help-0

[slate monolith]

cause if they have the same number the combined mean would be 74

does that make sense

[stone solstice]

Right oh ok ye

[stone solstice]

What i was thinking

So is it possible to just make up an amount

For redmond

And double that for power

[slate monolith]

I dont think that would help

now look at the row for boys and girls

[stone solstice]

Oh

So for boys and girls

Redmond

[slate monolith]

wait we dont know that mean

[stone solstice]

Crap

This is so confusing😭

[slate monolith]

ah we can figure it out actually

for redmond, adding girls brings up the avg from 68 to a 72

and girls at remond have a 76

[stone solstice]

Ah yea

[slate monolith]

what does that mean

[stone solstice]

That means

[slate monolith]

same as the first row

[stone solstice]

Equal

Boys and girls

[slate monolith]

yes

[stone solstice]

Ok

[slate monolith]

now do power

[stone solstice]

Soo we know same amount of gitls and boys and redmond

[slate monolith]

and we know power has double the boys

[stone solstice]

Wait how do we know its double though

[slate monolith]

from here

[stone solstice]

Oh ok yea

So we know that 68/n+80/2n=76?

[slate monolith]

uh

not quite

you dont need an equation but if you did it would be [68(n)+80(2n)]/3n = 76

just a weighted average

so what do we know about the girls in power

[stone solstice]

Theres less girls

Than boys

[slate monolith]

okay but how much less

[stone solstice]

60% less?

Cause 82 mean would entail 84 for girls

[slate monolith]

we are looking at B: 80, G: 90, BG: 82

[stone solstice]

Ye

Oh

[slate monolith]

this is a bit trickier so you might want to make an equation

[stone solstice]

Thats mean though right

[slate monolith]

yeah

[stone solstice]

So the equation would be (80n+90)/n=82?

Wait

The question says a and b are relstively prime

Like prime #?

[slate monolith]

not quite

we need to have a scalar of n there

so nx

[slate monolith]

it means they have no common factors

[stone solstice]

Oh ok

And so

(80xn+90n)/xn

=82

[slate monolith]

no

close though

we have to divide by the total number of students

[stone solstice]

Xn²

Oh

[slate monolith]

no

[stone solstice]

Ohh

So

It doesn’t give us total though😭

[slate monolith]

you dont need the number specifically

you know that its boys plus girls

in your equation how many boys are there

[stone solstice]

80

Or what

No

For boys

There’s x number

Or n

[slate monolith]

no

[stone solstice]

It’s x right i think

Oop

[slate monolith]

there are nx boys and n girls

[stone solstice]

Ah i see

Since theres more boys

The x is there

[slate monolith]

thats why you are multiplying 80 by nx and 90 by n

[stone solstice]

So

[slate monolith]

so (80xn+90n)/(xn+n) = 82

now do you see something

[stone solstice]

Ahhh

Yoy can

Subsittude

First equation

Solve for n

In first equation

Then use to solve for x

[slate monolith]

not quite

you will never know n

[stone solstice]

Shit lol

[slate monolith]

but you dont need to

look at the equation again

(80xn+90n)/(xn+n) = 82

[stone solstice]

Factor out

Xn+n

And it cancels?

Or factor out just n

Ohh

Factor x out

I think

Yes

That has to be it right

[slate monolith]

do the algebra

and show me what you get

[stone solstice]

Like solving for x?

[slate monolith]

ye

[stone solstice]

Ok

X=4?

so that means that there are four times more boys

than girls

[stone solstice]

did u get 4 as well

u still there man @slate monolith

[lone heart]

@stone solstice Has your question been resolved?

[slate monolith]

@stone solsticei went for a walk

[stone solstice]

oh okok sry bout that

i'm still here though lol

i'm at a roadblock

[slate monolith]

yeah thats correct

although you could have just simplified the fraction at the start

[stone solstice]

true lol ic

[slate monolith]

(80xn+90n)/(xn+n) = (80x + 90)/(x+1)

anyways

so lets lay out what we know

in Redmond, #B = #G
in Power, #B = 4#G

[stone solstice]

yea

[slate monolith]

#B_P = 2#B_R same as #B_Power = 2#B_Redmond

[stone solstice]

uh

[slate monolith]

this was the first ratio we did

[stone solstice]

oh ok right yea

i

c

wait hold on

can u check ur dm for a sec

[lone heart]

@stone solstice Has your question been resolved?

[lone heart]

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[mossy veldt]

Hello please help me with this

[mossy veldt]

If you know french

[lone heart]

@mossy veldt Has your question been resolved?

[lone heart]

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[small tide]

Uhh i need some help

understanding the Question

[real arch]

consider the triangle ECM

you're finding the angle at C

[small tide]

Oh

how tho?

[real arch]

because you know the side lengths of the base, you can find the length of its diagonals

notice that the length of the segment CM is that diagonal divided by two

[small tide]

so would AC be 12?

[real arch]

once you get that you can determine the angle using an inverse trig function and the height, which is given

[real arch]

no, remember Pythagorean theorem

[small tide]

Oh yea

uhhhh still stuuck..... its late at night and im tired...

.close

[lone heart]

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[alpine sable]

Can anyone help me proove this?

[slender quiver]

,rotate

[real arch]

woah that's so sick

[alpine sable]

Im just starting trigonometry and idk what ti do lol

[alpine sable]

I have no idea what happened

Oh it rotated

Lmao

[slender quiver]

something called rotating

:O

[real arch]

cool bot

[slender quiver]

ok what is ctg and tg

[long axle]

cot,tan

[alpine sable]

Like a/b and b/a¿

[alpine sable]

Yeye

Ig its different in my language

[slender quiver]

oh

uhm

what is cot and tan like uh extend it

[alpine sable]

Literally no idea what you mean

[slender quiver]

what is tan(x)

trig function/another trig function

[flat ridge]

$1-\frac{\sin^2\alpha}{1+\cot\alpha}-\frac{\cos^2\alpha}{1+\tan\alpha} = \sin\alpha \times \cos\alpha$

I think

[hot bluff]

for latex use \sin \cos \cot \tan so its not italics

[ocean seal]

a8d_

[alpine sable]

Yeah that's it

[slender quiver]

what is tan(x)
trig function/another trig function

[flat ridge]

$\sin\alpha\times\cos\alpha=\frac{\sin 2\alpha}{2}$

[ocean seal]

a8d_

[flat ridge]

I dont think that helps but idk

[hot bluff]

imo i'd leave rhs alone and focus on simplifying lhs

[alpine sable]

I have like no idea whats going on

[hot bluff]

do you know basic trig identities?

after 1351 problems id hope so lol

[alpine sable]

Ive done 0

This is the first

Of trigonometry

[hot bluff]

first trig problem ever?

[alpine sable]

Yeah

[flat ridge]

try $\frac{\sin^2\alpha}{1+\cot\alpha}\times\frac{1-\cot\alpha}{1-\cot\alpha}$

[ocean seal]

a8d_

[hot bluff]

well, you need to study trig identities first before you can simplify this

[alpine sable]

Ik this

[alpine sable]

Tf is sec and csc

[slender quiver]

something

[hot bluff]

secant and cosecant

[flat ridge]

sec = 1/cos csc = 1/sin

[hot bluff]

the inverses of sin and cos

[alpine sable]

Oh ok

[hot bluff]

you need to memorize all your basic identities before you can tackle a problem like this

the trig hexagon helped me a lot. https://www.mathsisfun.com/algebra/trig-magic-hexagon.html

[alpine sable]

This seems like its necessary for that problem

[flat ridge]

thats why I sent it lol

[hot bluff]

pythagorean identities will absolutely be needed for this

[slender quiver]

wow

[hot bluff]

it covers basically everything except double angle identities

[alpine sable]

Guess ima give up for now there's so much i dont know

.close

[lone heart]

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[merry warren]

How is this even possible?

[urban pine]

logs of negatives live in C

[merry warren]

oh right ty

[urban pine]

no idea how to do this tho lmao

[merry warren]

let me try for a little bit lol

the imaginary part of $\ln(-x)$ is always $i\pi$ right?

[ocean seal]

piduck

[merry warren]

$\frac{i-x^2}{\pi i+ln|x|} \Rightarrow -x^2$ must $=\frac{1}{\pi}\ln|x|$

[ocean seal]

piduck

[merry warren]

Now how do you solve that

[lone heart]

@merry warren Has your question been resolved?

[tacit arch]

,w solve -x^2 = log(|x|)/pi

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

Probably not true

[merry warren]

ig il just put that

.close

[lone heart]

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[tacit arch]

You should multiply by the complex conjugate in the top and bottom to solve for the imaginary part

i.e. make denominator real

[lone heart]

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[fallen bloom]

how to prove that arithmetical progression is increasing

[slender quiver]

yes

[fallen bloom]

in my case

how to prove

this is increasing

[slender quiver]

yeah

it converges

[fallen bloom]

i need to show why it is increasing can you help me with that?

[tacit arch]

Write it as 1- 1/(2n+1)

[slender quiver]

inf

[fallen bloom]

then

[tacit arch]

Write out some terms and look for a pattern

[fallen bloom]

got it thanks

but how can that

be written as 1-1/(2n+1)

[tacit arch]

Find a common denominator for this difference

[fallen bloom]

would that be 1?

because difference between them is 1

[tacit arch]

Do you know what a common denominator means

Like 1 + 2/3 = (3+2)/3

[fallen bloom]

i guess i do not know

[alpine sable]

This is not an arithmetic progression

[fallen bloom]

it's geomertycal?

[alpine sable]

Neither

[fallen bloom]

well if it is increasing a_n+1 - a_n should be greater than 0

[alpine sable]

It's not any specific type of progression that I know of

[fallen bloom]

isn't that right?

[alpine sable]

That is correct, yes

[fallen bloom]

well i tried to use it

and did not come to an end

[alpine sable]

very sad

[fallen bloom]

yup

word in between means find

should i use a1 + d(n-1) again?

[alpine sable]

Sorry, yes

[fallen bloom]

i tried

can you help?

[alpine sable]

Show what you tried

[fallen bloom]

so a_1 + (a_1 + (n-1)d) = 387

[alpine sable]

Yep

[fallen bloom]

is 2a_1 + (n-1)d correct then?

[alpine sable]

Yes

[fallen bloom]

now i am stuck at this

2a_1 + (n-1)d = 387

[alpine sable]

Find an expression for the other thing

The one on the right

[fallen bloom]

how?

should i simplify that?

[alpine sable]

Whoops, I have completely forgotten I was in this channel

You should be able to expand a_7+a_(n-6) using the formula

That's what I meant

[fallen bloom]

a_1 + 6d + a_1 + (n-7)d

is that right?

[alpine sable]

Yes

Now simplify

[fallen bloom]

2a_1 +6d + (n-7)d

can it be simplified more?

[alpine sable]

Yes

Factor out d

[fallen bloom]

right

2a_1 + d(6 + (n-7))

[alpine sable]

Mhm

Continue

[fallen bloom]

so, we have 2a_1 + (n-1)d = 387

we should be able to use that

[alpine sable]

Yes

[alpine sable]

Simplify this further

[fallen bloom]

oh

is 6 + (n-7) same as n-1

[alpine sable]

Indeed

[fallen bloom]

right so it will be equal

387

will be both

[alpine sable]

There you go

[fallen bloom]

you have been most helpfull today

merci

[alpine sable]

Sans problème

[fallen bloom]

.close

[lone heart]

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[stone ruin]

Don't even know where to start with the second one

[gusty gorge]

write det(A - lambda I) = det(MBM^-1 - lambda I)

and then use the fact that MM^-1 = I to rewrite the lambda I

[stone ruin]

but you can't group them like that can you?

[gusty gorge]

group what?

[stone ruin]

M and M^-1

[gusty gorge]

where did I group them

[stone ruin]

like

MBM^-1 doesn't just become B does it?

[gusty gorge]

it does not

where did I do that

[stone ruin]

ohhhhh

so like

rpelace I with MM^-1

[gusty gorge]

yes

[stone ruin]

i dont really see how that helps

[lone heart]

@stone ruin Has your question been resolved?

[stone ruin]

<@&286206848099549185>

[stone ruin]

.close

[lone heart]

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[vale ginkgo]

Can someone please help me with this question 14 please?

[flint belfry]

count the straight lines

then use Pythagorean theorem to find SR

[vale ginkgo]

,rotate

[vale ginkgo]

ohh

[flint belfry]

i tjink

think its c but idk

doing it mentally

[vale ginkgo]

hmm

but the thing is its not a triangle

there are 4 sides

[quiet vector]

well

u can cut this figure into a right triangle and a rectangle

[flint belfry]

why would you do that?

[vale ginkgo]

explain further

[quiet vector]

this

hmm

look at the point below q

join that point and s

[flint belfry]

find c

@vale ginkgo

thats what im saying

[vale ginkgo]

ohh

hold on

but

that means

is c 5?

is it b (13)?

ohhh

[wary stream]

How are you getting that?

[vale ginkgo]

so

since we do pythagorean theorem

we use the bottom triangle

[vale ginkgo]

in this picture here

so a^2 + b^2 = c^2

so A is 3 and B is 4

in the question it says the vertical distance between the adjacent dots it 1

so going back

3^2 + 4^2 = c^2

then makes

9 + 16 = c^2

then

25 = c^2

so 25 square root it 5

so c is 5

when we have found that out

we know that PQ and QR are both 4

4 + 4 + 5 is 13

am I right @flint belfry?

[wary stream]

Not quite the right answer

The process is correct, wrong answer

It's a 4 sided shape

Where is that 4th side?

[vale ginkgo]

ah no

14

yes you are right

sorry mb my mistake

so 14 is the answer?

[flint belfry]

yh

[vale ginkgo]

thanks alot

A hockey team has 6 more red helmets that blue helmets. The ratio of the red helmets to blue helmets is 5:3 . The total number of red helmets and blue helmets is?

can someone help on this question? please and thank you

.close

[lone heart]

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[deft creek]

hi guys i want to ask a question about math
so 80% chance is 4/1
or 4 red 1 white
so if i have 4 red 6 white
how many chance is it?

[frank apex]

number of desired divided by total

[sharp thorn]

80 percent is what?

[deft creek]

chance

no need anything

Guys?

[sharp thorn]

i dont understand what you mean by 80% chance is 4/1

it is 400%

[deft creek]

No wait let me explain

similar to this

@sharp thorn

but 4 red 6 white

how many %?

[sharp thorn]

oh right

add then

add them

and divide the nmber of red with the sum

[deft creek]

so 4 + 6/10?

4+6/4-10

[sharp thorn]

no

4/4+6

[deft creek]

0.4?

@sharp thornis this correct?

[sharp thorn]

yes

make in in percent

[deft creek]

04*100%

40%

@sharp thorni want to confirm if this is correct?

[sharp thorn]

yes

[deft creek]

okay thanks then

problem solved

[lone heart]

@deft creek Has your question been resolved?

[lone heart]

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[violet ore]

I don't understand why $a_n = s_n - s_1$

[ocean seal]

donut

[violet ore]

I tried writing out the first terms: $$s_1 = a_1$$ $$s_2 = a_1 + a_2 \Rightarrow a_1 = s_2 - a_2$$

[ocean seal]

donut

[rose sigil]

umm

[rose sigil]

it's not?

it looks like there's some typos in the pic but it doesn't say that

it should say $a_n = s_n - s_{n-1}$

[ocean seal]

💜𝓁𝒶𝓎𝓁𝒶💜

[violet ore]

oh

[rose sigil]

after the "we use that"

[violet ore]

how do I show that

[rose sigil]

s_n = a_1 + a_2 + ... + a_{n-1} + a_n and s_{n-1} = a_1 + a_2 + ... + a_{n-1}

if you subtract s_{n-1} from s_n you just have a_n left

[violet ore]

i see, thank you

[rose sigil]

yep ^^

[violet ore]

.close

[lone heart]

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[little cairn]

howdy

[real arch]

howdo

[little cairn]

I have been stuck on this for almost an hour

[raven haven]

show the diagram you drew

[little cairn]

Im thinking it is a parallelogram

so that AB=CK and BC=BK

[lone heart]

@little cairn Has your question been resolved?

[little cairn]

.close

[lone heart]

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[rocky urchin]

i cant understand this at all

[rocky urchin]

how would it be 3 and not 1

[little cairn]

because x=-4

so its 5-(-4)

which is 9

square root of 9 is 3

[rocky urchin]

ohhhh

i see

[little cairn]

ye

[rocky urchin]

i even thought at first it could be multiply but i forgot i had to remove brackets afterwards and add em

aight thanks alot

.close

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[minor otter]

For question 22 last time I checked if you have - - then it stays - -

[minor otter]

But the only way it works is if it’s + -

[real arch]

you're right, it doesn't work any other way

you can't multiply two negatives to get a negative

and you can't multiply two positives to get a negative

one has to be positive and one has to be negative

[alpine sable]

i feel like it's possible

[minor otter]

So u can see why I’m at a dilemma

Why I’m having*

[alpine sable]

for example if you multiply two numbers to get -32

and add two numbers to get -4

you could get the factors -8 and 4

bc -8+4=-4

and -8*4=-32

[minor otter]

But this specific case

[real arch]

those are still positive and negative

[alpine sable]

true

[real arch]

there isn't a way to have two negatives

when you have a negative b and c

if you have a negative b and c it will always be differing signs

[minor otter]

Is my expression factorable or not

Cause it’s killing me rn

[alpine sable]

it is factorable apparently

[minor otter]

It’s factorable it just doesn’t follow the rule

[alpine sable]

yeah

exactly

[minor otter]

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[midnight parcel]

I have this question where i have no idea where to start

[flat ridge]

Setup an equation that has an input like circumference_of_circle or radius_of_circle or perimeter_of_square then define a function in terms of that to calculate the length of total string that would be needed to make the total areas 25m^2

[midnight parcel]

i think the equation would be L = 4x +2pir

then i set that equal to the 25 m^2

[flat ridge]

but you need to define x in terms of r or vise versa

[midnight parcel]

ok

[flat ridge]

if I say r is the radius of the circle it will have area pi r^2 and circumference 2pi r
because you need 25m^2 the amount you still need will be 25-pi r^2 so the square must have that area

With that I get L = 2pir +4sqrt(25-pir^2)

then the rest is a standard optimization problem

none of this is necessary for part 1. A circle is the most efficient perimeter/area so just make a circle with area 25

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[fiery lodge]

is this how the empty set works when multiplying for the cartesian product? $$ P({∅} × {1,2})
{\ \emptyset,{\emptyset,1},{\emptyset,2},{{\emptyset,1},{\emptyset,2}}\ }
$$

[ocean seal]

qowu

[fiery lodge]

i'm not sure why it's formatting differently but it's this

[vale wigeon]

curly braces have a special meaning in LaTeX code

if you want to type actual braces you need to escape them: like this: \{ ... \}

anyway, there's some confusion here between sets and ordered pairs

[fiery lodge]

ah thanks

[fiery lodge]

it's supposed to be in roster notation

i mostly based my answer based off examples like these but i'm not sure where i messed up

[vale wigeon]

and roster notation it is in

{∅} × {1, 2} itself is { (∅,1), (∅,2) }

[fiery lodge]

thanks ann

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[rocky urchin]

where the 12x came rom

[rocky urchin]

should it not be 9?

[chrome salmon]

What?

[rocky urchin]

second line second term

[chrome salmon]

2(2)(3x) = 12x

[vale wigeon]

do you know how to expand (a+b)^2?

please don't say a^2+b^2 please don't say a^2+b^2 please don't say a^2+b^2 please don't say a^2+b^2 please don't say a^2+b^2 please don't say a^2+b^2

[rocky urchin]

thats what i was about to.....

[vale wigeon]

no, (a+b)^2 ≠ a^2 + b^2.

do you know how to expand products like (a+b)(c+d)?

[rocky urchin]

expand as in simplify them?

[coral thorn]

multiply

[vale wigeon]

expand as in expand.

[rocky urchin]

oh yeah

[vale wigeon]

as in apply the distributive law

[rocky urchin]

foil method right?

[coral thorn]

yes

[rocky urchin]

axc then axd

and then bxc and bxd

[coral thorn]

yes

[vale wigeon]

cringe.

first off the FOIL shit is cringe, and then you make it worse by writing multiplication with the letter x.

[coral thorn]

(a+b)^2 = (a+b)(a+b) not a^2 + b^2

[rocky urchin]

oh right i should use .

[rocky urchin]

i see

[coral thorn]

or *

[vale wigeon]

you should use *

[coral thorn]

• is better

[vale wigeon]

or \* to stop discord eating them

[rocky urchin]

thats better

[vale wigeon]

anyway

expand (a+b)(a+b) properly

write it down in full and don't skip any steps or symbols

[rocky urchin]

hmm still a bit confused

[coral thorn]

multiply (a+b) with (a+b)

[coral thorn]

like this

then state your answer

[vale wigeon]

you're confused at what exactly

[rocky urchin]

lets say its (2+3)^2 so i do 2.2 + 2.3?

[vale wigeon]

wrong slash

backslash not forward slash

there's no such operation as "and then" in math. (not to mention that even if there was, you'd still be two terms short.)

are you capable of working with symbolic expressions?

[coral thorn]

because you're squaring the entire expression, its not 2^2 + 3^2, its (2+3)(2+3)

[vale wigeon]

missing two terms and also missing the point im trying to make here.

[coral thorn]

so it would be (2 * 2) + (2 * 3) + (3 * 2) + (3 * 3)

[vale wigeon]

also using a point like this will make it sound like you're writing down decimals.

[vale wigeon]

i was going to !nosols you if i wasnt so desperate.

[coral thorn]

huh?

[vale wigeon]

i was hoping OP would have been able to write this himself.

[rocky urchin]

ahhhhh

[coral thorn]

he's confused with something, i'm just helping him out

[vale wigeon]

you're helping him out by just giving him the expansion readymade.

[coral thorn]

just clearing up the confusion for him

[rocky urchin]

i got it, lets take
(2x+3)^2 as example

[coral thorn]

yes, solve that now

[rocky urchin]

its 4x^2+12x+3

[vale wigeon]

"solve" bad

no

[rocky urchin]

wait wait

[vale wigeon]

the lone 3 should have been 3^2

[coral thorn]

try writing it out like i did before

[coral thorn]

like this

[rocky urchin]

(2x*2x) + (2x*+3) + (3*2x) + (3*3)

took long

[coral thorn]

what should the 2nd term be?

[vale wigeon]

\* or spaces around each asterisk

(who am i kidding, this is SO not idiotproof.)

[coral thorn]

yes that looks good

[rocky urchin]

gotcha, thanks alot both of you lol

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[tropic rose]

to do the dy would i do integration by parts

[tropic rose]

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[carmine knoll]

I don't know how to calculate the lengths a and d pls help

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@carmine knoll Has your question been resolved?

[carmine reef]

By solving the triangle outlined in green

You can get values of angles like CBD

[carmine reef]

Then you can calculate ABD and use that to solve the other triangle

[carmine knoll]

ohh

[carmine knoll]

i will try it thx

[carmine knoll]

!close

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[amber plover]

how this wrong

[keen pagoda]

@amber plover Consider the final statement again.

[amber plover]

i already got it thanks tho

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[weary grail]

Does anyone know why I have computed T^2 wrong?

[weary grail]

Apparently there shouldn’t be a power of t underlined in red

[marsh rapids]

the transpose is a linear operator

So you can simplify this

[weary grail]

Oh t is transpose 😑

[weary grail]

But I didn’t know this

[marsh rapids]

Yeah,
It can be t or T on the right or on the left
All 4 notations are possible

[weary grail]

Wdym by t or T ?

[marsh rapids]

$A^T, A^t, ^tA, ^TA$

[ocean seal]

mateo713

[weary grail]

Ahhh, the notation, got it

[marsh rapids]

But without spaces for left exponents ofc

[weary grail]

Yeah got it

[marsh rapids]

It's easily verified from the definition

[weary grail]

What does linear operator mean ?

[marsh rapids]

A -> A^t is linear

And involutive, i.e. is its own inverse

[weary grail]

Yeah this makes sense

[weary grail]

But this is interesting

So the transpose map being linear allows me to simplify the red right?

[marsh rapids]

Most things in linalg are linear, except stuff like inverses and determinants

[marsh rapids]

Yes. Along with it being an involution

[weary grail]

(A+A^t)^t = A^t + A

[weary grail]

Ah yeah for A^t)^t

Thanks for the help

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[vocal hawk]

is this classified as linear or non linear?

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@vocal hawk Has your question been resolved?

[vocal hawk]

anyone has any idea?

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[alpine sable]

i understand till the marked part but how did it make C-B subset of C-A ??

[slender quiver]

because x is c-b

[ocean hawk]

each step follows from the previous one

[alpine sable]

i don't understand how did C-B become a subset here?

[ocean hawk]

just by the definition of subset

[ocean hawk]

you start with x in C - B, then you show that x must also be in C - A

[alpine sable]

ok then?

[ocean hawk]

then what?

[alpine sable]

i understand x is in C-B and C-A but how did C-B became a subset here?

[ocean hawk]

$A \subset B \iff (\forall x: x \in A \Rightarrow x \in B)$

[ocean seal]

cwatson

[alpine sable]

ok

[ocean hawk]

so you start by assuming x is in C - B. To show that $C - B \subset C - A$ you must reach the conclusion that $x \in C - A$, which was done

[ocean seal]

cwatson

[alpine sable]

so can C-A be subset of C-B ?

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[burnt meadow]

Did they make a mistake?\

Or am I just missing osmething

full q

how did they factor the top

[long axle]

It looks like a mistake

[slender quiver]

D:

[burnt meadow]

ok tysm

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[pliant estuary]

Can somebody please tell me where did this sqrt go? I have the same answer, but in the step after the one with the red circle, i have
$$
\frac{y\sqrt{x^2+y^2}-x^2y}{\left(\sqrt{x^2+y^2}\right)^3}
$$

[ocean seal]

marejak023

[long axle]

Didn’t they multiply the top and bottom by sqrt(x^2 + y^2)?

$\frac {y \sqrt {x^2 + y^2} - \frac {x^2 y}{\sqrt {x^2 + y^2}}}{(\sqrt {x^2 + y^2})^2}$

[ocean seal]

Stephen

[pliant estuary]

but then there would be this term?
$$
\frac{x^2y}{\sqrt{x^2+y^2}}
$$

[ocean seal]

marejak023

[pliant estuary]

on the top

which is not in the next step

[long axle]

Yes, but then u make a common denominator on the top

Then once u do that, that common denominator in the top will go down to the actual denominator

[pliant estuary]

but doesnt to the actual denominator go this term?
$$
(x^2+y^2)^{-\frac{1}{2}}
$$

[ocean seal]

marejak023

[pliant estuary]

sorry so for many questions, i really suck at basic algebra lmao

thats 1/sqrt x^2+y^2

[long axle]

How’d u get this

Actually just do what I said here

[long axle]

This

[pliant estuary]

okey, thanks

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[tulip wolf]

This is on an edexcel non calculator ppq, I'm trying to figure out what the answer could be and why if possible. I honestly have no idea where to start here

[slender quiver]

125/100 = 100/x

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[final burrow]

#help-0 Hey mr bean, I would approach this using algebra. Let C be cereal and P be price. So Jack's idea can be shown as C x 1.25 = P. To see Sadias idea, we isolate C making it C = P x 0.8, so answer is 80%

[tulip wolf]

im a bit confused, how would I get the 0.8 part?

[final burrow]

0.8 would come from 1/1.25, ie we shifted the 1.25 from the left hand side to the right

[tulip wolf]

ooooooooh right

that makes sense now

tysm

[final burrow]

great, glad we could help 🙂

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[wheat isle]

to find the roots of -(x-2)

[wheat isle]

do you just solve for x

so x=2?

[vale wigeon]

finding the roots of a polynomial, or more generally of a function, means finding the inputs at which the function's value is zero.

so you solve the equation -(x-2) = 0 for x.

and yes, you get x = 2.

[wheat isle]

ohh

okay

and would that be real and equal?

[long axle]

Real and equal?

[wheat isle]

yeah the root

-(x-2)=0
x=2
so there would be 1 root/solution and it will be real and equal?

[round vapor]

2 is defo real, as for equal, it doesnt matter, because it is supposed to have only 1 root

[wheat isle]

so it would only be real? not equal

[round vapor]

pretty sure fundamental rule of algebra says for x^n, there are n solutions

[vale wigeon]

it's equal to itself if that's what you're asking.

but your polynomial is not a quadratic.

[gray isle]

there aren't any other things to compare it to

[vale wigeon]

your polynomial is linear, and so always has exactly one root.

(it can only fail to have exactly one root in case its leading coefficient happens to be zero, which it doesn't, by virtue of it being the leading coefficient.)

[wheat isle]

Does the discriminant work only on quadratics?

[vale wigeon]

there exist generalizations of the discriminant to higher degrees, but they are absurdly long.

even for cubic polynomials, the cubic version of the discriminant is itself a polynomial of degree 4 in the coefficients. (compared to the quadratic discriminant, whose degree is 2 just like the polynomial giving rise to it...)

so analyzing the behavior of even a cubic in terms of its discriminant gets much harder.

[wheat isle]

ah okay

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[cloud moon]

if I get one like for every 5 views, does it mean I have a:
• 5 to 1 ratio
or
• 1 to 5 ratio
?

[gray isle]

depends

on how you word it

like to view ratio would be 1 to 5
view to like ratio would be 5 to 1

[cloud moon]

Thank you ^_^

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[meager dagger]

Hi I have an equation that I'd like to solve : 2^n = k. How would you do that ?

[long axle]

Solve for n?

logarithms

[meager dagger]

Yeah for n

But I'm not very familiar with log in different basis, is there a way with ln ?

[thick grail]

change of base lol

[kindred anchor]

log(😅) =💧* log(😄)

[meager dagger]

Ah yeah ok thanks, so $$ln(2^n) = ln(k) \ \Rightarrow n.ln(2) = ln(k) \ \Rightarrow \ n = \frac{ln(k)}{ln(2)}$$

[ocean seal]

weareinthematrix

[long axle]

Yep

[meager dagger]

Ok, thank you !

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[alpine sable]

Question:

[alpine sable]

Mark scheme:

I know how to get to 24m^3 but I am struggling to understand the next steps to find h

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[alpine sable]

<@&286206848099549185>

[meager dagger]

So first maybe find the volume of the lower prism

in red

[alpine sable]

that would be surface area of cross section * length to find the volume of the lower prism so:
-the surface area of cross section is bh/2(area of a triangle) with h being 10m but what is the value of b?
-also what would be the length that would multiply by the surface area of cross section?

[meager dagger]

In green, that's your triangle so this is the cross section. Now the length is perpendicular to this cross section... You can think of this as a cube (rectangle, idk how to say in english) over a triangle. So on the front left, the side parralel to the one that is 1.2 is 1.2 too. Now the total length on the front left is 2m so what you're looking for, b (in purple) is 2m - 1.2 m

[alpine sable]

i see, so then i do 0.8*10/2 giving us the area of 4,
next i multiply 4(area of triangle) by 1.2(length perpendicular to the cross section) giving us the volume of 4.8?

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[meager dagger]

Err no, sorry I didn't say it well... Your prism isn't flat so the triangle is one face but the 1.2 is in the same plane as your triangle so it is irrelevant, the length is 5 m

Now the flowing speed is 20 l per minute, there are 60 min in one hour, so 20 x 60 = 1200 l/h. The liquid flows for 20 h so that's 1200 x 20 = 24 000 l at the end of the flowing. Now the volume of the triangular prism is (0.8 x 10)/2 x 5 = 20 m3. So in l that's 20*1000 = 20 000 l. There is more liquid in the pool that the volume of the rectangular prism so the rectangular prism is totaly full and there some water left in the rectangular part. There is exactly 24 000 - 20 000 = 4000 l left in the rectangular part. In m3, that's 4000/1000 = 4 m3. So what is the height of the water in the rectangular prism ? The area of the base is 5 x 10 = 50 m2. 4 m3 / 50 m2 = 0.08 m. So the total height is the height of the triangular prism plus the height we just found, 0.8 + 0.08 = 0.88 m

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[alpine sable]

Where did I mess up

[alpine sable]

looks fine to me (just remember the absolute values around x-11)

[winter light]

What is the question? You have to find if (for what x) it converges or diverges?

[winter light]

Yeah, I think so too

[alpine sable]

I think I’m confused about where it converges

[alpine sable]

How would I find where it converges

the ratio test tells us the limit needs to be <1 https://en.wikipedia.org/wiki/Ratio_test#The_test

ie find $x$ such that $\frac{|x-11|}{11}<1$

[ocean seal]

Toby

[chrome salmon]

Alright

[alpine sable]

11

[chrome salmon]

Why?

[alpine sable]

0 less than one

[chrome salmon]

So?

[alpine sable]

yes, it converges when x=11. But it also converges for more values of x. Rearrange the inequality to find a all values of x that converge

Is it like the expression < 1

yeah

[alpine sable]

this one

[alpine sable]

bruh

Huh?

X < 0?

[winter light]

Do you know how to solve |x| < 3 for example? @alpine sable

[alpine sable]

for the people using this channel currently can i finish my question from earlier i ran out of time when searching for solutions lol

[alpine sable]

open a new channel #❓how-to-get-help

[winter light]

If you are doing exercises with series/sequences you have to know very easily how to solve basic inequalities with abs value 😅

[alpine sable]

I just solved for it

I know how to solve for inequalities

X < 0

[winter light]

So what is the solution of this? @alpine sable

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@alpine sable Has your question been resolved?

[lone heart]

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[zinc cairn]

I'm kinda confused on how to solve this prob:

[zinc cairn]

I think B is false but not too sure

I think by the Spanning set thm, A & C should be true, right?

But B also seems to be true, but not sure

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[vast bobcat]

can someone explain why the three questions are not the same

I got 10 for all 3 but it’s only correct for a

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[red hollow]

Can someone see if I’m doing this right

[red hollow]

<@&286206848099549185> please someone lol

Idk how to do b so if someone can help me with that

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[fading abyss]

Could some explain to me how you know if you have to add 180 degrees or subtract it like in Sin and Tan?

[sudden rover]

I'm having some trouble understanding how to do this problem. Any assistance is appreciated.

[tacit arch]

!help

[lone heart]

Please read #❓how-to-get-help

[pseudo ice]

[in particular, it's not help channel 0 specifically that you're supposed to go to ]

[alpine sable]

∫(e^(2x) * sin(3x^2 + x + 5))/(4x^3 + 7x^2 - x + 2) dx = √(2x^2 + 5x - 3) + ln(x^3 - 4x^2 + 7x - 2)

[lone heart]

Please read #❓how-to-get-help

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[fading abyss]

<@&286206848099549185>

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[eternal pumice]

i need help

[slate monolith]

@eternal pumice#❓how-to-get-help

[slate monolith]

draw it out every time and youll see

to have the same sin value you need to stay on the same side of the x axis

so you do 180-theta

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@fading abyss Has your question been resolved?

[alpine sable]

Could someone help me with finding the intervals through the the f'(x) of a function?

[slate monolith]

#❓how-to-get-help

and

[alpine sable]

ty!

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[median oar]

Try sketching a graph of the quadratic

(Try not to use a graphing calculator)

Yeah quadratic is the same as parabola in this context

It’s good for certain applications

So when is that less than 0

What x values make the curve less than 0?

Not quite

That’s where x and y are both negative

We want when only y is negative

When x = 1/4 what is y

Know what

I’m asking a question

What is y when x=1/4

Oh

You sub it into the quadratic

Quadratic inequalities is usually asking when is the graph below the x axis

Or when is the graph above the x axis

Usually for a quadratic with roots a and b

[median oar]

This would be a<x<b

[median oar]

This would be x<a or x> b

For down facing quadratics

It was to get you to consider other values of x that might also result in y being < 0

Yes

Ok first consider the parabola ax² + bx + c = y where the discriminant is > 0

That means it has 2 real roots

When we ask for the roots of the equation

It does because discriminant is positive

That’s why I specified the discriminant is > 0

Anyway

[median oar]

What this is really saying is

Given ax² + bx + c = y

Find ax² + bx + c = 0

That’s when it intersects the x axis

Yeah?

It doesn’t matter how you solve it

It just matters that it means graphically, it intersects with the x axis

Now if we consider > < signs instead of =

Now we aren’t asking when the graph equals the x axis

We are considering when the graph is less than or greater than the x axis

So we want to provide a range of x values

In this graph

We can see that when x is between the 2 roots the curve is under the x axis

When x is less than the left root or greater than the right root it’s above the x axis

So when we are asked to find 6x² + 5x < 4

Yes

Now for you question, which answer satisfies this

What do you mean by all values of y

Yes

(0,10) is not on the curve

The curve is special because it satisfies the quadratic

I’m in here a lot generally so you should see me around

I don’t help people in dms because it’s easy to spread misinformation and miss certain tricks

Lots of fantastic people help out here

You could just solve for the roots

Then look at the coefficient of x² to see if it’s face up or face down

Then determine whether you have a<x<b or x<a or x>b

If the question asked for 6x² + 5x > 4

You’d have…?

Instead of this what would you get

Mhmm

Here’s how I’d do it