help-10

[random olive]

So it that the final answer?

[unreal musk]

Basically yep, you get (with signs corrected!) that e2 = f1 - 7f2 and e1 = -f1 + 8f2, as they asked!

[random olive]

Okay yay, thank you!

[unreal musk]

A pleasure, hope that helped!

[random olive]

Yes you were very helpful

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[icy cape]

Simplify

[ruby lion]

Exponent rules

[icy cape]

Can you elaborate

Would you do

9^1/3 * 5^1/3

For numerator

and

9^1/3 - 3/4 * 1/3^1/3 - 3/2

Which is

9^-5 * (1/3)^-7

Or

1/(9^5 * (1/3)^7))

OR

1/59049 * third root of 7

?

i think thats wrong

a bit confused

[ruby lion]

So yeah looks like it will be useful to get the bases (45, 9, and 15) on the same footing
So splitting the 45 in to 9 * 5 is good
But into 3^2 * 5 is even better

Once those bases are on an even footing, I reckon it will be a lot easier

When I say even footing, I mean that 3 and 5 are the only numbers you need to multiply to make any of those bases

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[alpine gull]

struggling with this question about the antiderivative of f(x)

[inland matrix]

Note that there should be a +c at the end

That +c(constant) term actually makes a difference though

If c= -1/2, you get option c

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[edgy needle]

excuse me

[edgy needle]

can someone plz explain what this means

[timid silo]

what exactly confuses you

[edgy needle]

all of it

what does this mean

are we using like

cosine law or sine law or something

what

is that wher ethe cos and stuff comes frokm

[timid silo]

it's like per definition

\newcommand{\joe}[1]{\vb*{\vec #1}}
[
\joe a \vd \joe b = \norm{\vp{\joe b}\joe a}\norm{\joe b}\m\cos\theta
]

[edgy needle]

what the fish

[timid silo]

this is called the dot product

it's a scalar. I think at your level just take it as fact

[edgy needle]

erm

how am i supposed to understand it

is it just memorising

what the hell is this

[ruby lion]

Plug it in to the dot product formula 🙂

[edgy needle]

is that this

but im confused i dont understand the formula ):

[ruby lion]

This shows a proof for the dot product formula from the cosine rule

Make sure you know what is happening to turn one line in to the next

It's not important to remember though

If you just remember the dot product formula, it will help you a lot

[edgy needle]

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[worldly lagoon]

Why is the answer not just this?

Because 9x^2 matches to u^2 so u must be 3x so 3x * 3x = 9x^2

and a^2 matches 1 if you do 1^2 which is still 1

[latent walrus]

you ignored the 27

[worldly lagoon]

oh right its a coefficient

so would it be 27 *

or 9 *

[latent walrus]

also youre doing a u substitution, that needs to be accounted for

u=3x dx=du/3

so there is a factor of 27/3 which is 9 yeah

[worldly lagoon]

interesting, and the du/3 is just 27/3 but why is that factor applied as the 27 is brought out?

couldn't I have just brought the 27 out then integrated?

[latent walrus]

wouldnt change anything

youd still factor out a 1/3 and itd become a 9 nonetheless

[worldly lagoon]

I suppose I am not quite understanding, why is a 1/3 getting factored out in that case

wouldn't it just be this?

and then you have u = 3x and a = 1

so you have 27 * 1/1 arctan(3x/1) + C?

you say that because u = 3x we can't have just 27, it must be 27/3?

[latent walrus]

thats how u substitution works

we change dx into du

[worldly lagoon]

since we went from x to u and now the factors must be symmetrical?

[latent walrus]

if u=3x then du/dx=3 so dx=du/3

then you factor out that 1/3

[worldly lagoon]

ah

I get it now

the dx is the factor that is changed at the tail end I ommited that

thanks

[latent walrus]

no worries

[worldly lagoon]

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[crisp zephyr]

I need help with an integral.

[native inlet]

what is the integral?

[crisp zephyr]

integral from 0 to pi/2 of function (2a sin^2 (x))/(a^2 sin^2 (x) + cos^2 (x))

[crisp zephyr]

Can someone write it in Latex?

a > 0

[surreal forge]

is a confined to the set of integers?

[crisp zephyr]

no, a and x are real numbers

[crisp zephyr]

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[feral mulch]

HELPPP

this is my work, and im confused, why is cos =AD/AB

sory

[warm shale]

help a sad kid | desi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[feral mulch]

how can AB/AC = tan??

not BC\AB???

i see

[shut moat]

@feral mulch SOHCAHTOA

[feral mulch]

im asking why is the cos = ad/ab

in the solution

meanwhile in the picture, cos = ab/ac

this angle?

90?

can you pls explain to me?

why is the angle is 90

[shut moat]

You mean BDC

Opps bdc

[feral mulch]

aight

thanks for ur help

appreciate it

[dense imp]

cos theta = AD/AB = AB/AC, both the red and green triangle are tright triangles that have theta as their angle

AD/AB = AB / AC is the implication

[umbral topaz]

hippopotamus is must be 12 sm

feets i mean

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[surreal forge]

when is a number both a perfect square and a perfect cube?

sorta yeah

what if i just wanted to express the number in terms of a^something ?

ye

a^2 isn't a perfect cube normally and a^3 isn't a perfect square normally

i'm not sure how to rigorously explain this actually but for both of these things to be true you'd need to take (a^2)^3 = (a^3)^2 = a^6

(lcm(2, 3) = 6)

this seems right i think

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[cloud sparrow]

why do median and mode require continuos intervals while mean does not?

[dense imp]

it's not technically required to compute them, but think about how meaningful the median would be in a scenario with a large gap: say you had 100 occurrences of a value of 1 in your data and 101 occurrences of a value of 1,000,000
both the median and the mode are 1,000,000, but how well does that represent what is happening?

in this case mean gives you something halfway between

but here's another case where median is more meaningful and mean fails: say you have 100 values between 1-100 and a single value that is 10^60 (maybe this represents an instrumentation error in a scientific experimentation), the mean becomes completely meaningless because it gets skewed by the data given by the error towards a very high number and basically doesn't represent the "real data" at all, meanwhile if you calculate the median in this dataset, it basically should give you a pretty accurate representation of the middle ground of the good data. So deciding what to use \ what is meaningful depends on being aware of what to expect from your data.

[cloud sparrow]

hm? isnt that a limitation of mode/median? what my question was why is the stuff below the table necessary?

[cloud sparrow]

interesting nonetheless

[dense imp]

i don't know about that, just talking about basic definitions of mean\median\mode in standard math classes : )

[cloud sparrow]

well, appreciate your help eitherway!

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[obtuse pebble]

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[leaden pilot]

Could I receive some assistance in finding input tolerance and the ideal radius for the Flowjet?

[leaden pilot]

I originally tried the Largest Acceptable Radius-Smallest Radius which went wrong. So, (sqr927/pi)-(sqr923/pi).

I'm not sure about the last one.

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[distant seal]

would i go for the bottom one?

if not why?

[eager niche]

It’s a one sided limit

So no

[fossil crag]

You want to approach 5 from up, (+)

So you start bigger than 5

[distant seal]

x^2-x?

[fossil crag]

(x>5 if that was what you were hinting at)

[wary vigil]

you would use the bottom piece of the function if that's what you meant

[fossil crag]

Yes

[distant seal]

ok thank you

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[quick dove]

can someone help me with a logarithmic problem

[quick dove]

50/4+e^2x = 11

[tiny seal]

since this equation has one variable, we can single it out by undoing every operation in the reverse order

for example, in the equation, the last operation we do in the left side is +50/4

so, subtract 50/4 by both sides

then, continue this reasoning to get x

[tiny seal]

so, after this step, what would we have?

[obtuse pebble]

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[quick dove]

figured it out, thank you!

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[rotund crest]

i understand the steps but shouldnt the solutions be 25?

<@&286206848099549185>

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[oak knot]

hello there, could anyone give me a hint as to how to start solving this

[oak knot]

sorry i have nothing to show i have no idea where to start

[smoky vigil]

think of what else the log function is telling you, i.e. how its the inverse of the exponential function

then use your exp properties to turn a^x into a^2x

[oak knot]

Hmm

@grand stirrup would this be right

:o thats a neat trick

[smoky vigil]

ye looks good :)

[oak knot]

Oop one more if you dont mind

the answer i got for the 2nd was...

Sorry i probably went a little bit in circles to get to that lmaoo

[smoky vigil]

looks good, but could've been shorter ye

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[oak knot]

tysm!

[obtuse pebble]

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[coral nexus]

how do i simplify this to get r!(n-r)! as a denominator

[lilac sun]

r! = r(r-1)!

(n-r)! = (n-r)(n-r-1)! = (n-r)(n-1-r)!

[coral nexus]

oh i combine

.close

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[small vault]

how to multiply polynomials with different bases?

[lilac sun]

what do you mean?

can you elaborate?

[small vault]

like these

nvm

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[steel urchin]

A sigma algebra can be broken down into atoms

[steel urchin]

Which are individuell elements that make the set right

So the intersection of atoms is empty right

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[hallow hatch]

im pretty confused on how to do this

[soft tiger]

a) asks for an approximation using a left riemann sum, while b) asks for an approximation using a right riemann sum

[cunning burrow]

This is just riemann integration basically they are adding a bunch of rectangles to approximate the area. You will find many YouTube videos and examples in various textbooks

[hallow hatch]

right i understand that

i see what to do

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[serene swift]

does the derivative operator pass through the sum

[frosty spoke]

you need some uniform convergence I think

[serene swift]

Okay

[serene swift]

also this is mathematically incorrect notation right

[frosty spoke]

I mean strictly so, but it's not really a big deal

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[smoky vigil]

yeah way you would fix this it integrate with a dummy variable like x'(s) ds

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[proven nimbus]

Hello

[proven nimbus]

Can u help me find the value of this answer please

I don’t know if it’s -125

Or 125

[dense imp]

what do you know about negative exponents?

[dense imp]

it's neither

[proven nimbus]

Huh

Really?

[dense imp]

the sign of the exponent has absolutely no bearing on the sign of the expression as a whole

it kind of does a completely different thing

are you familiar with a reciprocal?

how $\frac{a}{b}$ is the reciprocal of $\frac{b}{a}$ ?

[warm shale]

Soosh

[dense imp]

and $\frac{1}{5}$ is the reciprocal of 5?

[warm shale]

Soosh

[dense imp]

@proven nimbus ?

[proven nimbus]

Ohhh ok

I see

Thank u

[dense imp]

so a negative sign in the exponent just means basically the reciprocal of the expression

$5^{-3} = \frac{1}{5^3}$

[warm shale]

Soosh

[proven nimbus]

I see now

Wait

How do I close

[dense imp]

this is something that confuses people often, just remember that flipping sign in exponent never flips the sign of an expression

!done

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[proven nimbus]

Kk tysm man

.close

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[quiet ermine]

f

[quiet ermine]

yo i need help w this one

[rich frigate]

Hey

[quiet ermine]

hi!

bro i nee dhelp w this one a lot

i got sat soon and idk what this is

[worldly oasis]

wait

[rich frigate]

Draw a perpendicular to diameter

[quiet ermine]

use the chord rule?

r is AB and if we use CD we could intersect them and use the rule

i think so

[versed stratus]

yes

draw a perpendicular from the cnetre of the semicircle to the chord

and join C to the centre

[quiet ermine]

Alr

Then?

[hollow solstice]

2r is AB

[quiet ermine]

Alr

[versed stratus]

The perpendicular from the centre to the chord bisects it

[quiet ermine]

we just need to find the arc length of CD?

this is confusing

hmm

[shut lagoon]

It looks like you need a lot of fancy stuff, but not really. Try to build a triangle with one vertex at the center of the circle, one vertex at D and one vertex in the middle of CD

[quiet ermine]

Alright

And the sine of the triangle is the length of the line?

[shut lagoon]

You could use sine, but tbh it's just Pythagora's

[quiet ermine]

Oh

A^2+CD^2=uh

A is the length

We just need to know the diagonal of the 2 and the length of CD

[quiet ermine]

That works

Since CD=2/3(AD)

AB*

we could rewrite

2/3(AB)^2+B^2=hm

we may just have to use the Law of Sine with this one

lets call that angle A

this is hella confusing

[shut lagoon]

You're complicating things for yourself

[hollow solstice]

Let centre be P you literally need PO, PD=r and OD is CD/2

[quiet ermine]

P meaning?

[hollow solstice]

Centre

[quiet ermine]

Oh so PO is the length

[hollow solstice]

Yes

They asked distance between them so perpendicular distances between them

[quiet ermine]

yep

and 1/2(AB)=P

[hollow solstice]

Whoa

AB/2?!

[quiet ermine]

XD

[hollow solstice]

Who be P?

[quiet ermine]

Since P is located right in the middle, i thought it was 1/2 AB

[hollow solstice]

P is a point

You mean PA=AB/2 , Yes

Its just pythagorus

Apply it

[quiet ermine]

Yep

[hollow solstice]

Sayonara

[quiet ermine]

goodbye

.close

[obtuse pebble]

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[nimble grotto]

would this be 5x? <@&286206848099549185>

[silver torrent]

you can rewrite that as sqrt25 * sqrtx^2

[timid silo]

roots take +/- dont forget

[ruby path]

note that the result of a square root is always positive

[silver torrent]

if you solve for a variable

youre not doing that here, youre simplifying

[timid silo]

u cld still get -5x or +5x

[silver torrent]

try it with x = 3
sqrt(25x^2) = sqrt(25 * 3^2) = sqrt(25 * 9) = sqrt(225) = 14
-5x = -5 * 3 = -15
-15 != 15

there you have it

[timid silo]

🤦‍♂️

[nimble grotto]

so in this case since x is being squared in the square root my answer could just be |5x|

[timid silo]

(-15)^2 = (15)^2

[ruby path]

yeah

but since x < 0

[silver torrent]

I might have made a mistake, since x < 0

[ruby path]

the absolute value opens up with a negative

[timid silo]

if x<0 u cld still get + or - 5x

bcs u still have the +/-5

multiplying it

[silver torrent]

but if you try it with -3
sqrt(25x^2) = sqrt(25 * -3^2) = sqrt(225) = 15
5x = 5 * -3 = -15
so the answer would be -5x I believe

prove me wrong though, im not sure

[obtuse pebble]

@nimble grotto Has your question been resolved?

[obtuse pebble]

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[chilly scroll]

how do i approach integral dt/t²(1+t)²

[fierce vale]

$\int \frac{\dd t}{t^2(1+t)^2}$

[warm shale]

Adam Chebil

[chilly scroll]

yee

[fierce vale]

use pfd

[forest sinew]

,w Apart[1/((t^2)(1+t)^2)]

[warm shale]

Results provided by WolframAlpha

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Requested by janniku

[chilly scroll]

Ah

so like i dont need to do ax+b things in numerator?

how do you know when you have ax +b and when only constants

That really confuses me

[forest sinew]

it will pan out

i believe what youd be solving here would be like

[frosty spoke]

did you mean to spell your name alprazolam, or is it some wordplay I don't get

[forest sinew]

lol

[forest sinew]

im being dumb

the answer is repeated linear factors dont pick up powers of x in the numerator

but, you could include them

i believe

youll find they were not necessary

[chilly scroll]

Oh okay these are just lengthy probs

[forest sinew]

there are shortcuts to partial fractions

ive just never used them personally

[chilly scroll]

same i hate these

[forest sinew]

sometimes guessing wrong and solving a more complicated problem when you didnt need to is enough to internalize it, too

[chilly scroll]

[forest sinew]

or use a calculator to do the hard work

wolfram has Collect and Expand

[marsh geyser]

Si could you find the way to make the partial fractions already @chilly scroll ?

[chilly scroll]

Ty sory forgot to close

[chilly scroll]

ye i know how to but i wont too muc work

.close

[obtuse pebble]

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[keen ingot]

Is it possible to prove the converse of something by actually showing the contra positive of it to be true?

[teal turret]

if ur original statement is true, then ur contrapositive is automatically true

[trim portal]

converse of something by showing that the contra positive of it to be true?

[teal turret]

if X, then Y implies: if ~Y, then ~X

[trim portal]

So if you have A -> B, then the converse would be B -> A. If you then try to prove B -> A, you can do that by proving ~A -> ~B if that's what you're asking

[keen ingot]

so prove the converse by showing the inverse?

I'm so confused

[trim portal]

Me too honestly, are you sure this is the question you wanted to ask?

[keen ingot]

If I know p -> q and someone asks me to prove the converse q -> p what approach should I use?

[trim portal]

just p -> q isn't sufficient to prove q -> p

so it would depend on the specific p and q given

[keen ingot]

but is there like a general approach to proving it

I know the converse is also true, that is given in the problem

but I have to show so

[trim portal]

No, it's even probable that you wont ever use the fact that p->q in the whole proof

there is no general approach, as knowing the converse isnt really helpful in proving the statement

[keen ingot]

okay

thank you

[trim portal]

what you could try is general approach for all implications

that is, assume p and somehow proceed to derive q

or in your case, assume q and somehow proceed to derive p

[obtuse pebble]

@keen ingot Has your question been resolved?

[obtuse pebble]

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[spiral jackal]

can i get some help on this question pls

[obtuse pebble]

@spiral jackal Has your question been resolved?

[spiral jackal]

did u use chatgpt for this 💀

<@&286206848099549185>

[timid silo]

no it is pretty simple math

[spiral jackal]

oh

sorry, just sounded like chatgpt wrote it lol

[timid silo]

i write it down on paper and then i ask google lens to convert it into text

[spiral jackal]

ah 😂

[timid silo]

cause if I write it on the keyboard my hands will die

[spiral jackal]

ye haha

did you draw out some diagrams

separate diagrams like the man, the lift then trhe whole system

[spiral jackal]

@timid silo hi mate could i get some help on this question too pls

i dont really understand how to solve it with not much info

[obtuse pebble]

@spiral jackal Has your question been resolved?

[spiral jackal]

.close

[obtuse pebble]

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[timid silo]

i need help with b, c, d

for a i got 99

for b) i did 24=-10+99*e^(20k)

i got -0.0539 but when i submitted it, it said it was the wrong answer

[long vigil]

You forgot the minus sign in front of the k constant

[timid silo]

so e^(20-k)

[long vigil]

e^(20*(-k))

[timid silo]

ohhh okay tysm, and for c) i did: -10+99*e^(26-0.0539)

so after i re do b, would i just replace -0.0539

[long vigil]

Yeah, you'd do the same.

If it is wrong still, then you probably need more precision in your k.

[timid silo]

i got 0.053437 for B

[long vigil]

Seems good

[timid silo]

and for C is it 14.67?

i dont really know how to do D) would i make A = 0? like the equation would be 0=-10+99e^(t-0.053437)

[long vigil]

yes

[long vigil]

You make T(t) = 0 , and find t

what you wrote, yes, but not A=0

[timid silo]

okok tysm

i got b wrong again

i dont know what im doing wrong

[long vigil]

How much precision do they ask for?

[timid silo]

they are asking for 6 decimals so i put 0.053437

[long vigil]

Cut or round?

[timid silo]

ohhh im stupid i rounded it to 0.053438

thanks so much for ur help!

[obtuse pebble]

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[languid sphinx]

what did i do wrong

[violet sentinel]

don't square the whole thing

$\int_0^3 \pi [ (6x)^2 - (x^2 + 3x)^2] dx$

[warm shale]

MellowDramaLlama

[bronze osprey]

simplify 6x-(x²+3x)

becomes -x²+3x

try again like this

[languid sphinx]

bro this my last attempt 😭

alright

[bronze osprey]

this is not right

the radius is f(x)-g(x) so we have to square the whole thing

wait

[languid sphinx]

okay it didnt work, but i have another attempt apparently

[bronze osprey]

it just wants the volume there

okay okay

[bronze osprey]

do this

[languid sphinx]

LMAO

alright

bro

lmaoooooo

[violet sentinel]

it happens, no worries.

[bronze osprey]

i just realised

[languid sphinx]

y u change ur mind

[bronze osprey]

i think i was thinking something else lol

[languid sphinx]

alright

ill do it

[languid sphinx]

justification? am i just forgetting the formula?

[violet sentinel]

no you've got the right idea. It comes down to the rules for integrals.

one second

$A(x) = \int_a^b \pi f(x)^2 dx$

[warm shale]

MellowDramaLlama

[violet sentinel]

right?

[languid sphinx]

waitttt

nah i get it i get it

[violet sentinel]

🙂

[languid sphinx]

because if you visualize it as two different solids being revolved around the x axis

which is essentially what it is

[languid sphinx]

then this is how u solve for that

[violet sentinel]

yep!

[languid sphinx]

awesome, thanks

.close

[obtuse pebble]

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[violet sentinel]

$\int_a^b \pi [f(x)]^2 dx - \int_a^b \pi [g(x)]^2 dx = \int_a^b \pi ([f(x)]^2 - [g(x)]^2) dx$

yeah you got the idea : )

[warm shale]

MellowDramaLlama

[obtuse pebble]

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[cosmic veldt]

what is min{(5-4a)/2, (-18+3a)/8}

[coral nest]

it depends on a

[scarlet gale]

It means to find out those two numbers separated by a comma and take the minimum one.

So, like min{3, 2} would be 2.

[cosmic veldt]

wts that (3+9a)/5 <= min{(5-4a)/2, (-18+3a)/8}

[scarlet gale]

min is the minimum of those two numbers, so they're saying that (3 + 9a)/5 is less than or equal to the minimum of those two.

Also if something is less than or equal to the minimum, it's less than or equal to both of them.

[cosmic veldt]

how solve for a

a<=?

[scarlet gale]

Well, you can do (3 + 9a)/5 <= (5 - 4a)/2 and then do (3 + 9a)/5 <= (-18 + 3a)/8 since it'll be less than or equal to both.

[coral nest]

both inequations should be true at the same time

so take the intersection of both solution

s

[obtuse pebble]

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[deep gale]

im not really sure where to start for this question. can someone help?

[deep gale]

im not really sure if definition 1 is apart of the question or if its for all questions after

so that might not be relevant

[obtuse pebble]

@deep gale Has your question been resolved?

[deep gale]

.close

[obtuse pebble]

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[gilded needle]

what's the goal

[cobalt walrus]

It's operation on functions

I have to add f + g

I'm stuck what to do next

[lunar mason]

bro tthe answer is 4

[gilded needle]

well the answer is correct as it stands

but you can simplify it further if that's the goal

[lunar mason]

yeah

[gilded needle]

try putting everything over the same denominator

[lunar mason]

and simplify it

then make the denominator the same

[cobalt walrus]

How?

[gilded needle]

do you know about common denominators?

[cobalt walrus]

How do I make them the same sorry

[gilded needle]

well if the second fraction had another factor x-3 in the denominator, that would do it, right?

[lunar mason]

no its simple

the add the numerators

and then simplify the denominators

[cobalt walrus]

I should multiply x-3 to the second factor?

[lunar mason]

yes

[gilded needle]

sure, but if you do that to the denominator, you also have to do it to the numerator

[lunar mason]

and then make the denominator the same'\

and then bam

answer is

4

[cobalt walrus]

So x-3/x-3?

[lunar mason]

yes

[cobalt walrus]

Do I multiply it to the first fraction too?

[gilded needle]

no you already have the (x+3)(x-3) in the denominator for that one, you want both fractions to have that denominator

so you only need to modify the second fraction

[cobalt walrus]

Oki lemme try

What's next? 😅

[lunar mason]

do thte simplification

y=mx+b

times the infinite range

and thats ur answer

[cobalt walrus]

Sorry what? 😅

[gilded needle]

you now have common denominators, so you can just add the numerators and combine into one fraction

[cobalt walrus]

1+2x(x-3)/(x+3)(x-3)

What do I do next with that?

[gilded needle]

simplify the numerator

1 + 2x(x-3)

multiply out the 2x(x-3)

[cobalt walrus]

Is this right?

@gilded needle

[gilded needle]

sure

[cobalt walrus]

There's no more steps next?

[gilded needle]

i mean all of the expressions are correct and equal

so it depends on the goal

or what you consider to be the most "simple"

for consistency you could either factor the numerator or multiply out the denominator i guess

[cobalt walrus]

Thank you!

How about for the B?

Oh wait lemme try it first

For the f-g, should I do the same with making the denominators the same?

I will multiply x-3 to the numerator and denominator too?

[gilded needle]

yea

[cobalt walrus]

The answer is negative?

@gilded needle

[obtuse pebble]

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[ocean pollen]

can someone help me?

[fallen garden]

VA = -3/2 HA = -7/2

[ocean pollen]

isn’t the horizontal asymptote the ratio of the lead coefficients?

[fallen garden]

To find the verticle asymptote you set the denominator to 0

Vertical asymptote is determined by the degree of the polynomials in the numerator and the denominator

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0

If the degrees are the same, the horizontal asymptote is the ratio of the leading coefficients.

u get that?

[ocean pollen]

yeah

thanks

[fallen garden]

perfect

wanna help me with my math

[ocean pollen]

i can try

what is it

[ocean pollen]

sorry idk how to do that

[fallen garden]

u good

[ocean pollen]

.close

[obtuse pebble]

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[timid silo]

How do I find the area of the shaded region?

[polar fossil]

it's the area of the square minus the area of the circles

[gilded needle]

what's with the dots in the middle of the circles, are they relevant?

[obtuse pebble]

@timid silo Has your question been resolved?

[royal mulch]

We know the area of the square is 12x12 =144.
Next, find the area of one circle, then multiply that area by 4. Notice that its 12m all the way across, so r = 12/4 = 3m (if that's helpful). Once you have the area of one circle, then multiply it by 4. And then use the idea @polar fossil gave!

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[unique grail]

could i get help with this

[unique grail]

it’s really easy but idk where i’m going wrong

it’s using venndiagrams to get probability

so u gotta make a venn first

and take the appropriate integers from the venndiagram to get a probability

[obtuse pebble]

@unique grail Has your question been resolved?

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[mortal timber]

I don't get how it's already in simplest form please explain

[neon eagle]

why wouldn’t it be

what can you cancel

[mortal timber]

Bcz if you factor t²+4= (t+2)² then you can cancel

Here is where I'm stuck

This is what I'm getting for the answer

[high crater]

wait

thats a sum of squares, not factorable (iirc)

[gilded needle]

you can factor it, but it has imaginary roots

[high crater]

i mean in R

[gilded needle]

yea

[tame python]

$t^2+2^2$ isnt the same as $(t+2)^2$

[warm shale]

matt07734

[gilded needle]

,rotate

[gilded needle]

wtf

[tame python]

you cant reply to images then type ,rotate

why do you all keep doing this

[gilded needle]

,rotate

[gilded needle]

haha there we go

[tame python]

its already in simplest form

[gilded needle]

because who can remember such fiddly things

[tame python]

its always replying to someone else's image

never anything else

very odd

[mortal timber]

t+4=(t+2)²

That's correct

[gilded needle]

of course it isn't, plug in t=1 for example

[mortal timber]

So your saying that t+4 can't be factored at all?

[gilded needle]

t+4 is already a first order polynomial

there's no further factoring possible

in your case, you have t^2 + 4, which cannot be factored in the real numbers

[mortal timber]

Ok I get it now thanks for your help

.close

[obtuse pebble]

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[inland thicket]

Guys if there is something that grows like 8 12 16 20, does this growth can be described with number 1.04?

[high lily]

no

[obtuse pebble]

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[gaunt raven]

The sum of all integral values of x such that x²-19x+89 is a perfect square is

[gaunt raven]

.help

[obtuse pebble]

Commands:

• clopen: .close, .reopen
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• factoids: .tag
• help: .help
• version: .version

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

[gaunt raven]

I'm unable to understand, if the question is wrong, or I'm just stupid

[polar fossil]

what have you done so far?

[gaunt raven]

So basically I tried 2 things...

First was that I equalled the eqn to t²
Then basically the whole eqn became an inequality whose value was greater than or equal to 0
I then solved the inequality and basically I got Infinitely many solns

Second was, I again totalled to t², but this time took the t to the left side..
Then used the quadratic formula and basically got 5+t² inside the root

[gaunt raven]

@polar fossil

[polar fossil]

hmm
when I look at this I think about how far apart one square is from another

like imagine if x was 100, the closest squares to 100² are really far apart

so there's really no way x²-19x+89 could be a square

[gaunt raven]

Ohh wait...
11 is soln to it

But how to find all

[gaunt raven]

Yh that's the thing, so that Infinite soln thing must be wrong in someway

[polar fossil]

one way
would be to find an upper and lower bound
and then try all of them in between

[gaunt raven]

?

Bound as in

[polar fossil]

as in maybe -50 < x < 100

[gaunt raven]

And then how will we* proceed tho

[polar fossil]

then we'd have to try 150 values of x

but once we've done that we'd know

[gaunt raven]

.close

[obtuse pebble]

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[shut marten]

When using u-substitution, don't we take the derivative of u?

[polar fossil]

yep

[shut marten]

u = w(x); du = w' dx

Ok, then I'm lost on a homework example

The derivative of sec^-1(3x) is not 1/(x(sqrt(9x^2-1))

[polar fossil]

,calc derivative of arcsec(3x)

[warm shale]

The following error occured while calculating:
Error: Undefined symbol of

[polar fossil]

,w derivative of arcsec(3x)

[warm shale]

Results provided by WolframAlpha

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

Requested by kitten.in.a.teacup

[polar fossil]

those are the same

[shut marten]

Those... are not the same.. I have a 3 in the denominator

Also, they are not what my homework is showing..

my example is from an online calculator.. not wolframalpha, but still...

Well.. ok, I see where they're dropping the 9 and moving the sqrt outside the radical..

But I thought you couldn't do that? Not across addition or subtraction

sqrt(9+16) != 3 sqrt(1+16)

But still... my example is giving me:

bump

<@&286206848099549185> Any ideas?

[polar fossil]

just pull one of the x's into the square root

[surreal forge]

i don’t mean to interrupt however this may be good to note

the question states C^2 = x^2 - 19x + 89 where C is an integer
then, C = sqrt(x^2 - 19x + 89)
the expression sqrt(x^2 - 19x + 89) can be rewritten as sqrt((x - 19/2)^2 - 9/4); therefore, it asymptotically approaches |x - 19/2|, and is bounded above by |x - 19/2|
(from here, i will remove the absolute value bars because the quadratic is symmetric about x = 19/2 anyway)
we also see that the fractional part of 19/2 is 1/2, so the closest potential values of C are at least 1/2 away from our upper bound of (x - 19/2)
thus, we can construct a bound of possible values of x > 19/2 by considering our bound for C:
(x - 19/2) - 1/2 is greater than or equal to sqrt(x^2 - 19x + 89)
squaring both sides, we have that x^2 - 20x + 100 is greater than or equal to x^2 - 19x + 89
equivalently, x is less than or equal to 11
therefore, by bounding our only possible values of x are 8, 9, 10, and 11, of which we can inspect that only x = 8 and x = 11 yield a perfect square for C

if u have any confusion about that then lmk but ye wanted to share

yea that too

[shut marten]

I don't understand what you mean by this...

[polar fossil]

$x²\sqrt{9+\f1{x²}} = x\sqrt{x²\lp9+\f1{x²}\rp}$

[warm shale]

hayley!

[shut marten]

.close

[obtuse pebble]

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[obtuse pebble]

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[tough copper]

Hi! I’m having trouble understanding what I do differently between calculating a limit from the negative side versus the positive, I thought you had to use values that approach the limit from that direction but I feel like I did something wrong here

[quartz carbon]

k

where is h?

[tough copper]

there is no h, maybe it's my handwriting?

[quartz carbon]

nah wait

[tough copper]

this is the question

[quartz carbon]

Yeah

since you are takin it to be greater than -1

substitute x = -1+h for positive

h is a number which is very close to zero

[tough copper]

so when calculating it from the negative side i use -1+h?

[quartz carbon]

no

-1-h

coz

you are headin below -1

lesser than it

so -h

note----> h/h=1

try solvin it now

[tough copper]

okay one sec

[quartz carbon]

k

waitin

[tough copper]

do i do everything else the same way

[quartz carbon]

yeah

[tough copper]

this is supposed to be the negative side

[obtuse pebble]

@tough copper Has your question been resolved?

[tough copper]

.close

[obtuse pebble]

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[obtuse pebble]

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[slim sentinel]

[Reference: Proof of Kolmogorov's 0-1 law from William's Probability with Martingales] Can you help understanding why in the step 1 the pi-system K generates the sigma-algebra X_n and why pi-system J generates the sigma-algebra T_n?
And why in step 3 the pi-syste K_infinity generates the sigma-algebra X_infinity?

[slim sentinel]

My attempt in the proving the first question of the first step is

But i have no clue for the other claims, or in general what is the method to prove when a family of set is equal to a sigma-algebra besides the double inclusion method

[obtuse pebble]

@slim sentinel Has your question been resolved?

[slim sentinel]

<@&286206848099549185>

[obtuse pebble]

@slim sentinel Has your question been resolved?

[obtuse pebble]

@slim sentinel Has your question been resolved?

[obtuse pebble]

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[unkempt tree]

Why do you have to factor out the sin would it not cancel out either way?

[dusk widget]

when you cancel out something containing x in it, you are deleting solutions

[unkempt tree]

Ohhh

shit thanks

[dusk widget]

7x = x^2 for instance

if you delete x

then you get 7 = x

[unkempt tree]

Ye you would lose

x = 0

[dusk widget]

which is a solution, but you're missing 0 obviously

yeah

you got it

[unkempt tree]

ye eeeeO

Thx bro

.solve

.solved

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

studying series, could someone make an exact similar question to this but with the function cos x?

[brave bramble]

ye

Or, do you want the question made

cos(x) ≈ 1 - x²/2! + x⁴/4!

[timid silo]

Thank you

.close

[obtuse pebble]

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[obtuse pebble]

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[blazing pivot]

Hello

[blazing pivot]

I need help

[plain stag]

then ask a question

[blazing pivot]

Ok

Is it okay if it’s grade 9 math ik I ain’t supposed to be here but exam is Tmr and haven’t studied once 😭😭

[plain stag]

if it's math, it's allowed

[blazing pivot]

Don’t know what I’m doing

[plain stag]

why aren't you supposed to be here?

[blazing pivot]

Thought highschool math wasent aloud for some reason

💀

[plain stag]

it is

,rccw

[blazing pivot]

What do I do now

[plain stag]

what have you done so far?

[blazing pivot]

Just waiting for a response, i’m not sure what to do right now

[plain stag]

so nothing

you could start by determining the angle at Q for this triangle

[blazing pivot]

No clue If I’m going to be honest

[obtuse pebble]

@blazing pivot Has your question been resolved?

[obtuse pebble]

@blazing pivot Has your question been resolved?

[dusty grove]

Do you know what the angles in a triangle sum up to

[blazing pivot]

180??

[dusty grove]

Ya

[blazing pivot]

Alright

[dusty grove]

So the you can find angle q

[blazing pivot]

So each one is 45?

[dusty grove]

Yes

And then you can find angle rqs

[blazing pivot]

90?

[dusty grove]

How’d you get that

For angle pqs?

[blazing pivot]

Wait nvm I’m wrong

Answers 135?

[dusty grove]

Oh yea nice

Idk if it makes sense to you then good ig

[blazing pivot]

Thank you

[obtuse pebble]

@blazing pivot Has your question been resolved?

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[cyan hatch]

Can someone explain 24 c and d

[timid silo]

Convert all of them to degrees and draw them

That's what I would do

[obtuse pebble]

@cyan hatch Has your question been resolved?

[cyan hatch]

Sorry is this is dumb but jow would I do that

[obtuse pebble]

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[pulsar swift]

find the number of pairs (x,y) such that x^2-xy+y^2=19

[pulsar swift]

im having trouble on where to start

can anyone help me

[daring rock]

x,y integers?

[pulsar swift]

Yes lol

[surreal forge]

i'd probably add and subtract xy to the left side

[pulsar swift]

i tried that but I didnt see how that would help

(x-y)^2=19+xy

doesnt bring any good results

[surreal forge]

that's not right btw

(x - y)^2 + xy = 19

[pulsar swift]

oops sorry

but

i still dont see how that works

[surreal forge]

imo it just makes the diophantine a little simpler to work with

since this isn't really a question that can be solved using some precise algebraic method

[pulsar swift]

oh should I just bash it out then?

im pretty sure theres a trick to this

i judt dont see how

<@&286206848099549185> can anyone help me?

[surreal forge]

i guess you could treat this problem like a quadratic and solve in terms of one variable

[pulsar swift]

how would you do that

oh wait u mean quadratic formula?

[surreal forge]

wdym

yes that

[pulsar swift]

ok thanks ill try that

[obtuse pebble]

@pulsar swift Has your question been resolved?

[obtuse pebble]

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[sharp ether]

How do I start solving this? I always get it close but I keep getting it wrong for some reason.

[golden night]

why the hell is it in feets

[sharp ether]

Idk but it’s in feet

[golden night]

well maybe youre getting it wrong beacuse you arent converting it into meters?

because its $6.90 per meter

[sharp ether]

Am I? I did the work…

[obtuse pebble]

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

[golden night]

we dont see it if you send the pic

[sharp ether]

Oh…

Um…

Give me on sec

I need to find the How much money will Cornell need to spend on the baseboard? It's a Unit Conversion problem. Cornell plans to remodel two rooms in his house this year. He wants to put new baseboard in both rooms, so he sketches their floor plans:

A Rectangle with length labeled 17 ft and width labeled 10 ft. There is a short gap in the bottom edge of the rectangle is 2.5 ft wide.

Another Rectangle with length labeled 20 ft and width labeled 14 ft. There is a short gap in the bottom edge of the rectangle is 2.5 ft wide.

Cornell lives in the United States and he plans to order a specialty maple baseboard for $6.90 (US) per meter from a Canadian company.
Note: the baseboard is sold by the nearest tenth of a meter.

I need to Give my answer in dollars, correct to the nearest cent.

[subtle sinew]

You restated the problem, why?

Did you attempt the problem?

Can you show your attempt?

And please don't open multiple channels either, close the other one using .close

[sharp ether]

Sorry

I tired this: 2(10+17+20+14)-2(2.5)=117ft

and then

117ft/112inchs/1ft1meter/39.37inches*$6.90/1meter=246.06553213

[subtle sinew]

Process looks good but pay attention to this part here

So you need to round that value in meters first

[sharp ether]

How do I do that?

[subtle sinew]

Then multiply by $6.90

[subtle sinew]

What do you get when you convert 117 ft to meters?

[sharp ether]

35.6616 meters

[subtle sinew]

Round that to the nearest tenth

[sharp ether]

35.66?

[subtle sinew]

No

Referr to this

[sharp ether]

oh um..35.7

[subtle sinew]

Yes

That's right

[sharp ether]

35.7 times 6.90?

[subtle sinew]

Now you multiply by $6.90 to get the total price