help-27

[pseudo basin]

can we see parts a-c please

[stark shale]

yea

[river gorge]

yeah

and then let u = x/a

[stark shale]

what are parts a-c ?

[river gorge]

i think Ann means parts a-c of the problem

[pseudo basin]

part a, part b and part c

yrs i do

yes*

[stark shale]

oh nothing it just get the derivative of inverse sinh(x)

which is written in there

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/resources/mit18_01scf10_ex101sol/

its here

problem is
when i integrate i get the correct result but i also get a 1/a outside

so it's not correct

😄

i get
1/a sinh^-1(x/a) + c
i have the extra 1/a

[devout snow]

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[devout snow]

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[stark shale]

.reopen

[devout snow]

✅

[stark shale]

help plz

[graceful cosmos]

Did you perform a u-sub to turn the x²/a² back into an x²?

x = ua
dx = a du

Will get rid of the 1/a

@stark shale

[stark shale]

mmm no i dont get that

i have set u = x/a

so in the square root i have
1+u^2

ok ok i see what you mean

damn i knew i was missing something in there

[stark shale]

thanks!!

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[devout snow]

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[oblique seal]

solve for x. Simple equation but I dont know how to arrive at the conclusion that x>1 except from simple observation that rhs is negative for x>1 and lhs is always positive except when x is 0

[oblique seal]

I multiplied both sides and arrived at x belongs to (0,log 2 of 4/3)

[neon folio]

first check the domain

[oblique seal]

x cant be 0 or 1

[neon folio]

ok

[oblique seal]

so R/{0,1}

[neon folio]

yeah

you could do u sub for 2^x

[oblique seal]

but how do I get x>1

[neon folio]

solve for u

[oblique seal]

who is u

2^x?

[neon folio]

yes

[oblique seal]

I already did that

[neon folio]

well its wrong

[oblique seal]

what did i do wrong

[neon folio]

how am i supposed to know

did you show your work

[oblique seal]

ok one sec

what did i miss

[neon folio]

this is wrong

you cant just work without the numerators

[devout snow]

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[oblique seal]

yeah you are right

thank you

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[neon folio]

cu placere

[devout snow]

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[mental shell]

can someone please please please spot the mistake and help

[topaz axle]

,rccw

[mental shell]

can you help ?

can anybody help guys ??

[devout snow]

@mental shell Has your question been resolved?

[mental shell]

I just keep gettin < 2a

instead of < a

[oblique seal]

the first one is good

n+y/2

[mental shell]

that's x xd

[oblique seal]

oh mb

[mental shell]

terrible handwriting

it's my bad

not yours

but please go on

[oblique seal]

i will call alpha a

[mental shell]

yea

that's whwat im doing too

[oblique seal]

-a<x<a
-a<y<a

if you subract them you wil get

0<x-y<0

[mental shell]

divide ?????

[oblique seal]

subtract

mb

[mental shell]

i am not

[oblique seal]

so (x-y)/2=0

[mental shell]

but like

isn't -a<-y<a

because if we take -a<y<a

and multiply everything by -1

we'll get -a<-y<a

[oblique seal]

no

when you multiply by -1 you change signs

[mental shell]

and order too

I am pretty sure you change order

-a < y

becomes

a > -y

it's like 1 < 4

it becomes -1 > -4

you can't just change the signe without the order

[mental shell]

because it would be absurd!

[oblique seal]

im not sure what you want to say

lets take for ex -3<2<3

if we multiply by -1

3>-2>-3

which is fine

[mental shell]

yes well apply that to -a < y < a

doesn't it just become

-a < -y < a

[oblique seal]

we got that relation from the absolute value

so it has to be that way

[mental shell]

so what do we do now

[oblique seal]

after you subtract?

-you add a<(x+y)/2<a with 0<(x-y)/2<0

[mental shell]

but

-a<(x-y)/2<a

can we just ask someone man

do you someone in this server ??

[oblique seal]

.

[mental shell]

what's that

[oblique seal]

you know that x<|a|

so -a<x<a

for y is the same

[mental shell]

okay got it

yes yes

and we get |(x + y)/2| < a right ?

and then we have -a<x<a

and -a<y<a

[oblique seal]

yes

[mental shell]

-a<y<a => -a<-y<a

so -2a<x + (-y)<2a

which means

-a<(x-y)/2<a

[oblique seal]

you did this wrong

-a-(-a)

=0

[mental shell]

that's not -a -(-a)

it's -a-a

= -2a

[oblique seal]

i think y just represents a value in the interval so multiplying by -1 doesnt make sense

the inequality is just a way to express the values y can take

[mental shell]

yeah to be honest i don't think what you are saying makes any sense man

thanks for your help tho

I appreciate it

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[pallid falcon]

How can matrices A,and C be determined for a state space system to get the desired output in question c?

this is the right answer

[devout snow]

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[shadow quest]

How do i do this ?

[winter torrent]

work is integral F along the path

[shadow quest]

Yea

Which formula do i use ?

[shadow quest]

@winter torrent

[winter torrent]

first one, just the field itself

[shadow quest]

I don’t understand

[winter torrent]

integral F dr

[shadow quest]

Yhea ?

Then what

[winter torrent]

uh then you get a number

[shadow quest]

????

[winter torrent]

[shadow quest]

what am i supposed to do

[winter torrent]

uh

find dr and then take the dot product with F

[shadow quest]

What is dr

And what about the curve

[winter torrent]

you'll need to parameterize your curve

r is the position on the curve

[shadow quest]

i have it parametrised

[winter torrent]

ok

[winter torrent]

so r = (2 + 2cost, 1 + 2sint)

[shadow quest]

Yhea

[winter torrent]

so find dr/dt and use that to rewrite the integral in terms of dt

[shadow quest]

Thats only half the curve

[winter torrent]

yeah it'll have to be in two parts

[shadow quest]

what is dr/dt ?

do you actually know how to solve this problem?

[winter torrent]

i mostly remember

dr/dt is the derivative of r with respect to t

[shadow quest]

so ?

[winter torrent]

so... $\int \vec F\cdot\dd{\vec r} = \int \vec F\cdot\dv{\vec r}{t}\dd{t}$

[woven radish]

hayley.bin

[shadow quest]

seems too complicated

i dont think thats how it should be done

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@shadow quest Has your question been resolved?

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@shadow quest Has your question been resolved?

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@shadow quest Has your question been resolved?

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[rough zealot]

Hello again

[rough zealot]

I need to check this one is it correct or wrong

[eager lodge]

,rotate

[eager lodge]

correct

[rough zealot]

What about this ?

,rotate

[rough zealot]

Is this correct?

[eager lodge]

yes

[rough zealot]

okay thanks

.close

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[rough zealot]

?

.close

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[scenic goblet]

i need help with this one because i dont know how to do it when it starts from a height other than 0

[scenic goblet]

.close

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[inland tiger]

I need help with desmos, is there a way to translate multiple functions and relations all at once to create patterns? eg. I need to translate this picture multiple times to the right:

[stone stump]

well for example the circles satisfy (x-0)^2+(y-0)^2=something

you can set the 0's as variables and then change those to move the circles

and you can probably do something similar for the others

[inland tiger]

can u show me that

https://www.desmos.com/calculator/wopjulcpe0

i need to duplicate the whole thing and move it to the right

[frozen aurora]

if you want to have kopies, you can also put a list in place of a variable

[inland tiger]

im new to desmos i have no clue what that means

[stone stump]

https://www.desmos.com/calculator/6kremwtega

this is just for the circles

I dont wanna work through the details for the other shapes

by changing the slider for a and b the circles move

[inland tiger]

is there any easier way to like maybe group all the functions together somehow

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[velvet coral]

WHAT IS THE VALUE OF sin2A + cos2A

[stone stump]

SORRY I CANT HEAR YOU

[velvet coral]

.close

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[frozen aurora]

💀

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[deep geyser]

Three planes have equations:
2x − y + z = 5
x + 3y − z = 4 , where a, b ∈ R.
3x − 5y + az = b
Find the set of values of a and b such that the three planes have no points of intersection.

[deep geyser]

can someon walk me trhrough it

thank you

[devout snow]

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[shadow quest]

They won’t intersect if they are parallel

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[lusty adder]

Guys can you help me with this please

[devout snow]

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[boreal bone]

suppose that set A is a subset of set B (A⊆B) does that mean the following is also true:
B⊇A ?

[stone stump]

yes

[boreal bone]

Alright, thanks!

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[cunning lake]

Can someone do this question for me?

[devout snow]

@cunning lake Has your question been resolved?

[cunning lake]

No

....?

<@&286206848099549185>

[restive river]

this is the graph theory i guess im not in mood to read it all. you know graph theory?

[cunning lake]

No...?

[devout snow]

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[cunning lake]

<@&286206848099549185>

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[humble ginkgo]

This problem can be approached using a probability tree. Let's denote the probability of the mouse choosing route i as p_i. Since the mouse chooses route 1 with twice the probability of route 2, route 2 with twice the probability of route 3, and route 3 with twice the probability of route 4, we can write:

p_1 = 2p
p_2 = 4p
p_3 = 8p
p_4 = 16p

a) To calculate the probability of the mouse being caught, we first need to find the probability of it choosing route 1 and then being caught. The probability of being caught at route 1 is 1 (100%) because there's a cat waiting there. So:

Probability of being caught = p_1 = 2p

b) To calculate the probability that the mouse escapes using route 3, we need to consider the probabilities of all the possible paths. The mouse can choose route 2, 3, or 4 and then escape through route 3. We need to sum up these probabilities:

Probability of choosing route 2 and then route 3: p_2 * 0.5 = 4p * 0.5 = 2p
Probability of choosing route 3 directly: p_3 = 8p
Probability of choosing route 4 and then route 3: p_4 * 0.5 = 16p * 0.5 = 8p

Now, sum these probabilities to find the total probability of escaping through route 3:

Total probability of escaping through route 3 = 2p + 8p + 8p = 18p

To find numerical values for these probabilities, you would need to know the value of p, which represents the probability of choosing route 1. Without that value, it's not possible to provide a specific numerical answer.

What answer are you getting ?

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[restive river]

Could someone help me find the derivative of this?

[restive river]

specifically how do you find the derivative of 7^x

i dont really understand it

pls anyone

help

!!

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[restive river]

how does he go form this to this

i get everything else except the ln(7)7^x

eeehelp

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[restive river]

pls anyone if u can help

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[sudden hawk]

@sour girder said u are dumb for not knowing this

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[naive sluice]

How can I solve this? Should I somehow find a and b first?

[devout snow]

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[dapper gazelle]

I would say yes

[naive sluice]

but how can I do that?

[dapper gazelle]

Find E(X) and Var(X) for any gamma distribution

I think that'd be part of the exercise

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[clever dirge]

Need help with some algebra. Having some issues with this -1

[clever dirge]

in the problem how does he get the -1 as the numerator?

[lunar harbor]

$-\frac{1}{y}=\frac{-1}{y}$

[woven radish]

Civil Service Pigeon

[clever dirge]

so we wrote the same thing

[lunar harbor]

yes

[clever dirge]

its different here tho

[lunar harbor]

because you input a function and its reciprocal?

I don't rlly see what you're trying to get at here

[clever dirge]

in the red in my work im not sure how to get my -1 to get on top

[lunar harbor]

$-\frac{1}{y}=(-1) \cdot \frac{1}{y}=\frac{-1}{y}$

[woven radish]

Civil Service Pigeon

[lunar harbor]

Honestly, this is basic algebra, so you might need to brush up on that a bit before you delve deeper into the calc

idk if you have old algebra notes or smthn

or you could probably find some notes/videos online

[clever dirge]

asdfasdf

this is it right? im pretty sure we had a misunderstanding

recipricol of both sides = that

[lunar harbor]

yeah that's fine

[clever dirge]

tytyt

.close

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[vernal blaze]

Hi! Could anyone help me with this:

[devout snow]

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[devout snow]

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[worn cape]

How do I simplify the top to get the bottom?

[worn cape]

oops wrong image

[brisk totem]

denominator gives you everything you need

[worn cape]

How do you mean sorry?

[brisk totem]

how do you get a 3 in the denominator but keep the value the same

[worn cape]

You multiply the top by 3, I get that

I just don't get where the constant in the numerator comes from (as in when you multiply the brackets out, you get an 8

[brisk totem]

you get that by factoring out 8

[worn cape]

I see, how do you get from your t^5/3 terms to t^2 term?

[brisk totem]

look at the denominator

[worn cape]

sorry if these are silly questions it's 4am for me here

I'm still not sure I understand don't worry I'm just being slow

[brisk totem]

see how there’s a cube root of x that’s not in you original fraction
what’s cuberoot(x) expressed as x to some power?

[worn cape]

Yeah you put it in the denominator as a fractional power with 1 on the top is the nth root

and as it's negative it's on the bottom

but then you have the denominator the same as the final fraction

and you have -16t^5/3 on the top

and I'm just struggling to simplify/factorise etc. that to the numerator

[brisk totem]

you still haven’t answered my question of what is cuberoot(x) expressed as x to some power

[worn cape]

I did in a roundabout way

cube root x as a power is x^1/3

I see you're saying divide the 5/3 terms by 1/3 to get 6/3

[brisk totem]

so since x^{1/3} is in the final denominator, you probably want to multiply your original fraction by x^{1/3}/x^{1/3}

[worn cape]

ahh I see, thank you!! I didnt think to do that because I just instinctively 'moved'/wrote the negative fractional term on the bottom

cheers! haha

thank you for your patience, I've got severe ADHD which is just about manageable at the best of times but as I said it's 4am so no meds in the system haha

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[devout snow]

Please don't occupy multiple help channels.

[bitter patrol]

i dont get how to do this

[jade oak]

You know the fundamental theorem of algebra?

[bitter patrol]

can u give me a recap

[jade oak]

A polynomial of degree n has n roots

In complex numbers

[bitter patrol]

so its 3?

3 roots

[jade oak]

Not quite

[bitter patrol]

hmm

[jade oak]

There is another thing that says if you have complex root for a polynomial with real coefficients, then its conjugate is also a root

[bitter patrol]

o

ye

can u walk me through the problem

[jade oak]

(x-3) is the only factor that gives a real root

[bitter patrol]

mhm

[jade oak]

Next we have (x-i) which is another root

[bitter patrol]

ye

[jade oak]

But by this we know (x+i) must also be a root

Apply same thing for the other complex root

[bitter patrol]

mhm

so 5

[jade oak]

Yeah

[bitter patrol]

o

how about this

is it d

[jade oak]

Odd degree polynomials cant be even

If j*k is even it is possible the higher value from j and k is odd

[bitter patrol]

wdym

o

can u walk me through this

or is it common knowledge

[jade oak]

If you think about the definition of even functions, it should become clear why an odd degree polynomial cant be even

Less clearly, if any of the terms have an odd degree polynomial, it also doesn’t guarantee the function is even

So you want j and k to be both even

[bitter patrol]

so c

[jade oak]

Which is basically what b is saying

[jade oak]

For c, j and k could both be odd

[bitter patrol]

oh i see

so it is b

[jade oak]

b is saying k is even, so thats good

And 2 times and even number is also even

[bitter patrol]

ye

[jade oak]

So it must be b

[bitter patrol]

yea thx

i got it

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[jaunty gazelle]

Could someone check my work for this problem?

[devout snow]

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[sweet arrow]

send your work

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[umbral schooner]

iii

f(g(x) draw the graph

[ionic stump]

so it's like composition or whatever right

y = f(g(x))

we could start by pretending f(x) just equals |x| instead of |x| - 1

that would mean f(g(x)) would be |g(x)|

so anything that's like negative in that g(x) function

becomes positive

bc absolute value

ya feel me?

[umbral schooner]

yuhh i feel u

[ionic stump]

aight so

[umbral schooner]

i get i see

[ionic stump]

once u know that

then go back to the original

which is |x| - 1

or in your case because it's composition

|g(x)| - 1

the - 1 just shifts the entire graph down by 1

[umbral schooner]

alr

bet

thanks

[ionic stump]

np

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[sinful wave]

I'm lock in exercise 2 I don't know what to do for having Un

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[urban crystal]

Idk how to do this question

[urban crystal]

No. 3

[fervent jewel]

I’d start with the quadratic equation

For a, the -b before the discrimination is gone, so I’d say b=0

Then try to construct an equation that matches sqrt{-4ac}/2a from there

[urban crystal]

so the discriminant is √-2 right

a would be 1

[fervent jewel]

Yea something like that

[urban crystal]

gotcha thank you sm

i was going on the wrong path

i got a as 1/2 and c as 1

so it would be 1/2x^2+1

is that correct, sorry i don't have answers for these ToT

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[undone crystal]

Is this valid for all x>=0?

[undone crystal]

I'm not sure how to tackle this mess.

But by analyzing each side

Starting with the left side, it should eventually be negative

However the right side should always remain positive?

Thus this shouldn't work

But the sheet says that it's valid for all x >= 0

I'm gonna start applying some logarithm rules on the right side

I was able to factor out a ln x

This should prove that its not valid....

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[undone crystal]

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[pure meadow]

I don't get this step, can someone explain please

[dim knot]

Just normal multiplication
3 × 3^2 = 3^3

@pure meadow

[pure meadow]

Ohh

thanks

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[echo oyster]

roots

[brazen star]

yes?

[echo oyster]

one ill send a question

idk how to do this part

[main relic]

do you know the pythagorean theorem

[echo oyster]

no

also this is the middle part

[brazen star]

you don't know how to calculate square root of 4225?

[echo oyster]

idk how to do any types of root

i skipped a few grades of school

so im missing out on roots and i have no idea what thye are

[opal cloak]

wtf how do i do that?

[main relic]

okay then you need to know that as well

[opal cloak]

how can u skip grades?

[echo oyster]

let me search it up if ik it

bc i dont know things by name

[echo oyster]

happens

[echo oyster]

also isnt it simple u just need to add up a2 and b2 then root it out yeah

or am i wrong?

[main relic]

yeah

then root it out

[echo oyster]

yeye how do i do the root part for any give number

[main relic]

usually the ones they give you in exam are clean enough

so you can estimate by trial and error

for example we know 60^2 is 3600 and 70^2 is 4900

4225 lies between that, so it has to be somewhere in the middle

then i'd try 65^2 and compare again, and voila bingo jackpot

[echo oyster]

ohhh

ic

and are there any other methods

[main relic]

well

[echo oyster]

just asking

[main relic]

its a known fact that for all squares of 10k+5 end in 25

and the number before that should be in the form k(k+1)

4225 ends in 25, 42 = 6*7, so root must be 65

[echo oyster]

i think i get it

ill do answer some questions

and if i have trouble ill come back

i appreciate it @main relic

[main relic]

https://tenor.com/view/koharu-fell-gif-25643641

[echo oyster]

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[vital shoal]

how do i do this

[main relic]

let them be x1 y1 x2 y2 x3 y3

[vital shoal]

ok

[main relic]

on second thought

M1 M3 parallel to BC

so u can slope --> point slope

for all three of them

[vital shoal]

how is it parallell , AC could be higher or lower who knows

cause its just a sketch

no?

like the midpoint

of m1

isnt on the same level

as AC

@main relic

[main relic]

what

midpoint theorem

[vital shoal]

ohh

okay makes sense now

[main relic]

$M_1M_3||AC$

[woven radish]

candies

[vital shoal]

ok thx

ure my goat

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[dark sable]

So like

[dark sable]

Pigeonhole right

1/32864 chance right

well

[main relic]

R U HK

OMG

[dark sable]

there's 32864 possible coloring-

[dark sable]

Unfortunately no

[main relic]

BUT CHINESE AND TRADITIONAL

MACAU?

[brazen star]

Taiwan also uses traditional.

So.. Taiwan?

[dark sable]

I'm not from hongkong

[main relic]

o rly i thought taiwan simplified

sad

where

[dark sable]

and it's timo

yep

oh wait

Thailand

I keep mixing up the Ts

[dark sable]

There's a lot of orientations for this

maybe focus on the middle I suppose

This is hard

[brazen star]

So, the four corners have to be in the same color?

[dark sable]

how many ways to paint them so that there doesn't exist a rectangle with area greater than four with four corners painted the same color

Basically we want it not to have 4 corners the same color

[dark sable]

rectangle with area greater than four is a fancy way of saying it encompases like 4 squares or more

It's pretty painful when there's 3 squares

If it was only 2 then it'd be much more simple

[jaunty mantle]

(i'm not helping but i would have an aneurysm trying to understand what the heck the question is asking in chinese LMAO)

[dark sable]

I'm trying to do it piece by piece but each time I upscale it's pretty difficult

[main relic]

r u a chinese studier

[dark sable]

There is an english part for a reason

It's literlly above the chinese

ping me if ya'll have found a way

[brazen star]

(well.... it's the traditional one, not the simplified one, even i would get an aneurysm)

[jaunty mantle]

no im native but haven't read or done math in it in many years now

[main relic]

traditional > simplified no other opinion

[main relic]

rip

[brazen star]

so rectangle area >= 4 right...

hmm...

[devout snow]

@dark sable Has your question been resolved?

[devout snow]

@dark sable Has your question been resolved?

[devout snow]

@dark sable Has your question been resolved?

[brisk totem]

i solved it by what is basically casework but it feels stupid

treat columns individually, obviously you can’t have 2 identical columns.
then notice you can’t have a monocolor column (not hard to show imo)

then the question is equivalent to constructing 5 digit numbers from {1,2,3,4,5,6}
and taking care of nonsense overcounts which i can’t be bothered to do should get you there

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[devout snow]

@supple raven Has your question been resolved?

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[red bay]

Determine all functions f (x, y) that solve the equation
for example with a variable change u = ax + y, v = x, for any suitable value of the number a

[red bay]

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[floral cradle]

A golf ball is struck with an initial velocity of 47.0m/s at an angle of 28 degrees above the horizon. Determine the horizontal distance travelled by the ball if it rolls an additional 15m

[floral cradle]

For this question, I found the time in the Y but do I need to use initial velocity (y) or just initial velocity which is 47m/s

[topaz axle]

the smaller one

[floral cradle]

So vi in the y direction? I got 22.6 for that?

[mystic oak]

Solve for t_flight as a function of v_y first

[floral cradle]

What do you guys get as your final distance? I'm getting 201m but I'm not sure that's correct

[topaz axle]

horizontal is 41.5, vertical is 22.06

[floral cradle]

Ye that's why I got too

[topaz axle]

4.5 seconds to fall

,calc 186.7+15

[woven radish]

Result:

201.7

[mystic oak]

You shouldn't be feeding him the answers

[floral cradle]

Alr thx, makes sense I got the same thing using vi y

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[spark cradle]

where can I find someone to help me with my maths assessmen? The topics are functions, derevatives python, stationary points, Maclaurin series and Taylor series

[spark cradle]

like someone in dms that can solve them whilst I stream the questions

[fiery merlin]

isnt the point of an assessment to test what you know

and not other people

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@spark cradle Has your question been resolved?

[supple knot]

You've already been told
#help-15 message

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[raven swift]

the original paper size is 11*8.5 11 being lenght and 8.5 being width, if i made 1.5in cut on the four corners, what would the volume be?

[winter torrent]

you should try it with a physical piece of paper and scissors

[raven swift]

ik the answer but im very confused tho

like if i did 1.5

the volume is 66in^3

but how tho?

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[wild creek]

I just had this problem on a test and I was wondering if someone could tell me if I solved it correctly...
A force of f(x) = ax² - b acts on a 4.8 kg object through a distance of 50 m, what is the final velocity?
a = 0.8 N/m²
b = 1.2 N
x₁ = 125 m
v₁ = 250 m/s

[wild creek]

I just calculated the work performed by the force with
∫ 0.8x² - 1.2 dx from x = 125 to x = 175

and added that energy to the initial kinetic energy and solved for v to get
v₂ = 664 m/s

my only concern is that I'm not sure if I wrote the integral correctly. The units for 'a' kind of threw me off.

[dense jay]

a has those units because x^2 has units m^2 dw about it, i think what you did is sensible

ill check the calculations though, one mo

[wild creek]

yeah, I was thinking about how 1/m² cancels x², but that just makes it seem like the integral should be
∫ 0.8 - 1.2 dx

[dense jay]

the units cancel, theres nothing cancelling x itself

it just means the combined thing of (ax^2) has units N

your calculations seem to check out

[wild creek]

Thank you for your help! I think I just need to get more comfortable with what the units are doing in physics problems.

[dense jay]

no worries

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[wide tundra]

how do i do this

[hybrid snow]

#❓how-to-get-help

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[strange smelt]

is this correct? the objective is to factorize it

[dense jay]

,w factorise 3/2 x^6-3x^5-2x+4

[woven radish]

Results provided by WolframAlpha

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

Requested by aldrnari_

[dense jay]

yup

[strange smelt]

alr ty

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[low blaze]

I am doing some questions to do with implication. One of the questions I have come across is "A is not sufficient for B." and I have to find a statement for A and B which will return true. My approach was: "A is sufficient for B" is logically equivalent to A -> B, which is logically equivalent to NOT(A) OR B. Since A is not sufficient for B then we need a statement which negates this, which is logically equivalent to [A AND (NOTB)], using De-Morgans Laws. For this expression to return true A needs to be true and B needs to be false. But my problem is how do you find statements for this? I don't know what I can substitute for A and B that would make sense

[proud perch]

A function being continuous is not sufficient for it to be differentiable

A woman being hot is not sufficient for her to be wife material
etc etc

[low blaze]

how did you come to that conclusion?

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[graceful cosmos]

"A is sufficient for B"
Is just A → B

So if you want "is not sufficient", just come up with an A and B, where it's not always the case that A → B.

Me being in Paris is not sufficient for the moon to be made of cheese.

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[rough tiger]

what is this asking me??? i dont understand

[rough tiger]

if anyone open for 1 on 1 chat would be great.

voice chat that would be*

[graceful cosmos]

Huh. I agree with your answer. That should be 48

[rough tiger]

well i typed 75

the red triangle means that was the right answer

means i answered wrong.

[graceful cosmos]

Gotcha. Do you see above how the 8•6 is in 48's spot?

[rough tiger]

yes

[graceful cosmos]

8•6 = 48

[rough tiger]

ohhh

okay

sooo

next i multiply 57 and 9?

[graceful cosmos]

Yep

,calc 9*57

[rough tiger]

ohh

[graceful cosmos]

Aight

[rough tiger]

513

[graceful cosmos]

Yes I agree with 513

[woven radish]

Something went wrong!

An unexpected error occurred while processing your command!
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If the error persists, please contact our friendly support team at our support guild!

Exception

aiohttp.client_exceptions.ContentTypeError: 0, message='Attempt to decode JSON with unexpected mimetype: text/html; charset=utf-8', url=URL('https://api.mathjs.org/v4/')

[lost tide]

plug in 2 for x and 5 for y

and then add and multiply

[rough tiger]

so 2+5

thats 6

[lost tide]

no because of the 9 thats being multiplied by the y

[rough tiger]

well

7

[lost tide]

it should be 9*5

• 2

[rough tiger]

ohhhh

i see it

[lost tide]

so 47

on the inside

[rough tiger]

so i see the 5 replaces the x

[lost tide]

no

the 2 replaces the x

because x = 2

the 5 replaces the y

[rough tiger]

ohh yea yea cuz then we'd have 2 ys

[lost tide]

because y = 5

[rough tiger]

so 2+9

[lost tide]

wha

no you forgot the y again

its 9 multiplicated by y

not just 9

[dry oxide]

,, 8(2+9(5))

[woven radish]

!Yajat!

[dry oxide]

Bodmas?

[lost tide]

?

[rough tiger]

so it wants the whole equation?

[lost tide]

it just wants you plug in 2 and 5 and then multiply/add everything

[rough tiger]

show me an example? cuz i cant plug in 2 and 5 just like it has to be typed specfic way?

[rain otter]

ok you use the distributive property here

but since you have numbers defined everywhere inside the parantheses, you use your pemdas property of multiplying, and then adding, and then distributing the 8 with whatever you've got from inside the parantheses

[rough tiger]

i wound up figuring it out. i just pluged in 8(2 + 9 * 5)

[rain otter]

mhm

[rough tiger]

now on

[devout snow]

@rough tiger Has your question been resolved?

[devout snow]

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[warm tree]

yo

[warm tree]

can someone help em

me

this os my question

how do i do it with long division

hello?

[jade oak]

!status

[devout snow]

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

[warm tree]

3

[jade oak]

Show work for how u got it

[warm tree]

i did it in school but i threw my paper away

lets just say 1

can we start agian

[jade oak]

Rip ok

Do you know basic long division?

[warm tree]

yeah

i dont know how to do reverse long division tho

[jade oak]

wdym reverse long division

specifically the reverse part

[warm tree]

like u have to find it reversly like u have to find the value

of d

they give u the answer but u have to do it reversly

[jaunty mantle]

if u know x-2 is a factor you can divide by x-2

[jade oak]

The answer is not given. They give you a factor. You want to find d so that when you divide the polynomial by x-2 you get another polynomial

[jaunty mantle]

factorise the quartic into (x-2)(cubic)

perhaps you will see some more information about d once you do this

[warm tree]

okay

thank you

let me try

im stuck here

how do i continue

@jaunty mantle @jade oak

[jaunty mantle]

minus

[warm tree]

isnt it plus because --=+

[jaunty mantle]

same thing

i prefer not to write the - before x^4

and just remember that i have top minus bottom

but it doesn't matter

go x^4 - x^4

you get 0

[jade oak]

what is -dx^3-2x^3

[jaunty mantle]

go -dx^3 - (-2x^3)

now it's a plus

[jaunty mantle]

now that would be wrong

[jade oak]

why

[jaunty mantle]

cos it's - - becomes +

[jade oak]

where r u getting the 2nd -

[jaunty mantle]

x-2

[jade oak]

Oh I assumed he did that part correctly

my bad

[jaunty mantle]

he's multiplied the entire expression by - for the "minus the bottom" and is adding them

it's still right i just dont do it that way

[warm tree]

i dont know how to continue from here

[jaunty mantle]

it's perfectly fine

[jaunty mantle]

align your powers

[warm tree]

how do i find d tho

[jade oak]

combine like terms

you need to keep going

once you finish the long division is when you can conclude what d is

[warm tree]

i continue because i need to get rid of the x^3 factor

then continue to the x^2 factor

[jaunty mantle]

you're here right?

[warm tree]

yeah

[jaunty mantle]

we know the next part will be something x^2

something * 1 = -d + 2

for the coefficient of x^2

what is something

[warm tree]

uh

im not sure 😔

[jaunty mantle]

,rotate

[jaunty mantle]

what is ?

[warm tree]

is it 2

wait no

[jaunty mantle]

(-d+2) - something = 0

what is something

[warm tree]

2

[jaunty mantle]

-d + 2 - 2 = -d ≠ 0

so no it's not 2

[warm tree]

OH

4

[jaunty mantle]

-d + 2 - 4 = -d - 2 ≠ 0

so no it's not 4

[warm tree]

im so confused right now

[jaunty mantle]

i have some quantity

apple

i minus something from this

i get 0

apple - something = 0

what is the something

[warm tree]

apple

[jaunty mantle]

ok

i now have (-d + 2)

i minus something from this

i get 0

(-d + 2) - something = 0

what is something

[warm tree]

is it not 2

[jaunty mantle]

????

[jaunty mantle]

.

i have apple

i minus apple

i get 0

i have (-d + 2)

i minus ???

i get 0

[warm tree]

so wouldnt 2 be the apple and if u subtract 2 u get 0

[jaunty mantle]

what

[warm tree]

-2+2-=0

[jaunty mantle]

i have APPLE

i minus APPLE

i get 0

i have (-d+2)

i minus ???

i get 0

[warm tree]

is it negative 2

i dont get it

lmaooo

[jaunty mantle]

it's literally just (-d + 2)

you litearlly replace everything you see

i wrote apple

you minus apple

i write banana

you minus banana

i write 500000

you minus 500000

i write (-d + 2)

[warm tree]

so you have -d

[jaunty mantle]

you minus (-d + 2)

[warm tree]

oh i thought u meant what d is

LMAO

[jaunty mantle]

it doesn't matter what exactly i write

WE DONT KNOW WHAT D IS

we only know that (-d + 2) - something = 0

[warm tree]

im so dumb

i thoguht u were talking abt

2

[jaunty mantle]

because the something needs to minus to 0

by long division

[warm tree]

like in the parenthesis

[jaunty mantle]

right?

i have (-d+2)x^3 - ?x^3 = 0

what is the ?

[warm tree]

-d+2

[jaunty mantle]

exactly

[warm tree]

👍

[jaunty mantle]

,rotate

[jaunty mantle]

now we are here

what's this subtraction equal to

what is 8x^2 - (-2)(-d+2)x^2

[warm tree]

where did the (-2) come from

oh

wait

nvm

isnt d then -4

[jaunty mantle]

how do you know

[warm tree]

because then u subract the 2

then u get 6x^2-(-d+2)x^2

so its bassically 6=-d+2

[jaunty mantle]

that's multiply

[warm tree]

oh so u have to divide

[jaunty mantle]

8x^2 - (-2) MULTIPLY (-d+2)x^2

[warm tree]

that would mean that d is -2

[jaunty mantle]

how did you get d = -2

[warm tree]

u divide -2 but its being subratcted

so its 2

so 8/2=4

4=-d+2

[jaunty mantle]

woah

let's start from 8x^2 - (-2) * (-d+2)x^2 = 0

what do we do

[warm tree]

divide tje -2

[jaunty mantle]

divide what by -2

[warm tree]

8

[jaunty mantle]

8**/2** x^2 - (-2) * (-d+2)x^2 NOT EQUAL 0

[warm tree]

oh wait what if u just plug in a number

just overall

[jaunty mantle]

ok what number

[warm tree]

idk like any number or a zero

[jaunty mantle]

plugging in numbers is fine

but you dont even know what to plug in

how can we separate 8x^2 - (-2) * (-d+2)x^2 = 0

for just d

[warm tree]

wait ima brb

im so sorry

ill be back soon

oh wait my test got postponed

ill just do it later

any ways

cya and thanks for helpign

[devout snow]

@warm tree Has your question been resolved?