

[native cloud]

Ohh yea

[exotic belfry]

so now we have ax-1 = a(x-1/a)+k. again resolve the brackets, what do you get?

[native cloud]

I don't understand where the k comes from

[exotic belfry]

hmmm, its your question!

[native cloud]

I really don't understand what you're trying to imply

[exotic belfry]

do the same you did before for a(x-1/a)

[native cloud]

k = 1?

[exotic belfry]

what do you get for a(x-1/a)?

[native cloud]

ax-1

Oh wait

MB

[exotic belfry]

so you have on the left ax-1 and on the right ax-1+k

[native cloud]

k = 0

Huh?

[exotic belfry]

any question left?

[native cloud]

Uhh no

Thanks for helping!

.close

[lone heart]

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[dawn crest]

im trying to use wolfram to understand how to do a limit and it gave me this result at the end. isnt it an indeterminate form? D:

[dawn crest]

this is the function, its supposed to give -infinity as x approaches -infinity but i dont get how

And this is what I did

[civic stream]

you should analyze the 2 halves of the function seperately

so take the limit for x^5 - 3 and e^(1-x^3)

[dawn crest]

did that

[civic stream]

yeah so it works out to positive infinity* negative infinity

which is just negative infinity

[dawn crest]

oh so its not indeterminate?

[civic stream]

no

[dawn crest]

i must have gotten confused with infinity -/+ infinity

thank you :D

.close

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[lone heart]

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[plain zodiac]

how do i solve this trig identity im completely lost

[vale wigeon]

could write everything in terms of sin and cos

[plain zodiac]

what do i do with the tan when i make it sinx/cosx? i dont know what to do with it after

[tardy stag]

common denominators

[vale wigeon]

you have $\frac{\frac{s}{c} - s}{s^3} \overset?= \frac{1/c}{1 + c}$

[ocean seal]

Ann

[vale wigeon]

using the pro gamer move of abbreviating sin(x) and cos(x) as s and c to reduce the number of letters you need to write

[plain zodiac]

yeah but from here how do i get rid of the sinx/cosx and the 1/cosx?

im assuming thats the next step

[vale wigeon]

well you might wanna simplify each side separately

and in each case you may want to get rid of the skyscraper fractions first

[tardy tapir]

actually, just simplify the LHS

[plain zodiac]

yeah im trying to focus on the LHS but im at this part and i dont know where to go from here

mostly because i dont know how to deal wtih the sinx/cosx

[tardy tapir]

cancel a sinx

[vale wigeon]

do you know how to deal w/ skyscraper fractions

or nested fractions

[tardy tapir]

and take LCM

[plain zodiac]

no

[sharp moat]

Factorize with sin and transform sin^2 to 1-cos^2

[plain zodiac]

wdym

[plain zodiac]

its a sin^3x how do i get rid of one of them

[sharp moat]

With the sin you factorized

[young finch]

you know how to combine the fraction in the numerator right

[plain zodiac]

what does factorizing a sin mean

[plain zodiac]

common denominator it?

[sharp moat]

it’s making the expression more neat in this case
sin(1-sec) is just the numerator of your expression

[plain zodiac]

how do i get from

to

i understand how to solve the question from here

but i just dont know how to get to

[lone heart]

@plain zodiac Has your question been resolved?

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[lone heart]

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[olive ice]

How do i visualize this sort of thing?

[olive ice]

I've found the points A, B, and D, but i forget how to visualize it..

how would i know whether a vector like AC and BD are parallel or AB and CB are parallel

I guess i can just take the dot product to check right?

[azure needle]

send full question

[olive ice]

if it is 0, it implies they are parallel

[hushed locust]

dot product being 0 would imply the opposite, that they are perpendicular

[olive ice]

oh. right...

[olive ice]

yeah idk how i forgot that, i blame it on it being my bedtime

so this is the question... i dont know how it helps really but there you go lol

[olive ice]

How about this? I check the magnitude of AB, AD, BD,

which ever ones have equal magnitude, it means they are parallel

since the question says that it forms a parallelogram

[hushed locust]

they would be parallel if the cross product gives the 0 vector

[olive ice]

hmm, i take the triple determinant

and i multiply the middle square by negative

[olive ice]

i will do this, but is what i said correct above?

anyway thanks

.close

[lone heart]

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[hushed locust]

currently you have a triangle so none of them are parallel

[lone heart]

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[tender delta]

Apologies for the messy formatting but I just wanted to check if my answer was correct

[tender delta]

i think my sigma notation isnt correct here

but idk where

[iron sinew]

n starts at 0 i think

check if that works

[tender delta]

the answers are diffrent but ever so slightly

[iron sinew]

by decimals?

[tender delta]

yea

also shouldnt n always be starting at 1?

[iron sinew]

brb

[tender delta]

or like in this instance

[iron sinew]

nah cuz you have to account for the first drop

the full 16 cm

[tender delta]

gotcha

[iron sinew]

feet*

i think the formula you used is incorrect i just need to check real quick

[tender delta]

alright

Sn=a1(1-r^n)/(1-r)

thats what im using

[iron sinew]

it should be r^(n-p+1)

[tender delta]

whats p

[iron sinew]

with p being the starting value of n

in this case 0

[tender delta]

yea thats it

but how come the formula i wsa using is incorrect

unless i wasnt paying attnetion in class or i missed something it shouldve been right

[iron sinew]

i think yours assumes the starting value is alwats 1

[tender delta]

ooh

yea that makes sense

[iron sinew]

really cool exercise btw

[tender delta]

its for my precalculus summer course lol

[iron sinew]

just remember: Sn= a(p)* (1-r^(n-p+1))/1-r (p starting value of the series)

[tender delta]

alright thank you

[tender delta]

wait but if its a(p) then wouldnt the entire euqation be 0

because we are starting at 0

[iron sinew]

a(0) in this case is 1y

16

16 * (1/4)^0 = 16

[tender delta]

i dont think i get it

[iron sinew]

alright

this is a geometric series

[tender delta]

yea

[iron sinew]

the expression you chose is 16* (1/4)^n

[tender delta]

mhm

[iron sinew]

i think i was confused too

your first answer is actually correct but the expression for the series is off

[tender delta]

1365/64?

[iron sinew]

if we wanted to evaluate it starting at 1: the expression is 16*(1/4)^(n-1)

[iron sinew]

yes

[tender delta]

so then a1 is 16

oh yea wait i see it

[iron sinew]

yeah

[tender delta]

that was my original expression but i overthought it

and erased it

i was overanalyzging the part hwere it says rebound

i assumed we were looking at only the part when it rebounds

[iron sinew]

yeah its kinda vaguely wordes

worded*

sorry if i caused any confusion

[tender delta]

its all good

[iron sinew]

do u have any more questions

[tender delta]

i dont think so

[iron sinew]

then type .close to free up the room

[tender delta]

.close

[lone heart]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[marsh kelp]

how do i solve x' = 4x + 2t

[tacit arch]

is x' = dx/dt?

[marsh kelp]

yes

[tacit arch]

https://tutorial.math.lamar.edu/classes/de/Linear.aspx

[alpine sable]

Do you know how to solve differential equations by means of the integrating factor?

[marsh kelp]

yes

i think im just blind

wait that link is interesting

do i just make up μ(t)

you know i take that yes back

[molten pivot]

just use the characteristic polynomial

then undetermined coefficients for the particular solution

[lone heart]

@marsh kelp Has your question been resolved?

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[patent topaz]

i have 4 solutions on the complex plane, 2 representing the sqrt of a -ve number and the other 2 representing a real number \pm i. how would i derive the equation?

[dark star]

hello?

anybody here??

[patent topaz]

hi,yes

so hi, yeah, i'm trying to come up with the polynomial that results in 4 solutions but i think what's throwing me is the fact that 2 of them have no x component

<@&286206848099549185>

[grave quartz]

!show

[lone heart]

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

[west girder]

just post the original q

[patent topaz]

points are 0\pm2i, 2x\pmi. diff of squares leads to (0-4i^2)(4x^2-i^2)=4(4x^2+1)=0

[grave quartz]

I don't get what that means please latex or picture

[patent topaz]

sorry, hold up

$$(0,2i)\(0,-2i)\(2,i)\(2,-i) are solutions on the complex plane to an eq with real coefficients. Find the polynomial equation.

[grave quartz]

U need $$ after

[patent topaz]

$$(0,2i)\(0,-2i)\(2,i)\(2,-i)$$

[ocean seal]

WayneTundra

[west girder]

do you mean 0 \pm 2i?

[grave quartz]

right so we have $2i,-2i$ what can you tell me about these?

[west girder]

and 2 \pm i

[ocean seal]

SWF ;)

[patent topaz]

$\sqrt{-4}$

[ocean seal]

WayneTundra

[grave quartz]

not what I was getting at