help-10

[frosty shale]

I’ve looked through my math book and can’t find anything about even or odd functions

[obtuse pebble]

@frosty shale Has your question been resolved?

[obtuse pebble]

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[green plank]

Hello, how do I factor x^4 -13x^2 + 40

[trail cliff]

Hello!

[green plank]

hi

[trail cliff]

so what have you tried so far

[green plank]

13 is prime

so no numbers

no variables

in common

and cant group by factoring

idk what to do

i cant use any special products

[dark mango]

factors of 40

that add to give -13

@green plank

[green plank]

-8, -5

[dark mango]

(x^2-8)(x^2-5)

[green plank]

but then i get
z(z^3-8) -5(z-8)

i cant factor z^3 with z

sorry i mixed z with x

[green plank]

how

[dark mango]

huh

factors of 40 that add to -13

its the same as a quadratic but just change to x^2

[green plank]

yea

[dark mango]

cuz u have a x^4 x^2 and x^0 term

[green plank]

z^4-8z-5z+40

but if i factor wont i get

[dark mango]

what

[green plank]

z(z^3-8) -5(z-8)

[dark mango]

z?

[green plank]

sorry

[dark mango]

im not sure where u getting this from

[green plank]

its z

i put x before

its just a variable

[dark mango]

yea i meant hte equations ur showing

[green plank]

wait a sec

[dark mango]

ur factoring this x^4 -13x^2 + 40 ?

which is just (x^2-8)(x^2-5) ?

im confused how ur confused

[green plank]

AH

IM SORRY

IM DUMB

[dark mango]

lol

[green plank]

i just realized

thx for ur time

[dark mango]

no worries

[green plank]

.close

[obtuse pebble]

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[teal smelt]

how would i evaluate 3pi/2 - pi/2(4/5)

[dark mango]

is it 2 * (4/5)

or (pi/2) * (4/5)?

[teal smelt]

2(4/5) is the denominator

[dark mango]

so (3pi/2) - (pi/1.6)

[teal smelt]

yes

[dark mango]

you can just make them have common denominators of 8?

then subtract

[teal smelt]

ty

[obtuse pebble]

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[rough glacier]

how would i do that

.close

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[teal smelt]

I would like to know how to do i)

[teal smelt]

and what steps i should take to solving it

[trail cliff]

So

we know every 4 seconds one cycle is taken

so its ?=4t

then its the amount of air left per 4 seconds=4t

@teal smelt so ?v=4t

[teal smelt]

would the 2200 ml not matter?

im supposed to graph it as a trig function after

im seeing the 2200 as a vertical shift of +2200ml bc theres always 2200 left

after inhale and exhalee

@trail cliff

<@&286206848099549185>

[trail cliff]

$(2200)t/4$

[warm shale]

Bestower

[trail cliff]

is my idea

[teal smelt]

can you explain how you got to that @trail cliff

and how it would translate to a trig function

[trail cliff]

My idea was that every cycle produces 2200 ML of volume of air

each cycle is 4 seconds

tbh I am a little confused here and likely have gotten it wrong as now it looks incorect

I do hope someone is able to assist you here

[teal smelt]

<@&286206848099549185>

.close

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[severe verge]

i'm not sure if i'm doing this right ?

[obtuse pebble]

@severe verge Has your question been resolved?

[severe verge]

<@&286206848099549185>

[obtuse pebble]

@severe verge Has your question been resolved?

[severe verge]

<@&286206848099549185>

[severe verge]

<@&286206848099549185>

[obtuse pebble]

@severe verge Has your question been resolved?

[obtuse pebble]

@severe verge Has your question been resolved?

[rigid pine]

You performed the test to determine that the DE is exact correctly.
This means there exists some function f(x, y) such that f_x = 3x^2 - 4y^3 and f_y = y - 12xy^2.
To determine f, we can integrate f_x with respect to x as you have and f_y with respect to y as you have. But since calculating f_x from f(x, y) could eliminate terms of only y the constant of integration could be include terms of y. similarly for f_y.
Integrating M(x, y) and N(x, y) with respect to x and y, respectively, should lead you to x^3 - 4xy^3 + y^2/2 = c*.
I personally like to integrate M with respect to x and N with respect to y and then form a new function which contains all the terms of both.

[obtuse pebble]

@severe verge Has your question been resolved?

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[cobalt socket]

https://i.imgur.com/wqreF9P.png

[cobalt socket]

Particular solution using the Method of Undetermined Coefficients

got this

can someone double check?

had these for the homogeneous solution

meaning i dont have to do anything special

[obtuse pebble]

@cobalt socket Has your question been resolved?

[obtuse pebble]

@cobalt socket Has your question been resolved?

[obtuse pebble]

@cobalt socket Has your question been resolved?

[obtuse pebble]

@cobalt socket Has your question been resolved?

[viral blade]

why nothing special?

or well ig however you find a non-homogenous solution

but yeah that looks good for homogenous

[cobalt socket]

for if a solution already belongs to the homogeneous equation

u would get like y_p=kxe^2t for example

or a double root

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[bleak eagle]

How would I go about proving 10 part a? I know I have to do three cases where x is positive, negative and zero but I’m having trouble with the case where x is negative

[royal basin]

and what trouble are you having?

@bleak eagle

[obtuse pebble]

@bleak eagle Has your question been resolved?

[bleak eagle]

This is what I have but I don’t think it makes sense

[royal basin]

Using the definition of the absolute value of x, we hvae that |-x| = x.

no

that is just wrong lmao

[bleak eagle]

That’s what I’m saying!

[royal basin]

-x is positive, so |-x| = -x.

what you've written makes perfect sense and it's just false

[bleak eagle]

Okay for sure, but how can I adjust what I have? Should I just scrap it and try again?

[royal basin]

scrap it and try again.

[bleak eagle]

Okay!

Could I say |x|=-(x), and |-x|=-(x)?

Like this? Does this make sense? Lol sorry, I’m not sure why this is confusing me so much

[jade vault]

sure but in that case x<0

also note that |x|=|-x|

[bleak eagle]

Right, but that’s pretty much what I’m trying to prove, right?

[jade vault]

oh

so are you clear with the proof?

or are you confused somewhere still?

[bleak eagle]

Does that case in the picture above make sense? I’m pretty positive I have the other two cases down, but does that one for x<0 sound good?

[jade vault]

yep

it does make sense

[bleak eagle]

Okay cool, thank you!

.close

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[manic lintel]

re(z)im(z)=re(w)im(w)=p where p is a prime number and z and w are gaussian integers
a) find |z/w| b) supposed that |zw|=q where q is a prime number, find all possible complexx numbers z and w

[obtuse pebble]

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[manic lintel]

.close

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[distant rampart]

20. A jar contains only solid red and black marbles. The number of black balls is five times the number of red balls.
    Quantity I: The probability that a randomly selected ball from the jar is red
    Quantity II: 1/5

A-D)
I is greater than II
II is greater than I
I is equal to II
The information is insufficient

[distant rampart]

$\frac{r}{r+b} ,\ \frac{r}{r+5r} =\frac{r}{6r} =\frac{1}{6}$

But I don't know why this doesn't work

[warm shale]

dgh

[final thunder]

What’s the answer?

[distant rampart]

1/5 is greater than 1/6

[winter cargo]

let number of red balls be r
then black balls would be 5r
so, probability = possible outcomes/total outcomes = r/5r+r = 1/6

[final thunder]

Yeah but what’s the actual answer, you said it didn’t work

[winter cargo]

yeah then 1/6 < 1/5

its supposed to work rt?

[distant rampart]

$\frac{r}{r+b} ,\ b=5r\rightarrow \frac{\frac{1}{5} }{5+\frac{1}{5} } =\frac{1}{5} \times \frac{5}{6} =\frac{1}{6}$

[warm shale]

dgh

[distant rampart]

Is this correct?

Since b = 5r, then r = b/5

[rapid wagon]

that would make sense yes

[final thunder]

This doesn’t make sense

[distant rampart]

why

r = red, b = black

[final thunder]

How does b=5r imply the next statement

[distant rampart]

what's the probability of picking a red ball

i.e. r = b/5

[rapid wagon]

picking a red ball is 1/6 though?

[distant rampart]

$b=5r,\ r=?\rightarrow \frac{\frac{b}{5} }{b+\frac{b}{5} } =\frac{\frac{b}{5} }{\frac{5b+5}{5} }$

[warm shale]

dgh

[distant rampart]

$\rightarrow \frac{b}{5} \times \frac{5}{5b+5} =\frac{b}{5b+5}$

[warm shale]

dgh

[distant rampart]

and since b = 5r, we get

$\frac{5r}{5\left( 5r\right) +5} =\frac{5r}{25r+5} =\frac{5\left( r\right) }{5\left( 5r+1\right) } =\frac{r}{5r+1}$

[warm shale]

dgh

[final thunder]

Mistake here

[distant rampart]

hmm yeah

5b+b/5 right?

[final thunder]

Yes

[distant rampart]

$$b=5r,\ r=?\rightarrow \frac{\frac{b}{5} }{b+\frac{b}{5} } =\frac{\frac{b}{5} }{\frac{5b+b}{5} }$$

[final thunder]

It should simplify to 1/6

[warm shale]

dgh

[distant rampart]

$=\frac{\frac{b}{5} }{\frac{6b}{5} } =\frac{b}{6b} =\frac{1}{6}$

[warm shale]

dgh

[distant rampart]

okay thanks

[final thunder]

[distant rampart]

.close

[obtuse pebble]

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[timid silo]

does 5xy:15x simplify to

1. xy:3x
2. y:3
3. none of above

[distant rampart]

$\frac{5\cdot x\cdot y}{15\cdot x} =?$

[timid silo]

well, what do you think it would be?

[warm shale]

dgh

[distant rampart]

which factors cancel

[timid silo]

im assuming its y:3

because x cancels

and 1y:3 = y:3

true or flop

[distant rampart]

$\frac{5\cdot x\cdot y}{15\cdot x} =\frac{1y}{3}$

[warm shale]

dgh

[timid silo]

yep you are right

good job

[distant rampart]

Unless it's $\frac{15x}{5xy} =\frac{3}{y}$

[warm shale]

dgh

[timid silo]

cool thanks; i was away on the day my teacher taught this so im lacking LOL

don't be scared of the variables, they act the same way as normal numbers do

they always violate me💀

if you know 3 divided by 3 is equal to 1, then you can rest assured that x divided by x is going to be 1 too (except for when x=0 but don't worry about that for now)

LOL

thanks again

.close

[obtuse pebble]

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[lament atlas]

I am trying to prove this limit by selta epsilon notation

But can someome tell me why this is a proof

[royal basin]

,rccw

[lament atlas]

Ah sorry

I already have the proof

But i don t understand why

[royal basin]

well the second line is written indirectly

the subsequent lines are concerned with finding an n_ε that works

[lament atlas]

But what exactly should be the value of n_epsilon for it to work

[royal basin]

well if you want an integer then you can round 1/ε - 1 upwards

[lament atlas]

But that makes epsilon almost -1 right?

[royal basin]

no???

epsilon is an arbitrary positive number...

[lament atlas]

Omg

I see

It s a big nr

Right?

[royal basin]

1/ε is big yes

[lament atlas]

-1 makes it an integer?

[royal basin]

no

[obtuse pebble]

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[magic comet]

I'm confused about what this question is asking... what "space" is it talking about?

[magic comet]

this is the definition of connectedness we're using

and I'm not sure on which space is the topology imposed on

[royal basin]

...apparently constant maps don't exist

[magic comet]

sorry could you elaborate?

[zenith raft]

it doesn't even say continuous map lol

[magic comet]

yes...any idea what the question mean?🥹

[zenith raft]

it just means arbitrary space but I don't think the question was written correctly

[magic comet]

do you mean it's supposed to mean continuous maps?

[zenith raft]

probably

but that still doesn't fix it

it would make sense if it was "continuous surjective map" or something but I think it makes no sense as it is :c

[obtuse pebble]

@magic comet Has your question been resolved?

[zenith raft]

if the structure of the question is still unclear, another way to say it would be
"if X is a connected space then there exists no "map" from X to {0,1} with..."

[magic comet]

what would be the reasoning if the question was surjective continuous map?

oh, I guess if the question means the input space is connected then its trivial

hmmm

weird...okay I'll ask the instructor later🥺

thanks for the help!

[zenith raft]

np and sorry for that question

[magic comet]

.close

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[stiff harness]

Can someone give me some tips about this question pls

[stiff harness]

Q1

[obtuse pebble]

@stiff harness Has your question been resolved?

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[silver plover]

what does the prime symbol mean? ie j'

[old nymph]

in what context

[silver plover]

in general

in real analysis

[obtuse pebble]

@silver plover Has your question been resolved?

[novel knoll]

Derivative of j probably

[old nymph]

in terms of derivatives yes

also can have other meanings depending on how deep you get into real analysis ._.

[zenith raft]

it could also just be a variable name

[silver plover]

i was doing de morgans laws

and there was j'

didnt know what it meant

[novel knoll]

Sounds like complement of j then

[old nymph]

yeah

[novel knoll]

(And not much to do with real analysis)

[silver plover]

does compliment mean the opposite?

[old nymph]

google something first

[old nymph]

^

real analysis is totally different from this shit

[novel knoll]

Say your “Universe” is X then the complement of j is just all elements in X and not in j

[silver plover]

so compliment means 'not' then?

[novel knoll]

https://en.m.wikipedia.org/wiki/Complement_(set_theory)

[silver plover]

ok cool

thanks

[old nymph]

close the ticket if ur done

[silver plover]

.close

[obtuse pebble]

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[willow hare]

Hello
I have a problem where i need to show cuberoot of 3 is irrational.

I have assumed its a rational number and worked that 2p^3+p^3=g^3. However i dont think i can use fermats last theorem here since the 2p is not in brackets. Am i correct? If so how could i proceed?

[rigid lintel]

you dont need fermats last theorem

[willow hare]

It would have been nice

[rigid lintel]

well i mean would it

the proof is so advanced

imagine if all we could do to prove cuberoots were irational was to use fermats last theorem

that would terrible

[willow hare]

It works for cuberoot of 2

Anyway, other ways to proceed than fermat?

[kind hawk]

in the end it's a circular argument

fermat at some point needs that those roots are irrational

[wild swallow]

[kind hawk]

try to do the same thing as for the square root of 2

[willow hare]

Ok

[rigid lintel]

estimating how complicated the answer to a question should be is incredibly important

in the context of studying mathematics of course

in real life you have no clue

[wild swallow]

studying mathematics isnt real life

[willow hare]

Its my introductory course in my uni so i dont think i need to do anythink that crazy here

[kind hawk]

you dont

[wild swallow]

it might be the case that when using massive sledge hammer theorems

the proofs to those theorems assumed what you were trying to prove in the first place

and then you run into circular logic

[rigid lintel]

lmao

absolute classic

[royal basin]

something something rational root theorem on x^3 - 3

surely that ought to work

[kind hawk]

also not bad

[willow hare]

Would have been interesting to see if my professor would have caught that.

[kind hawk]

I wanted to throw eisenstein into the ring but that seemed a little overkill

[rigid lintel]

sounds like a sledgehammer ngl

[wild swallow]

the proof to rrt is basically the same argument you'd make

[royal basin]

not as much as fermat would

[willow hare]

.close

[obtuse pebble]

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[pure root]

hi

[next reef]

hello how are you

[pure root]

i am fine thx

i wanted to know about something

can you help me?

[next reef]

uhh

[rigid lintel]

[next reef]

lel

[pure root]

ye so first are equations and formula same?

[rigid lintel]

a formula is an equation

but an equation is not necessarily a formula

[pure root]

what is E= mc^2 an equation or formula?

[rigid lintel]

both

[old nymph]

lmao

[wild swallow]

[old nymph]

im not sure about their definition

An equation is made up of expressions that equal each other. A formula is an equation with two or more variables that represents a relationship between the variables.7 May 2022

google

w

[wild swallow]

7 May 2022

so basically formulae need variables ig

[pure root]

so i can do :
E = mc^2
E x 1 = mc ^ 2
E x (sin^2@ - cos^2@) = mc^2
sin^2@ - cos^2@ = mc^2 / E

omg

[wild swallow]

[rigid lintel]

sin^2 + cos^2

[wild swallow]

not if the sign is a - in the middle

[rigid lintel]

= 1

[pure root]

oh so sin^2@ = mc^2 / E - cos^2@

oh i thought i did a discovery smthing

[rigid lintel]

sadly

no

[pure root]

like you can have more energy at different slopes equation smthing...

[rigid lintel]

well your cos and sin are totally unrelated to the equation

you kind of just

multiply by 1

in a fancy way

[pure root]

oh

[rigid lintel]

sorry

[pure root]

can you say why does....

1 + 2+ 3+ 4 +... to infinity = -1/12

[rigid lintel]

i could try haha

but theres much better explanations on youtube than i could ever give

[pure root]

ye i saw someone mention this

this was made by a guy named RAMANUJAN

[rigid lintel]

ramanujan was a brilliant man

[pure root]

so that got me intrested in maths

[wild swallow]

ramanujan was so brilliant that his name is in caps

bruh

[rigid lintel]

bruh ramanujan lived to only 33

actually

32

[wild swallow]

short lived

v tragic

[pure root]

oh i wish he could live more

but if he lived more there will be butterfly effect and none of us would technically exist

[rigid lintel]

lol

facts tho

[timid silo]

Riemann zeta function of -1 would result in the 1+2+3+4... series. Normally the zeta function is bound to inputs above 1, but the analytic continuation of the function allows for negative inputs.
Evaluating this analytic continuation of the riemann zeta function at -1 would result in -1/12
It's a bit of a cheat, but it has some applications in physics and some subareas of math.

[pure root]

oh

[timid silo]

This is the riemann zeta function

[wild swallow]

@stable rain look

[pure root]

omg as a 10th grader i am speechless

[stable rain]

ew

no

[wild swallow]

youd know all about this

[stable rain]

so

this is what 10th graders do now?

[wild swallow]

yes

they study L-functions

[rigid lintel]

isnt the internet wonderful

[timid silo]

ζ(2) = π^2/6 btw, pretty fun

[rigid lintel]

i only study W-functions

L + ratio

[wild swallow]

[stable rain]

???

wat r L functions

[pure root]

no we study hmmm..... i guess the most complex thing i studied in maths till now is...

hmmm....

algebra one that something

[rigid lintel]

a meromorpohic function of the complex plane

🤓

[pure root]

Wait what was that equtaion called where there is d =+-root b^2 - 4ac / a2

[stable rain]

oh

LOL

[wild swallow]

theyre some bs

that you define with like

[timid silo]

Sounds like the Quadratic equation

[wild swallow]

infinite products

[stable rain]

qudratic formula

[pure root]

oh ye quadratic

math is easy but there is somthing called optional math that is hard

[stable rain]

ur formula is wrong btw

lol

[pure root]

wat

[timid silo]

Yeah it wasn't spot on haha but we got the spirit

[stable rain]

wow

u must b genius

[pure root]

ye optional math is a 400 page book

it has somthing like hmmm functions

[wild swallow]

wow

[pure root]

and sin theta cos theta

[stable rain]

what r those

[wild swallow]

if i had to read a 400 page book id make it optional too

[stable rain]

oh

[timid silo]

Complicated yet useless.

[pure root]

then i dont even knew sin @/2 existed

[stable rain]

..

[stable rain]

same

whats that

[pure root]

ye the teacher filled the whole board

[timid silo]

👀

[pure root]

the us and foreign students so lucky

[stable rain]

sounds like me finding partial derivatives

[stable rain]

wot

[pure root]

from their memes where they say 2+2 is hard

[wild swallow]

LOL

[pure root]

i think the most complex thing for them in bachelor is sets

[stable rain]

[wild swallow]

calculating 4 pages of partial derivatives when you can just do a 2 line computation

[stable rain]

sets

are pretty hard

[pure root]

no they very easy

[stable rain]

LOL

[pure root]

i just create my own formula somtimes

[stable rain]

u must be genius then

[stable rain]

amazing

[old nymph]

sets aint that hard tbh

[pure root]

no i still want to know more about it

[timid silo]

Same. Selfmade is almost always better quality as store-bought.

[pure root]

i am avrage ig

[stable rain]

wow

thats aweasome

im below average by like 15 points

[pure root]

yes like why learn them if your own using logic

[stable rain]

can u help me understand the

lines in graphs

[pure root]

yes

[stable rain]

im so lost on that rn

[pure root]

x and y is coordinates

graph is very easy

[timid silo]

[stable rain]

nono

like

i dont get what they mean

[wild swallow]

LOL

[stable rain]

equipotential or streamline

[pure root]

there are points in graph

[stable rain]

they form some weird line

but im confused

snow showed me some weird

[wild swallow]

go back to your own channel

[stable rain]

x and dots

D:

👽

well

this channel is like

for fun rn

LOL

[timid silo]

$\frac{x^{3}-27x+54}{-\frac{x^{4}}{12}+9x-20}$

[warm shale]

Jehare

[timid silo]

Nice graph

[pure root]

e

$\frac{x^{3}-27x+54}{-\frac{x^{4}}{12}+9x-20}$

[warm shale]

Umen

[pure root]

.close

[obtuse pebble]

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[wild swallow]

[stable rain]

the beast

who mastered set theory

n makes their own branches of maths

n formulas

[obtuse pebble]

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[vagrant dirge]

consider px^2 + (p-3)x + p = 0 where p is a real number
Find the values of p such that the equation has one (repeated) real solution

[vagrant dirge]

I am having trouble just understanding how to solve this

[royal basin]

find discriminant in terms of p, set equal to 0, solve for p.

[vagrant dirge]

Oh my gosh thank you

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[timid silo]

Hello

[timid silo]

I need some help

on the wuestion

x+2x+x=16

lol jk

x=4

umm

lemme send a screenie of the question

[ruby moth]

Ok. Can I help you?

[timid silo]

Here!

[ruby moth]

What did you try to do first?

Hello?

[old nymph]

yp

dont ignore this chat

[obtuse pebble]

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[placid totem]

The vectors are not perpendicular, is that correct?

since u*v=2

and not 0

[kind hawk]

=-2

but yes

[placid totem]

aight, thanks

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[lean garden]

Bit confused on how the interval (pi, 4] can be in the sigma-algebra generated from rationals in [0,10]

[kind hawk]

the rationals are dense

[lean garden]

so even if the open side of the interval starts from an irrational number because the rationals are dense we can just pick up there?

[old nymph]

💀

[lean garden]

idk

[kind hawk]

let q_n be a rational sequence that converges to pi from above

what can you say about the intervals (q_n, 4]

[lean garden]

i guess that (q_n, 4] would also converge to (pi,4]?

but that

it would just be rationals all the way

which are definitely suitable intervals we can pick for the sigma algebra?

the whole interval (pi, 4]?

[kind hawk]

(q_n, 4] are clearly in the sigma_algebra

[lean garden]

yep

[kind hawk]

so then also the union of those is

[lean garden]

yep

[kind hawk]

and the union is clearly (pi, 4]

[lean garden]

ah

that makes sense since the q_n converge to pi

thanks!

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[twilit dock]

Cuba drew the Rhomboid ABCD and the triangle XYZ. The length of side AB and the length of side XV are both equal to 6cm.
ABCD has a height Va of 3 cm. The content of the triangle XYZ is five times smaller than the content of the Rhomboid
ABCD. Calculate the height Vz of triangle XYZ

[obtuse pebble]

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[plain pine]

I need to use the bot, it will be quick

[plain pine]

$25^2 = (x+3)^2 + (4(x+2))^2$

[warm shale]

Vast

[final thunder]

#latex-testing

[stable rain]

yes

[plain pine]

.close

[stable rain]

quic

[obtuse pebble]

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[sturdy bronze]

show that for any real number the inequality is true

B and C pls

[rigid lintel]

,rccw

[obtuse pebble]

@sturdy bronze Has your question been resolved?

[obtuse pebble]

@sturdy bronze Has your question been resolved?

[halcyon plover]

Use cases

Negative, positive and zero

[obtuse pebble]

@sturdy bronze Has your question been resolved?

[obtuse pebble]

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[vivid flicker]

Can someone show me why this converges and how to get the sum?

[vivid flicker]

By doing the ratio test I arrive at a divergent series, so I'm lost

I always end up at this

[stable rain]

um

that seems ok

take that

n lim of k to inf

[obtuse pebble]

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[teal slate]

Hi can i please assistance

[stable rain]

lol

hi

[teal slate]

Which Number should I use for the height that’s all I want to know

[stable rain]

4

[teal slate]

Okay thanks 🙂

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[stable rain]

🥣

[teal slate]

Wait last question why wouldn’t we use the two Incase I get a similar question like this in the future

.reopen

[obtuse pebble]

✅

[stable rain]

er

height is perpendicular dist

[obtuse pebble]

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[teal slate]

Oaky thanks

[obtuse pebble]

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[hallow crest]

(x-5)/(x+7)-(x-8)/(x-1)

[hallow crest]

i recognize the lcd is (x+7)(x-1) i just dont know if im canceling things out or simplifying using distribution in the numerator after cross multiplying

[twin sapphire]

the general way would be to expand the numerator

and if you want a factorized form in the end

solve the quadratic

[hallow crest]

the quadratic in this one cancels out

my simplification leads me to (-5x+61)/(x+7)(x-1)

is this correct?

[twin sapphire]

,w simplify ((x-5)/(x+7))-((x-8)/(x-1))

[warm shale]

Results provided by WolframAlpha

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

Requested by Benjamin#3570

[hallow crest]

🙂

also thats a crazy helpful tool

[twin sapphire]

i aint doing the calculations

[hallow crest]

no problem

[twin sapphire]

seems right

[hallow crest]

i just missed these on the exam i had

which was lame cuz i got everything else right

so im gonna review adding and subtracting variable fractions

ty for the assistance

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[vast sun]

is the addition of 4 consecutive natural numbers a multiple of 2

[vast sun]

with proof

[timid silo]

ye

[vast sun]

i tried 2k (a multiple of 2) = n + (n + 1) + (n + 2) + (n + 3)

[timid silo]

label the first number as n

and have the rest of the numbers follow

like the 2nd number is n+1 and so on

[vast sun]

yes i did that

[timid silo]

yeah thats right

add up all the ns to show that you can factor it by 2

[vast sun]

thats 4n + 6

everything

[timid silo]

yeah and thats even

because you can divide it by 2

2(2n+3)

thats the proof

[vast sun]

oh my god im so dumb

thnx

i'll just write that on my hw paper

[obtuse pebble]

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[cosmic veldt]

What's the best way to get a degree in math with as minimal studying as possible?

[fickle turret]

Sounds like you'd be a great engineer

[cosmic veldt]

All I wanted to do was code ffs 💀

[frail tulip]

you could do a cp degree instead?

[cosmic veldt]

im exaggerating, im already in computer science i just fucking hate math rn

[frail tulip]

degree level maths isn’t super straightforward, there’s a lot of subtleties which you have to put effort into to get it right

ahhh

what math are you doing?

[cosmic veldt]

calc

[rigid lintel]

well hating math is part of the process

you hate it

then you realise

its not actually that bad

and then you excel

[cosmic veldt]

i think its the fact that theres a shitton of stuff u memorize just to forget later

at least for cs you are working towards something that's desirable (at least for me since I like coding and its good money too)

its like i feel like math is a pyramid scheme

you study math to become a math professor

and teach others math

[rigid lintel]

i would argue math is a field of study for which you have to do very little memorisation

sure you can memorise how to do stuff in math but then you dont actually know how to use it

math is far from a pyramid scheme my dear

applications are often in collaboration with other fields

but math is still incredibly useful by itself

try googling "hedgefund quant salary"

[cosmic veldt]

the heck is that

[rigid lintel]

an illustration of how math can be used

[obtuse pebble]

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[timid silo]

how do I solve this

[obtuse pebble]

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[dull shoal]

Hi, about question D, I have cost=0 . Should my solution be on the general form or in specific form ?

[trail cliff]

maybe send the image in question?

the whole question

[dull shoal]

oh yeah mb

I mean, should i add the period to my final value of t ?

like am i supposed to write just pi/2 or pi/2 +pi*k

[obtuse pebble]

@dull shoal Has your question been resolved?

[dull shoal]

<@&286206848099549185>

[dark mango]

so velocity is derivative of position and acceleration is derivative of velocity

[dull shoal]

oh yeah my problen was just with the notation of the soluton for a(t)=0

[dark mango]

oh

[dark mango]

whats the issue exactly?

[dull shoal]

im trying to solve cost=0

and im not sure about how im supposed to express t

[dark mango]

just write down both solutions

0 < t < 2pi

[dull shoal]

oh yeah

ty

They ask what is true about the velocity at those times

I guess the velocity is constant ? @dark mango

[dark mango]

yes

[dull shoal]

Oh that simple ? I thought i needed to plug into the v(t) lol

[dark mango]

when a(t) = 0 velocity is constant

im assuming thats all they want

[dull shoal]

aight ty

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[hybrid lantern]

Seems to be a textbook error in b. Should it say "multiplying or by interchanging two rows" ?

[obtuse pebble]

@hybrid lantern Has your question been resolved?

[trail musk]

Yeah, they just dropped the "or"

[obtuse pebble]

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[minor parrot]

Is this correct combinatorics for picking cards (without repetition)?

[lean drum]

Taking the ACT next week, any tips?

[obtuse pebble]

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[fresh pike]

i need help

[fresh pike]

is this

only linear

CAN

SOMEONE\HELP

<@&286206848099549185>

this is niether right\

BRO

.close

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[timid silo]

.close

[obtuse pebble]

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[drifting pier]

What's a complex number?

[obtuse pebble]

@drifting pier Has your question been resolved?

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[royal shard]

alpha

a greek letter

it often means an angle

[obtuse pebble]

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✅

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[obtuse pebble]

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[strange stump]

I don't get 6b

[strange stump]

Just tell me how to do it

[zinc yew]

what have you drawn so far

[strange stump]

Let me send it

[daring rock]

You could bisect two of the 60 deg angles to make 30 deg angles

[strange stump]

I'm familiar with that

but not with the 120 degrees

[daring rock]

If you draw bisectors in two of the angles, they will intersect in the center of the triangle

[strange stump]

I don't get it

Is it possible if you can use paint to show what you meant? (doesn't have to be accurate)

[daring rock]

yeah one sec

[strange stump]

Ty

[daring rock]

If you bisect the 60 degree angles, you make 30 degree angles

Then the remaining angle has to be 120 degrees automatically

Because it's in a triangle with two 30 deg angles

[strange stump]

I see

The compass length should be the same since I am bisecting the angle?

[daring rock]

Not sure what you mean. Are you asking me how to bisect the angles?

[strange stump]

Nope

Actually nvm I get it

[daring rock]

Cool 👍

[strange stump]

thanks

.close

[obtuse pebble]

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[haughty venture]

Need a bit of help: I got 2 formulas. x(y+120)=4500. y^2=z. I am trying to find z

[royal basin]

what are x, y and z?

[haughty venture]

x is one side, y is other size, and z is what im trying to find

[royal basin]

one side and the other side... of what?

yeah this is all hard to follow without a diagram tbh

[haughty venture]

i dont really get the problem tbh

[royal basin]

as in "i don't get what you are not following" or "i don't get what to do in the problem i sent"?

[haughty venture]

second

sorry for late responce

no they dont

i think second

first*

because 120^2=14400, and thats > 4500

ofc ;-;

Honestly the problem wording is confusing

i think i got it otherwise

[warm shale]

dev

[haughty venture]

also dont need help with this but this is paiiin I need to go back to old notes

[warm shale]

dev

[haughty venture]

portal so

I think ill do first

[obtuse pebble]

@haughty venture Has your question been resolved?

[timid silo]

x(x+120) = 4500

[obtuse pebble]

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[dense osprey]

It is known that the surface area of a hot air balloon is given by s(r) = 4πr^2 where r is the radius of the balloon in meters. Find the surface area of the balloon as a function of time if the radius is increasing with time t (in seconds) according to the formula r(t) = 2/3 t^3

[dense osprey]

help me pls

[obtuse pebble]

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[obtuse pebble]

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[tender eagle]

Hello, I had a question on how to transform/graph the function f(x)=|x| to the function g(x)=-2f(-(1/3x+2))-1
I believe I got the graph correct, but I am not to sure If I executed it correctly.

I got the points (-6,-1), (0,-5)

[gilded needle]

those points are both on the graph of g, is that what you are asking?

[tender eagle]

Yes

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

Not sure if this should be here, but any ideas?

[timid silo]

ah okay so it is just a second order differential equation

F(t) = ky + δdy/dt + m d^2y/dt^2 i would guess?

[obtuse pebble]

@timid silo Has your question been resolved?

[old nymph]

discord.gg/physics

[timid silo]

eh, the question becomes a question of how to solve the differential equation anyways

but sure

[obtuse pebble]

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[timid silo]

How to find the equation of SR?

[gleaming blaze]

what do you mean by equation of SR?

[old dagger]

U know the properties of trapezium?

[timid silo]

it's like y=mx+c ig

[old dagger]

Yes

Y = mx +c

[timid silo]

Yes

[old dagger]

PQ is parallel to SR right?

[timid silo]

Yea

[old dagger]

So wht happen to their gradient

[timid silo]

Same ?

[old dagger]

Yes

Then wht to do

[timid silo]

Find the equation of SR w the gradient?

[old dagger]

Yes

Find the gradient of pq first

[timid silo]

1/3

Then it's y=1/3x +c ? I cant find the y-axis tht it goes through

[rain aurora]

USE THE 2 POINT FORMULA

for PQ

then cuz its parallel, it has same gradient

then u use the point gradient formula

[timid silo]

Idk wht tht is tbh...

[rain aurora]

this is 2 point formula

this is point gradient

[timid silo]

I see

[rain aurora]

yes

THEN U WILL GET THE ANSWER

🎉

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

.close

[obtuse pebble]

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[placid totem]

does ⟨u, u⟩ just mean dot product of vectors u?

[placid totem]

or something along those lines

[fast bolt]

Vectors cannot be computed by their norm without additional information. For example <(1,0)> and <0,1> both have norm 1 in the standard metric of R^2.

[placid totem]

So we have to give them some value?

since its not given in the question

[fast bolt]

I think the question's wording is off.

[placid totem]

Its translated so probably yeah

[fast bolt]

If I said find a number such that |x|=1, you cannot tell me that number. If I instead told you to find me a number such that |x|=1 and x>1, you would be able to do so. Likely a translation issue, otherwise a bad question.

[zenith raft]

actually I don't think I would be able to find you a number such that |x|=1 and x>1 🥲

[fast bolt]

x>0 👀

[placid totem]

but do we show it like this or ?

u is the matrice / vector [1 5]

and v is [3 1]

.close

[obtuse pebble]

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[inland thicket]

Im reading textbook about matrices and I cant understand what means if and only if

[inland thicket]

can someone explain what is if and only if

[royal basin]

"A if and only if B" means "if A then B, and also if B then A"

[inland thicket]

hmmmmm

[lean trail]

It means that A is a necessary condition for B

[inland thicket]

very complex to read that textbook

[royal basin]

you mean necessary and sufficient.

big difference there.

[inland thicket]

idk how i will survive college

[lean trail]

Sufficient also

[obtuse pebble]

@inland thicket Has your question been resolved?

[obtuse pebble]

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[fringe sail]

Hi yes, so

[fringe sail]

This is the question, andd

It asks me to give the difference of the stamps

I have the stamps, my work is here.

Yet I cannot find the difference

Can you guys help me 😭

<@&286206848099549185>

[warped fulcrum]

Well they're both square right?

[fringe sail]

Yes

[lean trail]

You can only ping after 15 minutes have passed

[fringe sail]

Oops

[warped fulcrum]

Well say x is the length of the smaller stamp then 3x is the length of the bigger stamp?

[fringe sail]

My bad

[fringe sail]

Mhm.

[warped fulcrum]

Okay well since the differences of the squares should be 128

We get indeed (3x)^2-x^2 = 128

So as far as I am looking into your solution it seems right

We get 9x^2-x^2 = 8x^2 = 128

[fringe sail]

Uhuh?

[warped fulcrum]

x^2 = 16

So x = -4 or x = 4 but since x can't be negative it is x = 4

So the length of the smaller stamp is 4

And the bigger stamp is 3*4 = 12

[fringe sail]

Thank you

Very much

For helping me

[warped fulcrum]

No worries

.close

To close

[fringe sail]

.close

[obtuse pebble]

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[fringe sail]

Thanks!