help-10

[lyric pawn]

am i on the right path?

[spiral maple]

Is C invertible?

[lyric pawn]

yeah

[spiral maple]

then yes

[lyric pawn]

thanks!

.close

[obtuse pebble]

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[stoic shell]

Pointers? Can’t figure out a way to connect 2m and 2m+2 when I plug in m+1

[stoic shell]

In addition, when you plug in 0 for m, you get 1 for the even dimension equation which doesn’t make sense since 0 dimensions should have a volume of 0?

Ok that explains the 0 dimension part, but what about the proving part. The article doesn’t have a reference to that

<@&286206848099549185>

[obtuse pebble]

@stoic shell Has your question been resolved?

[obtuse pebble]

@stoic shell Has your question been resolved?

[obtuse pebble]

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[timid silo]

Quick question: when will m(m-1200) be a perfect square

[fervent cradle]

try thinking about prime factorisation

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

I thought about it

Im stuck

[sterile wyvern]

To start, maybe consider m^2-1200m-n^2=0 and find the determinant. We should impose it to be a perfect square

@timid silo

[timid silo]

Ye i tried that

[sterile wyvern]

m is an integer right?

[timid silo]

Find the determinant?

Yeah

M is a natural number

[sterile wyvern]

What did you get for it?

[timid silo]

I didnt look for the determinant

Oh wait is it just the thing under the root

[sterile wyvern]

I am referring to "b^2-4ac"

[timid silo]

Ye ye

1440000 + 4n²

Now i have to look at when this will be greater than 0 right

[sterile wyvern]

Isn't it (1200)^2+4n^2 ?

[timid silo]

Oops yeah

[sterile wyvern]

Ok, then we impose
(1200)^2 + (2n)^2 = c^2, for some c
That is a pythagorean triple

[timid silo]

c must be a positive integer?

[sterile wyvern]

Mm, I guess we can assume so, as it is squared

[timid silo]

I mean c² must be a perfect square right?

[sterile wyvern]

But then solutions will be in the form (1200 +- c)/2

Well, c^2 is always a perfect square

It's (1200)^2 + (2n)^2 that needs to be a perfect square

[timid silo]

Yeah my statements mafe no sense

[timid silo]

Wheres that coming from

[sterile wyvern]

That is the quadratic formula

If (1200)^2 + (2n)^2=c^2, with c>=0,
sqrt((1200)^2 + (2n)^2)=sqrt(c^2)=c

[timid silo]

I still dont see what i should be doing

[sterile wyvern]

So, the question reduces to finding all pythagorean triples a,b,c such that a=1200 and b is even

[timid silo]

Oooooh

Ye

That makes sense

And now how can i find all the triplets

[sterile wyvern]

First, actually if we use the reduced quadratic formula we get something a little simplified
m = 600 +- c

(600)^2 + b^2 = c^2

Is it correct?

[timid silo]

Yessir

[sterile wyvern]

Good, then we may use this parametrization for primitive pythagorean triples, where m and n are coprime

You can find it here
https://en.wikipedia.org/wiki/Pythagorean_triple

The multply anything by some factor k to obtain also non primitive ones

[timid silo]

Should i factor 600 now?

To get m and n

And then find all the triplets?

[sterile wyvern]

We swap a and b in the parametrization though

[timid silo]

Yeah i see

[sterile wyvern]

Yes

[timid silo]

Wait so b is 600 or 1200

[sterile wyvern]

We let 600=2mn

[timid silo]

Ok

[sterile wyvern]

Oh wait

[timid silo]

So i gotta factor 300

[sterile wyvern]

Actually we should already introduce k I guess

[timid silo]

Uhh

[sterile wyvern]

So, 600 = 2kmn, where m and n are coprime

[timid silo]

Cant i introduce k later?

After i found all the possible pairs?

I mean triplets

[sterile wyvern]

I think not, because we care for non primitive solutions as much as for primitive ones

[timid silo]

Yeah but we can find those at the end i think

[sterile wyvern]

In the sense that just 600=2mn would not be recoverable later

[timid silo]

Oh

Ok

[sterile wyvern]

Because then multiplying by k would alter 600 right?

[timid silo]

Makes sense

Yeah i get it

Ok so now i have to find all the m n and k

[sterile wyvern]

So, 300=kmn, m and n coprime

[timid silo]

Where m and n are coprime

Yeah

[sterile wyvern]

,w factor 300

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Mat#9616

[sterile wyvern]

I hope there was a quicker solution lol

[timid silo]

Now i still have to find all the possible solutions for m n and k

There seems to be quite a few of them

[sterile wyvern]

Yes, this is the boring part

So like m=2, then n=3, 3*5, 3*5^2, 5, 5^2

[timid silo]

Actually

Does it make sense that m>n?

I dont think so

[sterile wyvern]

Yes, right

I was thinking n>m, but let's do that instead

[timid silo]

Yeah yeah oops

I meant that

n>m

Makes no sense

[sterile wyvern]

Also, c=k(n^2+m^2) is symmetric in n and m, this is also relevant

[timid silo]

How

[sterile wyvern]

It's not ahah, n>m already does it

Sorry

[timid silo]

Its ok

[sterile wyvern]

What if you count all n=p for p a prime and I count all composite n?

[timid silo]

300, 1
150, 1 2
100, 1 3
75, 1 2 4
60, 1 5
50, 1 2 3 6
30, 1 2 5 10
25, 1 2 3 4 6 12
20, 1 3 5 15

First number is m

The other numbers are n

I just didnt check for coprimes yet one sec

300, 1
150, 1
100, 1 3
75, 1 2 4
60, 1
50, 1 3
30, 1 5
25, 1 2 3 4 6 12
20, 1 3 5 15

Those r the possible values for m and n

And i also left the other list for the k values

[sterile wyvern]

Are we doing m>n?

[timid silo]

We are doing n>m

I swithed them again lol

No wait

Aaaaaaah

Yes we were doing m>n

Hows this so confusing

So ye now we fpund the possible values for m n and k

Should we calculate all the triplets now?

[sterile wyvern]

$$300=2^2\cdot3\cdot5^2$$\
$$n,m | 300, ,0< n<m, (n,m)=1$$\
$$M=600 \pm \frac{300}{nm} (n^2+m^2)$$

[warm shale]

Mat

[timid silo]

Yes

[sterile wyvern]

Is it enough as a solution?

[timid silo]

Thats the solution for?

The entire problem?

[sterile wyvern]

Your problem

[timid silo]

Rlly?

[sterile wyvern]

Yes, why are you surprised?

We were counting for that!

[timid silo]

I thought we are going to get something simplier

Ok nvm i understood now

[sterile wyvern]

There are many solutions I feel, maybe another approach would find something more easily parametrized

[timid silo]

Yeah probably

[sterile wyvern]

Where did you the the problem from?

[timid silo]

I was doing another problem

Then i got stuck at this part

And so i thought the solution was going to be simplier

[sterile wyvern]

Oh lol, so you needed a smooth formula?

[timid silo]

Yeah lol

Myb the whole approach to that problem was also wrong tho

[sterile wyvern]

Anyway, this also counts negative M

No it doesn't, nevermind

[timid silo]

A negative squared number?

How

[sterile wyvern]

Ahah yeah

No wait it does

[timid silo]

Rlly?

[sterile wyvern]

Yes, if m<0, m(m-1200)>0

[timid silo]

Oooh ye

I thought m had to be the perfect square

This problem took long enough

[sterile wyvern]

Yes, I am getting tired as well

[timid silo]

Can i actually tell you what the initial problem was

[sterile wyvern]

Sure, I am curious

But then I have to go ahah

[timid silo]

20m=k(m-15k)

I dont even remember what i had to find tho tbh

I didnt write it down

I tried to solve this problem for a guy on this srv

Myb i just had to find integer solutions for k and m

The only solution i found was k=40 and m=1200

Anyway tysm for the help

.close

[obtuse pebble]

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[sterile wyvern]

Interesting

You're welcome, bye!

.close

[obtuse pebble]

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[obtuse pebble]

@nova marsh Has your question been resolved?

[timid silo]

@west mauve read #❓how-to-get-help , this channel is already in use.

its fine, we jsut have a system to keep everything running well.

unfirnitly i dont know anything aobut vector spaces so i cant really help you much

good luck xihiro

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[gilded needle]

how far did you get with 34?

looks good so far

what's 3^2?

the question asks for the answer in scientific notation

doesn't scientific notation usually look like a * 10^n where 1 <= a < 10?

[idle thunder]

you already have the something

you already posted it

[gilded needle]

in particular, a should not be .9

it's a correct answer, but is it technically scientific notation? depends on how you define scientific notation

i think if it's normalized, the mantissa should be >= 1 and < 10

well how does your book define it?

sure

but then there are many valid answers

0.9 * 10^11

0.09 * 10^12

0.009 * 10^13

etc

[keen rune]

Hello guys, can someone help me with B question?
should I use the basic Arithmetic Prog. for both of them and to multiply each side with 360€ and 400€ respectively?

[obtuse pebble]

@timid silo Has your question been resolved?

[keen rune]

<@&286206848099549185>

[obtuse pebble]

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[timid silo]

<@&286206848099549185>

[spiral maple]

#❓how-to-get-help

[upbeat plinth]

.close

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[muted meteor]

hellom

[muted meteor]

for this one I don't really know where I went wrong

So that’s my work for it

Wait I see it, I left out the 2 on the bottom

[obtuse pebble]

@muted meteor Has your question been resolved?

[obtuse pebble]

@muted meteor Has your question been resolved?

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[onyx dock]

how can i type this out

[civic zealot]

$\sqrt[3]{x}$

[warm shale]

Zybikron

[onyx dock]

oh cool thanks

.close

[obtuse pebble]

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[acoustic pelican]

Need help parametrizing y = sqrt(1+x^2) for 0<=x<=1

[tardy epoch]

It's already parametrized

(x, sqrt(1+x^2)) works

[acoustic pelican]

okeh ill give it a go, its for a line integral question

and i originally used cosh and sinh and i couldnt solve it

ok so

this should be (3sqrt(3)-1)/6

with the above parametric

[obtuse pebble]

@acoustic pelican Has your question been resolved?

[obtuse pebble]

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[unique shale]

Hey

[unique shale]

Can I get help with area of composite figures

<@&286206848099549185>

[idle thunder]

hey protogen

[unique shale]

Hey

[idle thunder]

post a problem/specific part of a concept you need help with ^^

[unique shale]

So funny story after I did my exam and went to grade 8

I forgot everything about composite figures

Now it's the last term of grade 8

I have a exam tomorrow

I don't know anything

[idle thunder]

okay

https://www.youtube.com/watch?v=z4Lat1uOQI4

[unique shale]

I actually watched that video

[idle thunder]

any specific part of it making you struggle?

[unique shale]

I still don't understand

Yes

[idle thunder]

which part?

[unique shale]

Length x width

How do u know what exactly to multiply

[unique shale]

Take this problem for example

[sonic wharf]

You can split it into two different pairs of rectangles. Both options will give you a full answer if you’re looking for total area

[unique shale]

Oh

Like this

[safe mantle]

No

[unique shale]

?

[sonic wharf]

These are not rectangles

You can still calculate areas with trapezoid formula, but it’s needlessly more complex

Just make a horizontal or vertical line putting the corner in one rectangle or the other

[sonic wharf]

The extra length of one of the lines on the other portion relative to its parallel friend will tell you the second dimension of the first fella

[sonic wharf]

Sure, or vertically. Either works.

Do You see how to get the dimensions for these rectangles now?

[unique shale]

Yes

Thanks of all the help

Can I get help for a another thing before I close

Still on the topic of area

How do you find the area of a circle using only the radius

[sonic wharf]

equation for a circle’s area is pi r^2

[unique shale]

Can u explain

[safe mantle]

Square the radius and multiply it by pi

[unique shale]

Ohhhhhhhh

Like

R2 ×π

[safe mantle]

Yea but dont forget the ^ symbol

[unique shale]

Okie

I'ma dot close now

Thanks

Hopefully I pass my exams

[safe mantle]

Good luck

[unique shale]

Thank you I'll need all the luck I can get

.close

[obtuse pebble]

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[short spruce]

what

x^{-2} is not a squared term

it's a reciprocal square

i don't know what that means

[sonic wharf]

There’s still only one variable, x

But it has a term to a different power than the quadratic expression form requires - it isn’t quadratic

[obtuse pebble]

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[gloomy carbon]

Can I use a formula to solve this?

[obtuse pebble]

@gloomy carbon Has your question been resolved?

[stray cave]

what have you done so far?

[gloomy carbon]

Honestly, none. I don't know how to solve it, sorry.

[stray cave]

no worries, have you learnt about permutations?

[gloomy carbon]

Yes

[obsidian isle]

There are 90,000 five digit numbers.

[stray cave]

Above asked for numbers that doesnt include 0 and the digits mustn't repeat.

[obsidian isle]

I know.

[stray cave]

is it 9C5?

[obtuse pebble]

@gloomy carbon Has your question been resolved?

[gloomy carbon]

Can I know what formula did you use?

[copper latch]

So yk permutation, there are 9 digits, How many different ways you can order it?

[gloomy carbon]

9! ?

[copper latch]

No, your number should be 5 digits

P(n,r) = n! / (N-r)!

Its the formula

R is how many numbers you take from N

[gloomy carbon]

Oh 15,120. Thanks!

[vernal wren]

.close

[obtuse pebble]

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[slate lake]

Hei guys qnyone could help with a trigonometric equation please ?

[unborn sonnet]

@slate lake maybe post the problem haha

[slate lake]

For sure , my bad lol , sqrt root 2 sin2x =1 , for 0<= x<= 180

[unborn sonnet]

sin2x=1/sqrt(2)

then what must 2x be?

[slate lake]

Hm not sure i get it

[unborn sonnet]

so

first step is to put x left and all the rest right

[slate lake]

So sin x = 1/sqrt 2 / 2 ?

[unborn sonnet]

then you find the solutions that suffice the 0<=x<=180 rule

[slate lake]

Omg thanks dude

Appreciate it a lot

[unborn sonnet]

yw

[obtuse pebble]

@slate lake Has your question been resolved?

[dense wing]

anyone know how to do this

[obtuse pebble]

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[timid silo]

help ne

[timid silo]

ok

so

i have to solve

3x+1

[glossy ibex]

solve what

[timid silo]

3x+1

[glossy ibex]

its already in the simplest form

[timid silo]

oh hey friend detox

wait nvm

WAIT

I FINISHED IT ALL

[glossy ibex]

when did we become friends

[timid silo]

when u helped me with my math homework last time

[glossy ibex]

ah

ye

@timid silo the question needs more context

[timid silo]

no

i mean

smart

.close

[obtuse pebble]

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[vestal lily]

hello

[vernal wren]

When two exponents are multiplied, their powers get added

And when they're being divided then the powers are subtracted

[vestal lily]

im confused

a bit

[vernal wren]

So assume x to be a rational number

x² x x⁴ = x⁶

x⁴/x² = x²

[vestal lily]

yeah

[vestal lily]

yeah then what do i do next

[vernal wren]

Now try the question once again, instead of x you've got 4, in the numerator they are being multiplied so add the powers and then subtract the power that is there in the denominator

[vestal lily]

im a bit confuesed

ive been trying to do it and i get stuck

[spiral maple]

what's 4^2 * 4^5?

@vestal lily

[vestal lily]

8 25

[spiral maple]

??????

do you know what exponents are?

Ignore exponent laws for a second, did you really say 4^5=25??

[vestal lily]

sorry just really confused

[spiral maple]

what's 4^2?

As repeated multiplication, ie 4^2 by definition

[vestal lily]

8

[spiral maple]

???

[vestal lily]

so it will be 8

or 16

[spiral maple]

4*4=8?????????

[vestal lily]

is it 16

[spiral maple]

yes, 4*4 is in fact 16.

cause $4^2=4\times 4$.

[warm shale]

Mosh

[vestal lily]

oh thats easier sorry its 16

[spiral maple]

yes, so likewise, what will 4^5 be (as repeated multiplication)?

[vestal lily]

that will be 4x4x4x4x4=1024

[spiral maple]

yes

I didnt ask for the fact 4^5=1024 but yes

[vestal lily]

sorry

[spiral maple]

so now what is 4^2*4^5?

It'll be $(4\times 4)(4\times4\times4\times4\times 4)$

[warm shale]

Mosh

[vestal lily]

do i add them togather

[vestal lily]

gives me 1040

[spiral maple]

I dont care about the actual values

also no it wouldnt

[spiral maple]

do you see a + anywhere in anything I've written?

[vestal lily]

no so its multiplication thenm

[spiral maple]

yes..

cause in the question, there is a * sign

so trivially you get $4^7$ since $4^2\times 4^5=4^{2+5}$

[warm shale]

Mosh

[spiral maple]

and cause there are 7 4's multiplied together.

[vestal lily]

ohhhhhhh i get it a bit now because im adding the powers togather

[spiral maple]

yes

(As was said explicitly already)

[vestal lily]

that makes soo much sense

[vestal lily]

is there any next steo

[spiral maple]

well duh

you've only dealt with the numerator thus far

there's still the entire concept of the denominator

[vestal lily]

alright sorry so what do i do

[spiral maple]

apply the other exponent law you were told about.

[vestal lily]

which is n

[spiral maple]

n is not a law

[spiral maple]

.

[vestal lily]

soo i have to divide them

[spiral maple]

Have you read the question you're asking about?

cause you shouldn't have to question the entire existence of it

we simplified the numerator, that means you know what is left to do.

[vestal lily]

yeah i did sorry i just get confused a bit sorry

and is that right

[spiral maple]

.

[vestal lily]

i havent divided it yet

oh no

[stable sparrow]

Ay what up cuh

[vestal lily]

so i have to put 4 2 x 4 5 =4 25

[spiral maple]

NO

WE

[stable sparrow]

You need a calculator for this

For sure

[spiral maple]

dont say stupid stuff.

[stable sparrow]

Do you not need a calculator?

[spiral maple]

1. No
2. Read if you want help
3. We've already gone over why 4^2*4^5 is 4^7

[vestal lily]

because it is 4 power 2 =4x4

yeah i get that

[spiral maple]

You dont

cause you just said bullshit, despite me having already told you the answer

but anyway, yes, $\frac{4^2\cdot 4^5}{4^4}=\frac{4^7}{4^4}$

[warm shale]

Mosh

[stable sparrow]

Hey you gotta calm down

Is this private?

[vestal lily]

yeah i have that down in my book

[spiral maple]

yeah, I just don't like answering obvious/should be obvious questions.

[vestal lily]

and the i have to divide it with 4 n

[spiral maple]

??

the n is part of the answer

ie 4^(some power)

nowhere does it ever say divide by 4^n

[vestal lily]

oh sorry so i should divide top by the bottom

[spiral maple]

yes

you should the division you're actually given.

[vestal lily]

so do i divide 7 and 4 which is the power and leave the main the same

[spiral maple]

you dont...

Read the rules you were told about

[vestal lily]

oh sorry so i should multiply

not multiply

[spiral maple]

Read the rule

and tell me what you dont understand about it

Cause it's apparent you havent read it imo

[vestal lily]

the rule here sorry a bit confuese

[spiral maple]

No

The rule for dividing exponentials

Cause that's what we're doing now...........

[vestal lily]

i have to subtract the powers

[spiral maple]

Good, you finally read

[vestal lily]

so it will be 7-4 =3

[spiral maple]

that would be the power, yes

[vestal lily]

and 4 will stay the same

[vestal lily]

so it will be 4 3

[spiral maple]

4**^**3

[vestal lily]

oh that was actually a lot easier can you also help me with another question please

[spiral maple]

no

and stop pinging me every single message

[vestal lily]

alright

.close

[obtuse pebble]

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[bright geyser]

is the zero vector by defn

[bright geyser]

const?

[spiral maple]

wdym

0 vector never changes in the space; once the operations are defined the 0 vector is made

@bright geyser

[bright geyser]

ty

[obtuse pebble]

@bright geyser Has your question been resolved?

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[timid silo]

Not sure how to approach h

[solemn ravine]

sqrt(ab) = sqrt(a)sqrt(b)

set ab = 8

what integers a,b multiply together to get 8?

[timid silo]

4 and 2

[solemn ravine]

so sqrt(8) = sqrt(4)sqrt(2)

sqrt(4) = 2

so sqrt(8) = 2sqrt(2)

so the answer to 4a is k = 2

now do the rest

[timid silo]

hmm?

I still don't get how that solves h

[solemn ravine]

what dont you understand?

[timid silo]

k != 2

[spiral maple]

Sqrt(1/2)=1/sqrt(2)

So rationalize it

[solemn ravine]

k definitely equals 2

ohhhh h

my bad my bad

[timid silo]

yeah h lol

[spiral maple]

It doesn't

[solemn ravine]

same rule applies here tho

sqrt(ab) = sqrt(a)sqrt(b) implies sqrt(a/b) = sqrt(a)/sqrt(b)

[timid silo]

yeah I get that part

so as mosh said Sqrt(1/2)=1/sqrt(2)

but not sure where to go from here

[solemn ravine]

"rationsalise" in this case means to make it so the bottom of the fraction doesnt have a square root in it

what would you multiply the top and bottom of the fraction by in order to remove sqrt(2)?

[timid silo]

hmm

do I need to multiply by a fraction

[solemn ravine]

we have a fraction a/b, you are comfortable with the fact that a/b = (xa)/(xb) right?

[timid silo]

what's x?

[solemn ravine]

any number

[spiral maple]

Non-zero

[solemn ravine]

ofc

so like lets say i have 3/2

6/4 = (2*3)/(2*2)

yes?

[timid silo]

yeah

[timid silo]

maybe multiply top and bottom with sqrt(2)?

[solemn ravine]

yes ❤️

[timid silo]

nice

I got sqrt(2)/4

[solemn ravine]

1/sqrt(2) = sqrt(2) / sqrt(2)^2 = sqrt(2) / 2

[timid silo]

but idk where to go from there

[solemn ravine]

should be sqrt(2)/2 not 4

youre done

you found k

sqrt(2)/2 = 1/2 * sqrt(2) as the question wanted

[timid silo]

ohh

[timid silo]

yup my bad

[solemn ravine]

no worries enjoy

[timid silo]

ok tysm

.close

[obtuse pebble]

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[arctic bison]

can someone help me by telling me if use law of sines or cosines

[obtuse pebble]

Please don't occupy multiple help channels.

[arctic bison]

no one answer my last question

[spiral maple]

Draw a diagram and find out

[obtuse pebble]

@arctic bison Has your question been resolved?

[arctic bison]

can you draw the diagram pls

or is this correct

[arctic bison]

hey

can someone help me with this

.closw

.close

[obtuse pebble]

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[dusky cradle]

help

[dusky cradle]

pls?

[dusky cradle]

answer 17?

[static beacon]

yo

[dusky cradle]

yo

tell me what is wrong

[static beacon]

yes

that is right

[dusky cradle]

what else is right

also q6

how do I go about it

[amber sentinel]

i think it would be easier if you draw the table instead of listing every of them

[dusky cradle]

wait okay

q6 tho

what do I do

[static beacon]

well

6^6 no

it can be a 2 and a 2 or 4 or 6 or 8 or 10 or 12

and that can happend to each number

so its 36

[dusky cradle]

is question 3 and 4 correct?

[ornate sonnet]

questions are never generally wrong...

[dusky cradle]

wdym?

math is either correct or incorrect

ur wrong

on all the questions you've helped me on

q 6 is 11

q 5 is 11

q 5/16

q3 1/10

do you know what u are doing

@ornate sonnet

@static beacon

[novel knoll]

q4 and q2 are wrong

[dusky cradle]

q2 a

[novel knoll]

No

[dusky cradle]

q 4 is 5/16

[dusky cradle]

yes actually

[novel knoll]

Oh read it wrong, yes

[dusky cradle]

...

[novel knoll]

…

[dusky cradle]

.close

[obtuse pebble]

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[obtuse pebble]

@timid silo Has your question been resolved?

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[fair hull]

hi

[fair hull]

can someone tell me how to get to the last part of the eqn from the middle part?

besides fully expanding then factorising again

.close

[obtuse pebble]

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[stray elk]

i have to find the pointy angle between the two lines

[obtuse pebble]

@stray elk Has your question been resolved?

[gloomy valve]

@stray elk Note the angle can be found using the dot product of the two directional vectors

So by writing m in parametric form it should be pretty easy

[obtuse pebble]

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[glacial oar]

hi can someone assist me through on how i can solve this?

im not entirely sure if theyre mentioning the whole alphabet and the 3 digits beinf 1,2,3

[keen cave]

,rotate

[scarlet gale]

@glacial oar You can think of it as you have A, B, C, 1, 2, and 3 to pick from.

So, a passcode could be AAB333.

Hmm, for part b, you'd need D in the alphabet, so say you have D, E, and F.

[glacial oar]

okok what abt c

[scarlet gale]

Well, you have four-figure passcodes, so you might have Letter, Letter, Letter, Letter, but that doesn't alternate between letters and digits.

What patterns of sequences would alternate between those?

[glacial oar]

so letter, digit, letter, digit?

[scarlet gale]

OK, and what else?

[glacial oar]

letter, letter, letter, digit
digit digit, digit, letter
is that it?!

[scarlet gale]

No, they need to alternate.

Which means to switch back and forth each item in the sequence.

So, LDLD is correct.

But there's one more that's correct.

[glacial oar]

DLDL?

[scarlet gale]

Good.

So, how many digits are there to pick from?

[glacial oar]

2 from each sequence given (?)

[scarlet gale]

No, what does the problem say about how many letters there are to pick from?

[glacial oar]

3 letters same with digits

[scarlet gale]

OK, so for LDLD, you have 3 letters, 3 digits, 3 letters, 3 digits to choose from.

Does that make sense?

[glacial oar]

mhm yeah

[scarlet gale]

You pick the first letter from your three available letters.

You pick the first digit from the three available digits.

You pick the second letter from the three.

You pick the second digit from the three.

So, how many LDLD combinations?

[glacial oar]

6?

[scarlet gale]

Why 6?

[glacial oar]

1st ltr, 1st digit, 2nd ltr, 2nd digit, and so on which are two so 6? thats how i assumed to get 6

[scarlet gale]

OK, let's go over the combinations.

Letters: D, E, F
Digits: 1, 2, 3

D1D1
D1D2
D1D3
D1E1
D1E2
D1E3
D1F1
⋮

So, there are more than 6.

[glacial oar]

wait soo

3^4 ?

[scarlet gale]

Yes, that's right.

[glacial oar]

oof so im gonna list all of them then

[scarlet gale]

So, what about DLDL?

No, you don't need to list them.

It only asks how many there are.

You know how many LDLD there are.

[glacial oar]

i have to since it says here 'State your possible outcomes by systematic listing' so i suppose it's the one u did?

or

am i wrong

[scarlet gale]

Does that maybe apply to other problems before this, like another section of problems that this one isn't in?

[glacial oar]

oh wait nvm i dont need to list

[scarlet gale]

Listing 243 different ones will take a while.

[glacial oar]

it's in the section where it asks

[glacial oar]

yeah i had to do the same with the grid table earlier with 4 given values it was time consuming

[scarlet gale]

It's good to do a few problems like that.

It gives you a picture of what's going on.

Like when I showed there were more than 6, you then figured out that you multiply 3 with itself 4 times.

[glacial oar]

yupp

so going back we have 243 combis for DLDL

do i just multiply 243 by 2?

[scarlet gale]

Yes.

[glacial oar]

so my answer for c is my outcome for 243x2?

[scarlet gale]

On some of these problems, like when you get into probability, leave it unmultiplied so that you can easily cancel common factors in the numerator and denominator.

So, you'd write 2 · 3⁴ in a fraction.

[glacial oar]

got it

[scarlet gale]

But here, you can do the multiplication.

And get 486.

[glacial oar]

so what abt B how do i determine the first and last figures r digits and the figures in the middle is the letter D

[scarlet gale]

Let's list a few of them to get the idea.

So, the first few might be:

1DD1
1DD2
1DD3
2DD1
⋮

So, how many of those will there be?

[glacial oar]

uhh

27?

[scarlet gale]

Almost.

How many choices for the first thing?

[glacial oar]

3

[scarlet gale]

How many choices for the second character?

[glacial oar]

3 still

[scarlet gale]

What do the middle characters have to be?

[glacial oar]

D

[scarlet gale]

Right, that's only 1 to choose from.

So, 3 · 1 ⋯

What about the last two characters?

[glacial oar]

i have no iea what chars ur mentioning AHH

hm

[scarlet gale]

Well, a character is just some symbol you write, like a letter or a digit or a space or punctuation mark.

So, 1DD1 has four characters.

[glacial oar]

oh wait it's D and (digit) so 2?

[scarlet gale]

Not quite.

Let's do this.

Let's say you can pick from Q, R, S for the first character and 1, 2 for the second character and 4, 5 for the third.

[glacial oar]

mhm

[scarlet gale]

So, let's list all of those out.

Q14
Q15

Q24
Q25

R14
R15

R24
R25

S14
S15

S24
S25

So, there are 12 of them, but there's a pattern here.

See how the 4 and 5 are attached to each possible combination of the first two characters?

[glacial oar]

yup

[scarlet gale]

Like Q1 has 4 and 5. Q2 has 4 and 5.

So, the last character multiplies everything by 2.

Q1
Q2

R1
R2

S1
S2

Like those 6, combined with two choices on the third gives 6 · 2 choices in total.

And the same thing here.

[glacial oar]

mhm yeah

[scarlet gale]

The number of first characters is doubled so that you can get each of the different combinations with the second character.

So, 3 · 2.

So, altogether, you have 3 · 2 · 2.

Do you see why?

We can try another way if you don't quite see it.

[glacial oar]

it seems rather complicated im sorry 😔

[scarlet gale]

OK, let's try it the other way.

Q
R
S

We have 3 first characters.

Then, when we combine them with 1 or 2:

Q1
Q2

R1
R2

S1
S2

It doubles the number of options.

Do you see that?

We now have 6 options.

@glacial oar

[obtuse pebble]

@glacial oar Has your question been resolved?

[obtuse pebble]

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[sleek sinew]

Can someone check my answers for b) and c) for #8?

Is the way i set up the shell diagram correct for 8?

[obtuse pebble]

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[sleek sinew]

<@&286206848099549185>

[leaden ibex]

When you fail at all rules

with one message

[tardy epoch]

Use .reopen next time

[obtuse pebble]

@sleek sinew Has your question been resolved?

[obtuse pebble]

@sleek sinew Has your question been resolved?

[obtuse pebble]

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[timid silo]

<@&286206848099549185>

[tardy epoch]

Read this

[timid silo]

o

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

i dont get how do i find the surface area

i get i do 1.5x2.6

then do the other 1.5x2.6

which is

3.9 and since there is 2 i dont need to divide

then i think id do

3.9x2

for the other side

so 7.8 for the triangles

the base is 15

would ijust

do 15x3

• the triangles

idk

[delicate bay]

u would divide this number. since 1 triangle is base times height divide by 2. so two triangles would just be one full triangle.

[timid silo]

yeah normally i would divide it by 2 but there's 2 triangles so it stays at 3.9

[delicate bay]

nevermind, i just saw you didn't divide. you're all good.

[timid silo]

rlly

i dont think the awnser is 52.8

[delicate bay]

15x 3

[timid silo]

45

+7.8

[delicate bay]

i mean, based on the math and calculating each side, that would work

[timid silo]

ayy

i got it right

gg

[delicate bay]

nice job

[timid silo]

.close

[obtuse pebble]

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[tall furnace]

Struggling to start this

[tall furnace]

I understand how to utilize differentials and separable equations but I don't understand hot to get part A. I have tried seperating and taking the integral, I have tried Isolating the W, and to no avail. I may be on the right track but I don't know where to go with the info I get.

[obtuse pebble]

@tall furnace Has your question been resolved?

[obtuse pebble]

@tall furnace Has your question been resolved?

[dull rune]

have you heard of a logistic differential equation?

[tall furnace]

No I have not

pulling it up now

[dull rune]

youve been given the solution to this particular logistic differential equation

[tall furnace]

thats the W(t) right?

[dull rune]

yea

in a) they want $$kW(1-\frac{W}{M}) > 0 $$

[warm shale]

ohNoiAmHere

[dull rune]

when k, M > 0

[tall furnace]

Right

wait

so do I just manipulate the equation to have W isolated then?

[dull rune]

so the first thing to notice is that you solve $$W(1-\frac{W}{M}) > 0$$ instead

[warm shale]

ohNoiAmHere

[dull rune]

yea

just manipulate for W

[tall furnace]

okay so k divides to 0

but then were left with W^2+W

W/M*

[dull rune]

yea or $$MW^2 - W > 0$$

[warm shale]

ohNoiAmHere

[dull rune]

with M > 0

[tall furnace]

Maybe im super brain farting but how do you isolate the W from there

[dull rune]

factor out a W

[tall furnace]

Ive gotten to this form before just with dW/dt

[dull rune]

$$W(MW - 1) > 0$$

[tall furnace]

but then its W(MW-1)

[warm shale]

ohNoiAmHere

[dull rune]

so either W < 0 and MW < 1

or W > 0 and MW > 1

[tall furnace]

doi, Im so dumb

I realized it as soon as I typed it out

[dull rune]

i feel that

do it all the time

it took me twenty minutes to do an integration by parts the other day :D

[tall furnace]

Okay sweet, thanks for the help. I looked up a logistic differential vid so hopefully that will help with the rest

[dull rune]

alr np

[tall furnace]

rip, I love those

[cold scarab]

hello

i need some help

.

.open

[dull rune]

try #help-6

[tall furnace]

.close

[obtuse pebble]

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[timid silo]

when theres an exponent on the f in f(x) does it mean anything?

and how would i solve this equation if it does? thank you!

[idle glen]

i think it means nth derivative in this case

[junior inlet]

you can keep finding the 1st, 2nd, 3rd, 4th, 5th, 6th, ... derivatives of cosine. are there any patterns?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

ohh that makes sense! i was thinking i was looking for the derivative but didnt know exactly where it said to look for it, thank you!

[timid silo]

wouldnt it just keep repeating? like how it ends up going back to the original equation after youve taken the derivative enough times

[junior inlet]

yep

so can you calculate those derivatives/

[timid silo]

yesyes, that makes sense, so then would the nth derivative part play a role in the answer?

[junior inlet]

i mean

you should try to calculate those derivatives first

to find a pattern

[timid silo]

because i know that the derivative is -sin(x) if it was first derivative

[obtuse pebble]

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[timid silo]

.reopen

[obtuse pebble]

✅

[obtuse pebble]

@timid silo Has your question been resolved?

[astral ivy]

f: cos
f1: -sin
f2: -cos
f3: sin
f4: cos
f5: -sin
f6: -cos
f7: sin
f8: cos
f9: …

[astral ivy]

Notice anything here?

@timid silo

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[craggy elbow]

Hello could someone help me with the mathematical equation for counting only the borders of cube field. I want to know how many cubes surrounding the area and not inside

[craggy elbow]

I want to know what is the equation

[scarlet mantle]

this is simply the area, so length multiplied by width

[craggy elbow]

Yeah but this will give me the entire anount of cubes

I want only the borders

[scarlet mantle]

oh gotcha

$(length * 2 ) + (width * 2) - 4$

[warm shale]

FeO

[craggy elbow]

Thanks i will try it :D

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[craggy elbow]

.reopen

[obtuse pebble]

✅

[craggy elbow]

It worked but I can't understand the explanation of that equation

Like why does it work?

Why -4 in the end

[scarlet mantle]

when you count the length and the width seperately you count each corner twice

so you have to subtract 4 to compensate

[craggy elbow]

Ohh i see thanks , and last question why do you multiply by 2?

[scarlet mantle]

each side has two "copies", for example with the width there's 6 blocks on top and 6 blocks on the bottom

[craggy elbow]

Ohhhhhhhhhh i got it

Thank you so much :D

[scarlet mantle]

no problem! best of luck :)

[craggy elbow]

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[wheat palm]

any help appreciated

[obtuse pebble]

@wheat palm Has your question been resolved?

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[robust sleet]

confusion identities

[high lily]

*compound angle

how exactly are you answering it words

[main lodge]

Do you know this identity: sin(a + b) = sin(a)cos(b) + sin(b)cos(a)?

[royal basin]

cofunction identities was probably what @robust sleet wanted to say

[robust sleet]

yes

need to remove auto orrect

[main lodge]

If you know that its quite an easy one to show

Yes

[obtuse pebble]

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[odd hedge]

(2sqrtw+2 +5)(2sqrtw+2 +5)

[odd hedge]

i cant really image it, idk commands

[timid silo]

So like this?

[odd hedge]

yes

[timid silo]

What's the question/ equation?

[odd hedge]

how do i foil it

the square roots confuse me

[timid silo]

Well let me give you a hint

a square root * the same square root = what's under the root

or this

$$ \sqrt{a} \times \sqrt{a} = a$$

[odd hedge]

under the root?

[warm shale]

Arabianonymous

[odd hedge]

yes

so

wil it be

4w+8?

for foiling the sq roots

[timid silo]

Yes

[odd hedge]

now to multiply it with 5

is it 10sqrtw+2?

just 5*2?

[timid silo]

yeah

[odd hedge]

i got

4w+33+20sqrtw+2

as my foil

[timid silo]

that's right

[odd hedge]

oh ok thanks 👍

[timid silo]

alright np