help-19

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[quick sonnet]

@acoustic pewter

[acoustic pewter]

X is strictly positive and x²+(1/x²)=14 calculate then √x +1/ √x

Help

[quick sonnet]

wait

<@&286206848099549185>

just wait for them to respond

if you're done just say .close @acoustic pewter

[acoustic pewter]

Ik

Ty

Hellpp

[spark swan]

This kind of problem is really easy once you have seen it done once:

the sketch is to compute x+1/x and then sqrt(x)+1/sqrt(x)

[acoustic pewter]

Am stupid

Help

[spark swan]

nono, its really tricky but there is a way to solve it fast:

[acoustic pewter]

Can u write it

[spark swan]

$(x+1/x)^2 = x^2+1/x^2+2 = 14 + 2$

[clever fjord]

WilmiRosa

[acoustic pewter]

Why adding the 2

Oh no

Wait

[spark swan]

have you spot it?

[acoustic pewter]

Its x² + 1/x² = 14

I need to go from it to

[dreamy thistle]

could multiply everything by x^2

and then do u = x^2

[acoustic pewter]

So from the first one I need to reach the second one

[dreamy thistle]

then solve as a quadratic

[noble forge]

compute (sqrt(x)+1/sqrt(x))^2

[spark swan]

yeaah, and we will make it but first we calculate (x+1/x) and then (sqrt(x)+1/sqrt(x))

[spark swan]

notice that (x+1/x) = 4

and with the same strategy:

[noble forge]

well, don't just give the answers away

[acoustic pewter]

Can u write it please

Tyy

[spark swan]

you can compute the other by yourself

[spark swan]

ok, ty

[acoustic pewter]

Yes yes

I get it

Omg

Thanks sm

I was kinda blind

.close

Oh its named after u @quick sonnet

U can close it

[quick sonnet]

ye

[acoustic pewter]

Tyy

[quick sonnet]

alright

.close

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[tulip carbon]

how do i write this up

[tulip carbon]

like 3x +12 = x

[spiral raptor]

x+12=3x?

are those x and 3x lengths?

[tulip carbon]

oh yeeah thats right ty

.close

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[tulip carbon]

4x−(x+3)=9

[tulip carbon]

so first i tought it was x=4 but it wasnt

[spiral raptor]

it is

*thought btw

[tulip carbon]

tf

the last one is the one im talking abt

ah wait

its write it without paranthese

im so stupid

[spiral raptor]

4x−x+3=9?

[tulip carbon]

idk

[spiral raptor]

bruh u said w/o parenthesis

[tulip carbon]

yeah thats right

but idk if thats right

it was but thats not the point

bye bye girl ;3

.close

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[faint charm]

guys

whats the math behind this?

this CSm formula for

the space in this space

why 110-0 there?

[smoky crystal]

formula of a triangle

$a = \frac{1}{2}bh$

[clever fjord]

accialto

[odd edge]

@faint charm Has your question been resolved?

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[cursive jackal]

Let L be the line of intersection of the planes 2x+3y+z=1 and x+3y+2z=2. If L makes an angle α with the positive X-axis then cosα=

[cursive jackal]

Cross product should be a vector not a unit vector right?

[stone cipher]

a unit vector is a type of vector

and it's common to normalise the cross product of two vectors

because it corresponds to a nice unit normal vector from a plane

[odd edge]

@cursive jackal Has your question been resolved?

[cursive jackal]

But it shouldn't be the unit vector?

I meant the product of two normal is not a unit normal vector?

[dry scarab]

why would it be?

[calm pier]

actually...

[tacit wasp]

Wait a minute, with the word "normal" are you meaning "usual" or "orthogonal" ? @cursive jackal

[dry scarab]

in the picture it's orthogonal to plane

[calm pier]

I get your problem... The cross product of 2 vectors gives an orthogonal vector to them.

idk where you got unit vector from

[tacit wasp]

Anyway, it would be useful/helpful for us if you send the question, not only the answer of this exercise😅

[dry scarab]

#help-19 message

[tacit wasp]

Ups, didn't see it sorry

[calm pier]

I think his confusion is the whether or not the cross product gives a 'normalised' vector or not...

and the answer is not in this case ...

normalised meaning of unit length

but since the normal to the 2 planes are not normalised, no the cross product just gives a orthoganol vector, that's not normalised. It then goes on to normalise the vector 'n', by dividing by its length...

[tacit wasp]

Since they want the direction cosine with the x-direction, you can either normalize the full vector and take its x component, or equivalently you can leave the vector "unnormalized", take its x-component and then divide it by the magnitude of the whole vector @cursive jackal In the answer they gave you they chose option 1

But in general, the cross-product of two vectors is unique, sometimes you scale it only because you're interested in its direction (e.g. for defining planes)

[cursive jackal]

The website is show that the cross product will be unit vector

[cursive jackal]

I send the question first then their answer

[tacit wasp]

Really? Can you send it?

[cursive jackal]

See n^ which means it is unit vector of n

Why are they showing the cross product will be a unit vector?

[blissful depot]

yeah and after I built it into a rectangle nothing helps

[tacit wasp]

Nope. The cross product of those two vectors is n, not a. And n is not normalizes

[dry scarab]

!occupied

[odd edge]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[blissful depot]

i noticed

[cursive jackal]

. close

.close

[odd edge]

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[boreal mist]

Can someone help me find the common ratio of the geometric sequence of -32, 16, -8, .........

[cursive jackal]

Just divide 16/-32

Or -8/16

[boreal mist]

-0.5?

[cursive jackal]

Like this

Yes

[boreal mist]

Do I have to turn -0.5 into 1/2?

[cursive jackal]

You can with sign (-)

[wooden python]

you mean -1/2?

[boreal mist]

ye

[cursive jackal]

0.5 and -0.5 are different

[boreal mist]

Is it required? I have to find the 7th term aswell

I know how to find the 7th term do DW

[cursive jackal]

You have to know what is nth term

T7 = a+6×d

[boreal mist]

I already did I got -0.5

a7

[cursive jackal]

Just plug in all the available data

a7 =-32-6×0.5

Wait a minute

Why alternative+,-

[boreal mist]

?

[cursive jackal]

-32,16,-8,4,-2,1,-1/2

So your answer will be -1/2

[boreal mist]

how

[cursive jackal]

First you have to ignore sign +-+- which is alternative

Now see that 32,16,8
Ratio =16/32

[boreal mist]

isn't finding the nth term formula for geometric sequence is an = a1 (r)n-1

????

[cursive jackal]

It is. I was doing it by arithmetic

Okay then by geometric mean
-32×(-0.5)^6

Power is positive so ignore minus sign

[boreal mist]

-0.5⁶ is 0.015625 right

[cursive jackal]

But 32 has - sign

Do not do it like this

[boreal mist]

?

[cursive jackal]

So your answer -.5

Or -1/2

[boreal mist]

okay so I'm right

I have to ignore 0 right

[cursive jackal]

Ignore why?

[cursive jackal]

0.5 and .5 same

[boreal mist]

Ahh okay thanks

.close

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[cursive jackal]

There are 3 boxes, one ball to choose
3 red 1 green
2 green 2 red
1 red 3 green
So probability of getting 2 red 1 green will be

[cursive jackal]

GRR,RGR,RRG
1/4 × 2/4 ×1/4 + 3/4 ×2/4×1/4 + 3/4×2/4×3/4 = 13/32

What is the difference?

[plain lagoon]

With this working, you're also counting if you're taking more than 1 ball from a box.

Like for example,
You take nothing from box 1
You take 1 green 2 red from box 2
You take nothing from box 3

which is not allowed 🙂

cmiiw

[cursive jackal]

Please elaborate more. I didn't understand

Is there any loophole with replace of that ball?

[plain lagoon]

You're basically ignoring the fact that you can only take one ball per box.

[cursive jackal]

That's not written specifically

[plain lagoon]

"There are 3 boxes, one ball to choose"

Is that not what this meant?

[cursive jackal]

By this counting are we not taking more than balls from a box?

[plain lagoon]

no, you're counting the probability of getting a specific color from the box

1/4 × 2/4 ×1/4 (GRR)

1/4 -> Probability of getting a green from box 1
2/4 -> Probability of getting a red from box 2
1/4 -> Probability of getting a red from box 3

3/4 × 2/4 × 1/4 (RGR)

3/4 -> Probability of getting a red from box 1
2/4 -> Probability of getting a green from box 2
1/4 -> Probability of getting a red from box 3

3/4 × 2/4 × 3/4 (RRG)

3/4 -> Probability of getting a red from box 1
2/4 -> Probability of getting a red from box 2
3/4 -> Probability of getting a green from box 3

And then you're just adding up the probabilities for each cases.

[cursive jackal]

If the examiner has seperated all boxes separately so we have to look probability by its color diffferently

.close

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[dawn oxide]

!help

[dawn oxide]

.help

[odd edge]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[dawn oxide]

.open

[tawdry cave]

.close

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[reef lily]

can someone please help me with this

not sure how to approach

[odd edge]

@reef lily Has your question been resolved?

[odd edge]

@reef lily Has your question been resolved?

[odd edge]

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[trim wharf]

dont know how to solve

[dapper comet]

can someone help

[dry scarab]

! occupied

[odd edge]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

@trim wharf Has your question been resolved?

[ruby stirrup]

,rotate

[ruby stirrup]

no

[ruby stirrup]

,rotate

[ruby stirrup]

no

@trim wharf So we have (b-1)^2 +4 = 9 + (1-a)^2

What are we trying to do here?

Solving for A and B?

[trim wharf]

yea

[ruby stirrup]

Well you can expand the (b-1)^2 and (1-a)^2

That gets you. (b-1)(b-1) + 4 = 9 + (1-a)(1-a)

Now you do foil for both

And what would you get?

[trim wharf]

b^2-2b+1=9+1-2a+a^2

[ruby stirrup]

That looks good but you forgot your 4 on the left side

So you would get b^2 -2b +1 +4 = 9 + 1 -2a + a^2

[trim wharf]

oh kl

[ruby stirrup]

So now you just add 1 and 4 on the left side
Add 9 and 1 on the right side
Get rid of the 5 on the left side by doing -5 to both sides, gets us b^2-2b = 5 -2a +a^2

[ruby stirrup]

Just out of curiosity can you explain what you did for your second line

[trim wharf]

thats another equation

[ruby stirrup]

oh

[ruby stirrup]

Alright sorry for the delay, lets start over from the top.
We have (b-1)^2 + 4 = 9+(1-a)^2
Subtract 4 to both sides
(b-1)^2 = 5+(1-a)^2

Square root (b-1)^2

Gets us b-1 = sqrt of (a-1)^2 +5

b = sqrt of [(a-1)^2 +5 ] +1

Do the same when solving for A

[odd edge]

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[mystic saffron]

I am confused about how to do this double containment

[mystic saffron]

in the first direction

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

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[sage slate]

“If 4 coins are flipped, what is the probability of exactly 2 being heads”
I used nCr(4,2) to get 6, then put 6/16 as my answer for the probability. Would using nCr work if the coin flips were not 50/50?

[wooden python]

with some adjustments yes

look up binomial distribution

in your case you would have 4C2 * p^2 * (1-p)^2 where p is the chance of getting heads

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@sage slate Has your question been resolved?

[odd edge]

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[worthy plover]

So I know how to do this with vectors in standard and component form, but I am unfamiliar with problems that look like this

I know that there are identities

But I'm unsure of how to go about solving the problem still

[odd edge]

@worthy plover Has your question been resolved?

[random thistle]

Cross products are compatible with scalar multiplication, so you can move that 2 outside

[worthy plover]

outside to where?

[random thistle]

Aaaaaalll the way out

[worthy plover]

2(kx(ixk))?

[random thistle]

$(a \vec{v}) \times \vec{u} = \vec{v} \times (a \vec{u}) = a(\vec{v} \times \vec{u})$

[clever fjord]

Learath2

[random thistle]

You forgot the original 2 outer 2, but yeah that’s about the idea

[worthy plover]

So it ends up being 4(kx(ixk))?

[random thistle]

Yes

[worthy plover]

and from there that's 4(kx(-j))

I think?

[random thistle]

Yes, no need to doubt yourself

[odd edge]

@worthy plover Has your question been resolved?

[worthy plover]

ok!

and from there I am certainly unsure

I don't see an identity for kx-j

I mean, can it be derived from one of the identities?

[random thistle]

- is just multiplication by -1

[worthy plover]

because of that it comes out to be (-1)(-i)=i? @random thistle

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[languid dew]

For question c

How does the solution get 6 roots

z^5 should only have 5 roots?

zoomed in versions:

[odd edge]

@languid dew Has your question been resolved?

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[lavish needle]

guys, what is the name of this symbol, and which topic i can search for to learn it?

[vapid pawn]

sigma notation

algebra 2

[lavish needle]

ok, thank you ❤️

.close

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[cold sage]

!status

[odd edge]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[sacred ice]

3

[cold sage]

what did you get and how did you get it?

[sacred ice]

i think it was in the 600s

not really sure

[cold sage]

you dont have your working?

[sacred ice]

i worked it on my calculator but i have cleared it

[cold sage]

aha, walk me through how you would go about it

[sacred ice]

i just worked out the area of each face

[cold sage]

its possible you just missed a side

[sacred ice]

oh

[cold sage]

would be worth giving it another go

if youve only done it once

[sacred ice]

iv tried 3 times

[cold sage]

i see, tell me what you do

[sacred ice]

i think at this point im just dumb

okay so i multiplied 17 by 14 for the front face then 15 by 8 for the front right angle triangle then x2 because the other side then i did 14x 15 for the rear side then 8 by 14 for the bottom

[cold sage]

you have double the total triangular face area

[sacred ice]

oh

[cold sage]

remember the area of one of them is 0.5bh which is 0.5(15)(8)

so for both its just 15*8

you probably just forgot the 0.5 because you knew you were doubling

[sacred ice]

so what would the answer be

[cold sage]

(15)(14)+(8)(14)+(17)(14)+2(0.5)(8)(15)

[sacred ice]

thank you so much

could i get the answer to another one too

[slender lion]

You want another answer?

[sacred ice]

yes please

[slender lion]

I'll just give you the multiplication and addition

Since you should learn how to quickly do these

[sacred ice]

okay

[slender lion]

(3x9) - Triangular faces

9x11 - The Hypothenuse face

4x11 - Side 1 face

[sacred ice]

and should the answer be 197?

[slender lion]

Okay, now I'm kind of confused because there could be 2?? Answers for the triangular face

4x7/2 on the bottom and 3x9/2 on top

But I assume you use the one ontop

And I'll check your answer

44+77+99+27

@sacred ice I think your answer is wrong as it's a little short

Can you show me your working out or train of though?

Thought?

[sacred ice]

im so confused

i put the answer in for what you said and it was correct

247

[slender lion]

Its because I missed one

Mbmb

[sacred ice]

Thanks so much

[slender lion]

The correct answer should be those added

[sacred ice]

Life saver

[slender lion]

Above the ping

[sacred ice]

yeah

[slender lion]

But I think you could use a better website because that question is very inconsistent

With 3x9/2 and 4x7/2

[cold sage]

its not inconsistent, youre assuming that the whole face is a right angle triangle which isnt necessarily true

just because it looks like one doesnt mean it is

if it were they would mark the 90 angle

[odd edge]

@sacred ice Has your question been resolved?

[odd edge]

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[weary jolt]

I need help with a paralellogram

[zenith tartan]

post the question

[weary jolt]

k

A parallelogram has a height of 3 ft and a base of 8 ft. Find the area of each shape that composes the parallelogram. What is the total area of thes special quadrilateral?

8 ft x 3 ft x 3 ft x 4.25 ft.

@odd edge

<@&286206848099549185>

!15mins

[odd edge]

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

[weary jolt]

ok

A parallelogram has a height of 3 ft and a base of 8 ft. Find the area of each shape that composes the parallelogram. What is the total area of thes special quadrilateral?
8 ft x 3 ft x 3 ft x 4.25 ft.

A parallelogram has a height of 3 ft and a base of 8 ft. Find the area of each shape that composes the parallelogram. What is the total area of thes special quadrilateral?

.close

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[tacit wasp]

Use the definition of absolute value...

[graceful crow]

wait am i in the right chanel for help

[tacit wasp]

Wdym?

This is a help channel, yeah

[graceful crow]

ok thank you

[sharp oak]

As x gets closer to -inf, 1 - 3x gets closer to +inf

Since 1 - 3x is a positive number, the absolute value bars aren't doing anything

[graceful crow]

so i write this?

[uncut remnant]

maybe, but why

is |1-3x| = 1-3x

[graceful crow]

so what i wrote is right?

[uncut remnant]

thats worth explaining

[tacit wasp]

This is it FYI (note that your a is 1 - 3x, hence it's a positive a)

[graceful crow]

because if the result gives something under 0 so negative we want to change the appearance to positive so we add a minus but in this case it’s positive and keeps getting bigger so nothing should be added?

[uncut remnant]

yeah so

[graceful crow]

is the final answer 0?

[uncut remnant]

as x gets very large and negative

1-3x gets very large and positive

looks right

[graceful crow]

is the answer 4?

[uncut remnant]

a good check is to plot on desmos btw

[graceful crow]

Am i right or not?

[quasi sparrow]

Check by plotting

[graceful crow]

Whats plotting

[odd edge]

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[light zodiac]

So liek the standard form give us the y intercept 8 i think fr

And umm

Idk x intercept

[dry scarab]

solve for y=0

[manic sleet]

Hint: ||The x-intercepts are where y=0, i.e. ax^2+bx+c=0 or (x-r1)(x-r2)=0||

[light zodiac]

I forgor how

[odd marsh]

when u have y = 0 what do u get

[light zodiac]

Uhh wouldn't it be like -2 and -4 idk

OK

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[green elm]

what is the question?

this entails just integrating v(t) i guess?

well how did you compute your answer

to get 578

but that's an equation for velocity

they are asking for height (position)

no..

for position you integrate velocity

like $$h(t) = h(0) + \int_0^t v(u),du$$

[clever fjord]

Bungo

[green elm]

you you have to integrate the v(t) formula

don't plug in time

integrate from t=0 to t=60

[unique meadow]

ohhh

but I just end up with a really long answer

nvm

well

I do again but

1 sec

does that sounds right?

[green elm]

wolfram agrees with you

i was too lazy to do it by hand haha

[unique meadow]

awesome thanks man I definitely understand now

[green elm]

cool

[unique meadow]

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[torpid vapor]

Hi i need help with question 23

let me screenshot my work so dar

far

[muted creek]

okay

nvm i saw something from above

[void yew]

Looks like ur done

[torpid vapor]

oh

wait

so would this be a full marks answer

for

Full proofs

or would i have to write words

[quasi sparrow]

Depends on your teacher

Or grader

[torpid vapor]

assuming yes

i have to write this in the beginning right

@quasi sparrow

[quasi sparrow]

Well that's just the definition

Writing the definition of stuff isn't usually always necessary when answering questions

But maybe your grader wants that idk

[torpid vapor]

ok ty

/close

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[south solstice]

I need help solving this

[woeful ravine]

Change cosx-1 into half angle

[south solstice]

half angle identity?

[woeful ravine]

Yes

[woeful ravine]

1-cosx =2sin^2(x/2)

Use this formula

[woeful ravine]

Now change sinx as 2sinx/2 cosx/2

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@south solstice Has your question been resolved?

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[modern mauve]

how is this wrong i thought the function is the same as t^-2 + t^-8

[mystic saffron]

? It's same as t^-1 + t^-7

[modern mauve]

oh is it?

i dont know my things apparently

[mystic saffron]

Yes

[modern mauve]

oh you are right i dearly apologize

[mystic saffron]

No worries

[modern mauve]

.close

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[dense lichen]

Solve for cos x + sin x + tan x

[sharp oak]

Well that's gonna be easy

[dense lichen]

how so? Ive been trying to figure this out for a while

[sharp oak]

Whoops, didn't realize those functions change

Apparently I only look at first letters when reading trig

[dense lichen]

its equivalent, if that helps

[zinc glacier]

change cot to cos/sin then do common denom

[zinc glacier]

Ok nvm that didnt work

[odd edge]

@dense lichen Has your question been resolved?

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[mystic saffron]

<@&286206848099549185>

[copper quarry]

<@&268886789983436800> this guy is trolling

[mystic saffron]

sorry i was lookin for my work sheet it is algebra 1

[copper quarry]

Why do you do this where you ping helpers instantly when you’ve been told to stop multiple times

!15m

[odd edge]

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

[mystic saffron]

he told me in 15 mins

[copper quarry]

that’s not how it works

You can’t open up a channel and instantly ping lol

The channel has to be open for at least 15 minutes

[mystic saffron]

ohhhhhh so i just say i need help and dont ping anyone unless someone dosent help me in 15 mins

[copper quarry]

Yes that’s how it works

[mystic saffron]

oh my bad

where do i get help

[copper quarry]

Here

[mystic saffron]

will u help me

[copper quarry]

no sorry

[mystic saffron]

oh thats fine its ok

i need help with a test i need to take tmrw can anybody help me

[cold gale]

Sure what do you need help with

[mystic saffron]

i just need help getting ready to resubmit this test cause its worth half of my grade

can u see the pictures above

[cold gale]

You got most of them correct, it should be ok

Do you have anything in specific that you need help on?

[mystic saffron]

oh like i mean i forgot most of them cause this was a while ago

but can i just do them and tell me if im right or wrong

[cold gale]

Sure

[mystic saffron]

can u help me with 4 5 6

[cold gale]

Ok

[mystic saffron]

Did I get it correct

[cold gale]

No

[mystic saffron]

let me try again

[cold gale]

And also remember that you do not and will not know the exact number for X, so do not put an equal sign

[mystic saffron]

oh sorry cuz i thought you multiply whats in the paranthesis first

[cold gale]

Na

[mystic saffron]

alr ima do number 5

gimme a min

[cold gale]

Wait, soz, I got to go now, sorry, bye, good luck. Ask your parents for help if you still need it

[mystic saffron]

ok

.close

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[mystic saffron]

can anybody help me get ready for my test tmrw

[odd edge]

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[tall portal]

syllabus ?

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@tall portal Has your question been resolved?

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[strong jewel]

For 12a why isn't it 8x2

Since n more than 7.98

[odd edge]

@strong jewel Has your question been resolved?

[strong jewel]

<@&286206848099549185>

[odd edge]

@strong jewel Has your question been resolved?

[strong jewel]

@peak aurora

<@&286206848099549185>

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@strong jewel Has your question been resolved?

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[woeful ravine]

I have substituted x^3=t
Then would integration f(t) dt = psi(t) be still valid, even if t is dependent on x?

[wooden python]

you forget that x exists until the very end

yes of course it is valid

[woeful ravine]

Thank you

[low locust]

it doesn't matter how the integration variable is called

x, t, phi, smiley, ...

[woeful ravine]

.close

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[sacred solstice]

stuck on question 5

[wooden python]

have you done questoin 2?

question*

[sacred solstice]

yes @wooden python

theres a pivot in every row

the first 4 columns form a basis for the column space

[wooden python]

so the column space has dimension 4

i.e. Col(A) is all of R^4

[sacred solstice]

yes

does that mean

every c in R4 can be written as a linear combianations of the colum matrix

so every c vector in r4 has a solution?

[wooden python]

wording, but yes

[sacred solstice]

whats the best way to word it?

[odd edge]

@sacred solstice Has your question been resolved?

[sacred solstice]

As REF of the augment matrix has a pivot in every row the basis of column space has 4 vectors. Therefore the dimension of the column space of A is 4.

Every c in R4 can be written in the linear combination of the columns of the matrix A. Therefore every vector c in R4, Ax=c has a solution

Therefore there is no such vector c such that Ax=c has no solution

@wooden python is that correct

[wooden python]

good enough probably

[sacred solstice]

what am i missing

[odd edge]

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[nocturne glacier]

solving with substitution

[wooden python]

!status

[odd edge]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[nocturne glacier]

i have begun but got stuck midway

[wooden python]

show current progress?

[nocturne glacier]

x=2z+10

all i have

[tacit wasp]

Yeah that's good, now you can replace x with that expression, in the other 2 equations

[wooden python]

ok, now you can replace x by (2z+10) in the other 2 equations.

you know how substitution works in 2 by 2 systems right

[odd edge]

@nocturne glacier Has your question been resolved?

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[tight shale]

Could someone help me to parameterize this curve?

[odd edge]

@tight shale Has your question been resolved?

[tight shale]

@jolly lantern

<@&286206848099549185>

[north crow]

multiply both sides by 25?

[odd edge]

@tight shale Has your question been resolved?

[tight shale]

There's an xy therm that I don't know how to work with.

[odd edge]

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[mystic saffron]

I need help with my maths homework

[marble laurel]

Sure. Could you please send your questions? Also next time, please get into the questions.

[mystic saffron]

The perimeter of a room can be surrounded with fifty 0.4 metre wooden edging strips how many strips of edging would be required of each strip was half a metre in length

[dry scarab]

!show

[odd edge]

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

[mystic saffron]

Question 4

[normal mauve]

First of all, what is the length of fifty 0,4 m pieces?

[mystic saffron]

0.4

Oh wait

Add them all up

[normal mauve]

Yeah, there's 50 of them

[mystic saffron]

It’s 20

[normal mauve]

Exactly.

Now, how many 0,5m pieces do you need to cover this distance? ( 20m )

[mystic saffron]

25

[normal mauve]

Sorry, I misread the question

[mystic saffron]

Actually for 20m it’s 10

[normal mauve]

25 pieces * 0,5m each give 12,5 m and we want 20

[normal mauve]

this would give 5m

[mystic saffron]

How?

[normal mauve]

If each piece is 0,5 m in length, 10 of them have 0,5 m * 10 = 5 m

[odd edge]

Channel closed

The owner is missing!

[mystic saffron]

Bruh

[normal mauve]

Idk what just happened, any other ideas?

[mystic saffron]

That’s my awsner

[normal mauve]

5 pieces?

[mystic saffron]

Would it not be 10 because if the rooms 20m and 0.5 x 20 = 10

[odd edge]

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[quasi sparrow]

is that "&" ?

[serene anvil]

YEAH

[quasi sparrow]

There's only one number that satisfies y=-y

[serene anvil]

so not need of spliting into two equations here?

[quasi sparrow]

Depends on your problem

You should just be using the definitions given to you rather than making up your own interpretation of them

[serene anvil]

so if it was say mod (x+2) = 4 then

[quasi sparrow]

?

Then what?

[serene anvil]

ok

[serene anvil]

x+2 =4 and x+2 =-4

so i was thinking of this logic

there

[quasi sparrow]

Not and

[serene anvil]

or?

[quasi sparrow]

Yes

[serene anvil]

why

[quasi sparrow]

Again, use the definition

[serene anvil]

both can't exist

[quasi sparrow]

What's the definition of |x|

[serene anvil]

dist of x from origin

[quasi sparrow]

No

That's the geometric interpretation

,tex .abs def

[serene anvil]

then?

[clever fjord]

riemann

[serene anvil]

oh okay

so why don't this work in my question?

@quasi sparrow

[tight crescent]

Take each condition seperately

You are trying to figure out when an absolute value of a number equals its opposite value

[serene anvil]

and shoud i always verify if its working?

[tight crescent]

What do you mean?

[serene anvil]

i mean by picking numbers lhs =rhs or not

[tight crescent]

No

[serene anvil]

so in here what i should be doing/

[tight crescent]

What is the absolute value of a number if the number is strictly less than 0?

[serene anvil]

it will become positive no?

[tight crescent]

The absolute value of a number is always positive

Look at the definition of absolute value

What is |x| when x < 0

[serene anvil]

-x

ya its positive nevertheless

shouldn't 0 also satisfy it

[tight crescent]

We'll get to that

Let's look at the equality you are trying to figure out

|y| = -y

[serene anvil]

yes

[tight crescent]

We know we can separate the absolute value into two conditions, when x is striclity less than 0 or greater or equal to 0

So let's take both seperately.

|y| equals -y when y<0

[serene anvil]

right

[tight crescent]

|y|=-y; y<0

So replace the absolute value of y with -y in the equality and add a condition when y is less than 0

You get

-y = -y; y<0

So you've figured out that the absolute value of y is equal to its oppposite for all negative values of y

[serene anvil]

ohhk

[tight crescent]

And then you're left with what the absolute value of a number is when that number is greater or equal to 0

[serene anvil]

so why does 0 wont work in the above case?

only < 0

[tight crescent]

It does.

-0 = 0

[serene anvil]

is your profile pic USS duluth?

[tight crescent]

The definition just says it's itself when it's greater or equal to 0

[serene anvil]

yes understood

thankyou!!

[tight crescent]

So you've figured out that the |y| = -y when y is less or equal to 0

If we take -4, we get |-4| = -(-4) or 4 = 4, which is correct.

If we take 0, we get |0| = -0, or 0 = 0, which is also correct

But if we take 2, we get |2| = -2, or 2 = -2, which is is not correct

[serene anvil]

rightt

do you suggest plugging number to check always?

@tight crescent

[tight crescent]

It can be a good idea because you can figure out whether you are not wrong (not necessarily correct though) or wrong

[serene anvil]

true bro

[tight crescent]

But with something like this, you can just try a negative number, 0 and a positive

[serene anvil]

in such case like x+2 =4 and x+2 =-4 we can directly split into 2 equations right?

mod (x+2)=4

one using when input is negative

[tight crescent]

Not sure what you mean

[serene anvil]

i mean like is it was mod (x+2)=4

@tight crescent

[tight crescent]

I don't understand. If you have two equations, x+2=4 and x+2=-4 you just solve each one for x

x = 2 and x = -6

[serene anvil]

no i expanded this _ mod (x+2)=4

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[noble delta]

never understood these

[tight crescent]

Do you know what a function is?

[noble delta]

ish

[tight crescent]

Right. Think of it as a machine.

It takes an input (usually denoted as x), the x then goes through the machine where all sorts of things get done to it (it might get squared, 5 might be substracted from it, etc.) and then it outputs a number (usually denoted as y).

[noble delta]

mhm

[tight crescent]

Here you have a graph of g(x). g is a machine, which takes the x, and then does things to it and outputs y

So the input is the x - axis and the output is the y - axis

If we for example take x = 1. Do you know what g(1) outputs?

Think of it as a line ( x = 1 ) and check where it intersects the graph

Then just read the y value from that point (that is the output)

[noble delta]

this dont work in desmos 😭

im trying to put it on a graph

[tight crescent]

No, just imagine the line x=1

[noble delta]

ok?

[tight crescent]

You see the line intersects the light blue line which is the graph of g(x) exactly once

That is a point denoted with (x, y). The first number is what you put in (1) and the second is what you get

[noble delta]

ok

[tight crescent]

So, if you pick x=1

What y value do you get

[noble delta]

uh

1?

[tight crescent]

Are you imagining this?

The purple point is where the line x=1 intersects the graph of g(x)

let's call it A.

You already know the first coordinate, x, which is 1

What is the y coordinate?

[noble delta]

oh

-2

right

[tight crescent]

Exactly!

Now what is g(3). This means you take x=3

[noble delta]

-1?

[tight crescent]

Yes!

[noble delta]

y = -1?

alr

[tight crescent]

Correct

Now what is g(-3)

[noble delta]

0?

[tight crescent]

That's correct!

And that's the whole magic to it

🙃

[noble delta]

ah thank you!

[tight crescent]

No problem 🙂

[noble delta]

.close

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[winged wharf]

Can someone help me with some density curve problems? Statistics

[winged wharf]

Anyone?

[odd edge]

@winged wharf Has your question been resolved?

[winged wharf]

<@&286206848099549185>

.close

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[obtuse rivet]

I have this question where I need to evaluate the function at the value -f(a). The question looks like f(x)=2x-5 how to I solve it?

[tall veldt]

It specifically tells you to "evaluate this function at the point -f(a)"?

[obtuse rivet]

Here I’ll show what it asks

[winged wharf]

I think it just wants you to put a negative sign on it

Im not sure tho

[obtuse rivet]

Could I change -f(a) to f(-a)?

[quasi sparrow]

No

[obtuse rivet]

Oh I thought I could. We’ll then I’m really not sure how to solve it

[quasi sparrow]

Plug x=-a into f(x)

[quasi sparrow]

You left out the word indicated from the question

[obtuse rivet]

I’ve done that one already

[quasi sparrow]

Oh

Then -f(a) is even easier

[obtuse rivet]

I need help with -f(a)

Oh it is?

How do I do it?

[quasi sparrow]

-f(a) is (-1) * f(a)

-any number = (-1) * any number

[obtuse rivet]

Ok

So do I insert for example -1a for f(x)?

[quasi sparrow]

...

That's not what I said at all

[quasi sparrow]

Did you see this

[obtuse rivet]

Yea

[quasi sparrow]

do you know what f(a)=?

[obtuse rivet]

2a-5?

[quasi sparrow]

Yes

Do you know (-1) * f(a) =?

[obtuse rivet]

Is it just -2a-5?

[quasi sparrow]

No

Use parentheses

[obtuse rivet]

Oh wait it’s 2a+5 right?

[quasi sparrow]

No

[quasi sparrow]

.

(-1) * (b-c)=?

[obtuse rivet]

-2a+5?

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[reef rapids]

which are true and which ones arent and why

[dry scarab]

do you know what those symbols mean?

[reef rapids]

yea

[dry scarab]

so what does N u Z = Q mean?

[reef rapids]

I know what the letters and the symbol means but i dont know what its telling me all put together

[dry scarab]

ok what's N u Z then

[reef rapids]

natural and interger

[dry scarab]

are you sure u is and?

[reef rapids]

its union

[dry scarab]

so what's a union of N and Z?

[reef rapids]

i dont know man

[dry scarab]

what's a union of {1,2,3} and {3,4,5} ?

[reef rapids]

{1,2,3,4,5}

[dry scarab]

ok, what's N

[reef rapids]

{1,2,3,4,5}

[dry scarab]

nope

[reef rapids]

?

[dry scarab]

how do you define N?

and Z?

[reef rapids]

N = 123
Z = -1 -2 0 5

[dry scarab]

so what's their union?

[reef rapids]

i dont knwo

[dry scarab]

what's the union of {-1,0,1,2} and {1,2}

[reef rapids]

{-1,0,1,2}

[dry scarab]

so what's the union of N and Z?

[reef rapids]

Q

[dry scarab]

please... <@&286206848099549185>

[reef rapids]

?

.close

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[dire dew]

hi

[tight crescent]

Hello

What do you need help with

[fringe bough]

hey, did you have a question?

or a problem you're workin on

[dire dew]

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxHi

Hi

[green elm]

that's a lot of x's

[dire dew]

It was a mistake

How are you doing

[green elm]

do you have a math question?

[dire dew]

Yeah

[slender crescent]

can you say your math question

[odd edge]

@dire dew Has your question been resolved?

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[livid briar]

Need help with number 7

I found it to be commutative, I also found it has no identity therefore no inverses

I THOUGHT I found it to be associative as well, but the book says otherwise

Here’s what the book says, I end up with the fractions but with just xyz on the numerator

And here’s my work

This time it’s just technical work, but I cannot seem to find my mistake

[green elm]

your work looks right to me

[livid briar]

So I’m right?

[green elm]

i think so

[livid briar]

I also checked online on math stackexchange and it seems people got the same result

Gonna need to write that down in the book

Ty!

[green elm]

yea the answer key is wrong, this is associative

[livid briar]

Heck yeah, I just found the incorrect solution online too lol

Ty and have a great day!

.close

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[obtuse rivet]

I need help with this problem

[scarlet junco]

Do you know a square that can be negative for x a real

[obtuse rivet]

What? Nope

[scarlet junco]

Do you know a cube that can be negative ?

[obtuse rivet]

Like -2?

[scarlet junco]

No like -2^3=-8

[obtuse rivet]

Oh yea I meant to put a negative in front of that

[scarlet junco]

So can there exist a square root that is negative ?

[obtuse rivet]

Yes

[scarlet junco]

Why ?

[obtuse rivet]

Oh wait no

A square root can’t be negative

[scarlet junco]

Ok, so can a cube root be negative ?

[obtuse rivet]

Yes

If the number under the cube root is negative it will always have a negative cube root

[scarlet junco]

Ok si what’s the difference between the square root and the cube root, can both of them take all real number ? Only one ?

[obtuse rivet]

Only the cube root can

The square root can’t take negative numbers

[scarlet junco]

Here’s your answer

[obtuse rivet]

Oh ok!

Thank you!!

[scarlet junco]

The domain of the square root would be all the non-negative real number but for the cube root it would be all the real number

[obtuse rivet]

Thank you for helping me understand

.close

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[twin wyvern]

how do we do b15

[sharp oak]

Find a span for it