help-10

[warm shale]

BillyElKid

[near veldt]

Ohhhh

But when the the rule of negative and negative equals positive rule apply?

[sand saddle]

when you have ONLY a product between numbers, in this case you have a product AND a sum so you have to use the distributive property

then you can use the rule 🙂

[near veldt]

Ahh the a in the product?

[sand saddle]

with $ab$ and $ac$ separately

[near veldt]

Is*

[warm shale]

BillyElKid

[sand saddle]

yees

is usual notation

$a \cdot (b+c)=a(b+c)$

[warm shale]

BillyElKid

[near veldt]

I’m making sure so I’m making an example to see if I understand

Is this correct ?

[sand saddle]

the first one is correct

[near veldt]

I’m a bit confused with the second one when there is no product outside the bracket :/

[sand saddle]

oooooh i see your confusion now

i will tell you a secret

[near veldt]

Okay! :D

[near veldt]

Ohhhhhh

Okay let me try again this time

Yes?

[sand saddle]

yeeeeeeeeeeeeeees

[near veldt]

Yayyyyy

So it should stay negative because

Originally the formula was already negative?

It shouldn’t affect the things inside the parentheses

I think I get what you mean

[sand saddle]

yep it should stay negative because is in this form yet $$a(b-c)$$

[warm shale]

BillyElKid

[sand saddle]

if you want to cancel the negatives then you have to expand it like this $$ab-ac$$

[near veldt]

But I notice here you write it this way = -2(y-yo)/g , as opposed to mine which was 2y-yo/g

Here

[warm shale]

BillyElKid

[sand saddle]

nice catch, that is because i wrote it like this $$a(b-c)$$

[warm shale]

BillyElKid

[sand saddle]

and you like this $$ab-ac$$

[warm shale]

BillyElKid

[near veldt]

You can cancel by multiplying with the things inside the parentheses? Ex: -(2a-6) > -2a+6

[sand saddle]

yes, that is the distributive property

[near veldt]

For easier calculation, would you say it’s better using a specific way?

[sand saddle]

notice that yours was 2y-yo/ -g , the minus - in g is important

[near veldt]

Yes

[sand saddle]

depends on the context, in some situations $ab-ac$ will lead you to simplified expressions usually respect to sums, and $a(b-c)$ too but respect to products.

[warm shale]

BillyElKid

[near veldt]

But I think it’s easier to solve later when you plug in the numbers into the y and yo compared to 2y-2yo

[near veldt]

What is this thing called ?

[sand saddle]

what thing?

[near veldt]

From 2y-2yo to -2(y-yo)

[sand saddle]

aa distributive property

[near veldt]

I thought it’s the opposite ?

[sand saddle]

aaaa

[near veldt]

Wouldn’t the answer for distributive property become more “open”?

[sand saddle]

ok ok, not really the distributive property is an equality so

[near veldt]

Like this?

[sand saddle]

doesn't have order

[near veldt]

It looks more simplified for the one that you did, is it simplyfacation ?

[sand saddle]

but when you go from this (2y-2yo) to this -2(yo-y) (using the distributive property) you are factorizing, but when you go from this -2(yo-y) to (2y-2yo) (again using the distributive property) you are expanding.

[near veldt]

Yesss that’s what I was trying to say

It’s called factoring?

[sand saddle]

yep= more compact = factoring

[near veldt]

I see I see

If I want to use calculator to find the answer for this

Wait

Not for that because it’s expanded version

Is it okay to not distribute it on line 3

Would that be called as factorized form/not expandable form?

[sand saddle]

yes if you don't want to do it, just simply not

yes

[near veldt]

I thought you have to expand every time there is a parenthesis in front of the product

[sand saddle]

not necessarily, in some cases that is literally suicide

for example look at this , what expression looks more friendly to you?

[near veldt]

The factorized one

It’s easier to plug in numbers on calculator

Is this the right way of factorized version ?

[sand saddle]

exactly this 👍

[near veldt]

Why is there a k ?

[near veldt]

Ummm I don’t think I’ve seen this before

[sand saddle]

is just an arbitrary number denoted by k. the thing is the left hand side of the equation is equal to the right hand side (RHS) but the RHS is incredibly more difficult to compute in a calculator

[sand saddle]

yes this is entirely correct

[near veldt]

If I want to put it in calculator, do I have to manually count the top then bottom then the whole radical or can I just type everything in?

[sand saddle]

you can just type everything in, but be careful you could make a mistake if you type so much digits operations without a "checkpoint".

[near veldt]

If I want to be extra careful and want to type one by one, for the inside radical first, should I type 2(y-yo) divided by -g or the other way around ?

[sand saddle]

this one ( 2(y-yo)) because if you use this (2y-2yo) you could make the following mistake (extremely common) 2y-2y0/-g that is $$2y-\frac{2y_{0}}{-g}$$ instead of what you want

$$\frac{2y-2y_{0}}{-g}$$

[warm shale]

BillyElKid

[near veldt]

Oh I meant it this way

[sand saddle]

aaaa sorry i'm dumb

[near veldt]

Like if I want to solve it one by one instead of typing the whole radical into calculator (because sometimes accident lack of bracket can change the whole answer)

Nono

:p

[sand saddle]

i would prefer the second one, but both ways seems fine to me

[near veldt]

I see I see

Also

The negative must put inside the radical?

Every time when you root something, the negative and plus sign has to be all inside the radical or does it matter ?

[sand saddle]

yes it is extremely important with the negative ( the positive is indifferent), because this expression

$$\frac{2(y-y_{0})}{g}$$ is negative for the context of your problem (i assume free fall or something like physics), so try to calculate the radical of -2 in your calculator.

[warm shale]

BillyElKid

[near veldt]

Yes it is for finding time in a free fall question!

Alright I finally understand this question

Thank you so much for your time to try understand and guide me through, I really appreciate the explanations! (:

.close

[obtuse pebble]

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[sand saddle]

no problem 🙂 have a nice day, i'm non-native english spekear so sorry if something i said lacked of sense

[near veldt]

Oh no I’m a non native speaker too, I thought it would difficult for you than for me to understand what I was trying to say xD and likewise have a nice day!

[obtuse pebble]

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[sand saddle]

xD i didnt even realize

[sand saddle]

.close

[obtuse pebble]

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[valid estuary]

<@&286206848099549185>

[obtuse pebble]

@valid estuary Has your question been resolved?

[drifting wraith]

the motion is symmetric, it takes the same time to fall down as it takes to reach the high point

with speed at the end equal to starting speed

so the total change is 2u

[obtuse pebble]

@valid estuary Has your question been resolved?

[obtuse pebble]

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[slate pagoda]

If you have a regular pentagon ABCDE with a center O. If the apothem of the pentagon is 1, what is the length of OA (which is equal to OB, OC, OD, and OE)

[slate pagoda]

thing is it would be so easy with pythag but i dont know what the side length is

so perhaps finding AB = BC = CD = DE = EA?

[tired shell]

you need trig

you know the red line is 1, and the angle is 36 (360/5/2)

[slate pagoda]

uh

[tired shell]

tan = opposite/adjacent will do it

[slate pagoda]

oh ok

so 36 = apothem/side?

wait no

its in radians i think

idk much trig at all

[tired shell]

degrees works too

opposite is half the side here

[slate pagoda]

so the side is 18 times smaller than the apothem???

[tired shell]

so tan(36) = side/2 / 1

,w tan(36 degrees) * 2

[slate pagoda]

so side = 2tan(36)

[warm shale]

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Requested by Plurmorant#1811

[slate pagoda]

okey thanks :D

.close

[obtuse pebble]

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[shut horizon]

Is it possible to take a limit of a function if it isn’t continuous?

[sand saddle]

yes of course

what is the limit of this function when x tends to 2 ?

[obtuse pebble]

@shut horizon Has your question been resolved?

[obtuse pebble]

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[left jay]

Is this correct?

[timid silo]

idk i failed math 5 times

[left jay]

Lmao awesome

[timid silo]

jp i never failed

Im currently at a B tho which is rlly bad 😭

[left jay]

I'm just reviewing my old math quizes for my mid term tomorrow haha

Me with a 50% 😭

[spiral maple]

,rotate

[late stump]

it should be $(-6, 240)$

[warm shale]

light

[late stump]

at least thats what i got

[left jay]

How did you get -6?

How did I get -6 on the quiz??? Lifes just a big ol mess lmao

[nocturne minnow]

Wait, that's a quiz?

[left jay]

Pass

Passed*

:(

Tryna see where I went wrong yk

[late stump]

@left jay

color coded for ur convenience

if its unclear, the sub-equation under the transformation equation is $y=-6f[-4(x+3)]+24$

[warm shale]

light

[left jay]

Ah I forgot to factor it out silly me

Thank you

[late stump]

np, happy to help

remember to .close whenever ure ready

[left jay]

.close

[obtuse pebble]

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[tulip plinth]

Hi, can someone tell me what to put in the 4 empty areas?

[nocturne minnow]

The next numbers in the sequence

[tulip plinth]

And how would I find that

[nocturne minnow]

Following the given formula

[tulip plinth]

I don't know how to..

[nocturne minnow]

$$a_n = -3a_{n-1}$$ Plug in 3 as n

[warm shale]

dldh06

[tulip plinth]

Not sure how to solve with the 3 in the corner because all I've been taught are exponents

[nocturne minnow]

It's just a notation

So if you plug in 3 as n, you get $$a_3 = -3a_{3-1}$$

[warm shale]

dldh06

[tulip plinth]

But it says to write the answers as integers or fractions

[nocturne minnow]

It's not complete yet

What's 3 - 1?

[tulip plinth]

2

[nocturne minnow]

So then $$a_3 = -3a_{2}$$

[warm shale]

dldh06

[nocturne minnow]

You know the second term, what's the second term?

[tulip plinth]

The second term is -4

[nocturne minnow]

Replace a_2 with -4

Now what's a_3

[tulip plinth]

3a?

[nocturne minnow]

No, did you replace a_2 with -4?

[tulip plinth]

wait what do you mean by _

do you mean to multiply

[nocturne minnow]

$\verb|a_2|$ is $a_2$

[warm shale]

dldh06

[nocturne minnow]

I didn't want to format it

[tulip plinth]

how would i format a2

[nocturne minnow]

It's just formatting text nothing relating to the problem

[tulip plinth]

nothing related to the problem yeah okay

.close

[obtuse pebble]

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[still oxide]

so nth root of unity doesnt apply to n=1 and n=2?

[nocturne minnow]

Don't use multiple channels for multiple questions

[still oxide]

ok

.close

[obtuse pebble]

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[frigid surge]

alittle confused with this, i used to be able to do these but i forgot

[short spruce]

for your composite function, you have a function f(x) that results in f(g(x)) when you plug in g(x)

g(x) is x^4, so whenever you see an x^4, that must be where you plugged in g(x) for x

so we can rewrite your equation as $$\frac{18g(x)-37}{22g(x)+49}$$

[warm shale]

a disappointing son

[short spruce]

is it easy enough to get your original function from there?

[frigid surge]

oh yes thank you

i got one more question

so g(x) is the sin(x) right

and f(x) the rest

[short spruce]

no

[frigid surge]

😢

[short spruce]

if you had that, you'd get $y=(3x+2g(x))^5$, which has 2 variables

[warm shale]

a disappointing son

[short spruce]

both g(x) and x

[frigid surge]

[short spruce]

think of it as an outside-inside type of thing

you know the chain rule?

[frigid surge]

idk maybe, im bad with terms but i know them, so maybe?

[short spruce]

well i'll just ask ya this

what is the outermost function of y?

[frigid surge]

the whole thing right

so the ( )^5

[short spruce]

yes, something to the fifth power

[frigid surge]

yar

[short spruce]

so there's your f(x)

and you're raising some function to that fifth power

that function is your g(x)

[frigid surge]

so f(x) do i put just ^5 or ()^5

[short spruce]

if $f(g(x))=[g(x)]^5$, what is $f(x)$?

[warm shale]

a disappointing son

[frigid surge]

(g(x))^5?

[short spruce]

that's f(g(x))

if you're asked for f(x), your equation should be in terms of x

[frigid surge]

i thought g(x) could be put down as just x

[short spruce]

g(x) is its own function

in this case, it's the inside function, 3x+2sin(x)

therefore f(g(x)) is (g(x))^5

where f(x) is in terms of g(x)

but you also need f(x) in terms of x

think of plugging in g(x) whenever you see an x

[short spruce]

.

that's what i showed here

[frigid surge]

i need a minute to process this

x^5

😌

[short spruce]

👍

[frigid surge]

omaigad i got it

thanks my man ༼ つ ͡º;˵◞ل͟◟ ͡;º˵ ༽つ

[short spruce]

of course

[obtuse pebble]

@frigid surge Has your question been resolved?

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[slow viper]

Hello

[slow viper]

Could someone help me with this question please

Q, the cuboid has a total surface area 150cm^2 and square base of side length is. x

[jolly ginkgo]

TSA = 6x²

[slow viper]

Determine the maximum volume As x variables

I’m here now. I got the volume of the cuboid. And I thought the maximum point will be when dv/dx=0…

And I got x=-3.53…. And 3.53…, but when I sub in those value. I won’t get same answer as my textbook

[obtuse pebble]

@slow viper Has your question been resolved?

[slow viper]

Not yet

[open karma]

Hi Mr/Ms. @slow viper
Can I ask you a question please?

How this equation happen to your V ?

[warm shale]

Arian

[open karma]

That's what you wrote right? @slow viper

$V=\frac{75x - x^3}{2} \V=\frac{75}{2}x-\frac{x^3}{2}$

[warm shale]

Arian

[open karma]

But i think this one is correct.

[slow viper]

Yes

[open karma]

So did I solve your problem?

[obtuse pebble]

@slow viper Has your question been resolved?

[slow viper]

I have to find the maximum volume as x varies

The answer from the textbook is 125cm^3

But I don’t know how to find it

[royal basin]

have you done maximization problems before

oh wait, i see your work up there

@slow viper yeah your dV/dx is wrong, it should be 75/2 - **(3/2)**x^2

[open karma]

I told him

[open karma]

First solve 2V equation

$2V=x(75-x^2)$

[warm shale]

Arian

[open karma]

Now you can solve it using try and test ...
Or another ways

We know that

Note: x( if you want that answer be the maximum ) is more little than sqrt(75)

$x<\sqrt{75}$

[warm shale]

Arian

[open karma]

And also we know that the x is positive

So $0<x$

[warm shale]

Arian

[open karma]

Then you can replace x from 1 or 0 to sqrt 75

Any way instead of this way

You can use calculus formula

Here is a picture

That show you how to calculate it

finding-a-differentiation-point.jpg

Well, did you get your problem solved? @slow viper

[slow viper]

Thank you for the detailed explanation! I’m still trying to figure it out

What the x value is

[slow viper]

Yes!!!!! I got it!! Thank you so much!!!

[open karma]

الحمد لله

Have a nice time.
And good luck 🌹 .

[timid silo]

.close

[obtuse pebble]

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[barren kite]

for question b, would it be nessecery to add the +c constant since you know the orginal equation?

[timid silo]

yes because the original equation can be ln($1+x+x^2$) +1234, which will still give you $\frac{1+2x}{1+x+x^2}$ after differentiating

[warm shale]

bertaunth

[barren kite]

ahh right ok

thankyou

.close

[obtuse pebble]

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[tall badge]

Could someone explain how they got 5pi/3 as a second value for part e

<@&286206848099549185>

[obtuse pebble]

@tall badge Has your question been resolved?

[obtuse pebble]

@tall badge Has your question been resolved?

[obtuse pebble]

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[wispy brook]

Find out A,b,c based on the information given

[wispy brook]

any ideas how to solve this ?

[jolly ginkgo]

What are c1 and c2?

[wispy brook]

we don't know it

its a linear programming problem

c1, c4 and A_B^-1 is known

and ive no idea how to get A, B... or what ever...

I know how you get A_B of A...

B = for example tells you which vectors to take out of the matrix A depending on the basic solution for example

B = {1,4} => take 1st and 4th column vector of A and then you have A_B

A_B^1 is the inverse I guess

[obtuse pebble]

@wispy brook Has your question been resolved?

[severe marsh]

can you translate the problem for us?

[obtuse pebble]

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[dense dirge]

can someone please give me a clear proof for the following question?
if q = (a^2+b^2)/(ab+1) prove that q is a perfect square if a, b and q are non negative integers.

[jolly ginkgo]

Did you try adding and subtracting 2

[dense dirge]

does that help though?

[dense dirge]

denominator's (ab+1) so...

[jolly ginkgo]

Idk yet

[dense dirge]

i saw a proof but it was one that no one can think of on their own

[jolly ginkgo]

Oh lol

[dense dirge]

its from IMO btw

[jolly ginkgo]

Oh ofc

[dense dirge]

i've edited the question btw

q is also a non negative integer

sorry about that

[dense dirge]

here

[jolly ginkgo]

Ok

[obtuse pebble]

@dense dirge Has your question been resolved?

[dense dirge]

<@&286206848099549185>

[dense dirge]

please help <@&286206848099549185>

uhm

can someone please give me a clear proof for the following question?
if q = (a^2+b^2)/(ab+1) prove that q is a perfect square if a, b and q are non negative integers.

[spiral maple]

Problem 6 moment

[dense dirge]

yea lol

i still havent come across an easy-to-understand proof

<@&286206848099549185> pls reply

should i close it? Cos i know this question has been a headache for mostly everyone who tried it

[severe marsh]

don't continuously ping the helpers

it will stack

[dense dirge]

oh

sorry bout that

i didnt know

[timid silo]

which ones are not easy to understand for you

[dense dirge]

the graph one

i also found the normal proof (using inequalities) hard, but i understood that

[timid silo]

imo easiest one is with actual division

you just divide (a^2+b^2)/(ab+1) using long division you get some sort of remainder, you set remainder = 0 as it is divisible and you get a=b^3 you put back in and it simplifies to b^2

[timid silo]

^

[dense dirge]

how exactly does it become b^3?

[timid silo]

divide (a^2+b^2)/(ab+1)

[timid silo]

you would get a/b and remainder of b^2-a/b and you can confirm that a^2+b^2=(ab+1) * a/b+ b^2-a/b but you know that the division must have no remainder so b^2 -a/b=0 so b^3=a you put a=b^3 to the original and get that q=(b^6+b^2)/(b^4+1) using long division you get q=b^2

[dense dirge]

niiicceee

thanks man

lol it was right under my nose the entire time wtf

and i was tryin this using inequalities 🤣

thanks again

.close

[obtuse pebble]

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[slow viper]

Could you help me with this?

[slow viper]

A rectangular block is such that the sides of its base are of length x cm and 3x cm. The sum of the lengths of all its edges is 20 cm.

And I have to find the volume of it

I can’t image the block

[scarlet gale]

If it only gives you the base sides, what's the height?

I mean, if they don't give the height, you can solve it, but the answer will be in variables rather than a number.

@slow viper They tell you that the sides of the base (the length and width) are x and 3x.

They don't tell you the height.

The sum of the lengths of the edges is 20 cm.

So, there are four edges that are the height, four edges that are the length, and four edges that are the width of the block.

4h + 4l + 4w = 20 cm

l = x

w = 3x

Solve for height in terms of x.

Then use V = lwh.

[slow viper]

Oh so means, my drawing is incorrect

Let me figure it out

[scarlet gale]

Yes. The front edge of the bottom (width) is x, the other edge of the bottom close to you (length) is 3x and the vertical edge (height) is h.

[slow viper]

??.

[scarlet gale]

Yes, now you also know the sum of the edge lengths.

There are four that hold up the top side.

Those are h.

There are four that are 3x long, they go horizontally parallel to you.

There are four that are x long. They go from where you are away from you into the paper.

[scarlet gale]

Right.

Now solve for h.

[slow viper]

Oh ok

Thank you! I got it!

[scarlet gale]

You're welcome.

[slow viper]

.close

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[timid silo]

vertical asymptotes of x2y-4xy-5y-6=0?

[scarlet gale]

@timid silo Move the 6 term to the other side, factor out y from the remaining terms, divide both sides by what's multiplied by y on the left, solve for when the denominator on the right is zero.

[timid silo]

so whats the result? xd

[scarlet gale]

We can't just give answers, but we can help you to get the answer.

[timid silo]

ohhh

thanks

can i ask now??

[scarlet gale]

@timid silo Sorry, this channel is taken by someone else. To ask a question of your own, see the new rules in #❓how-to-get-help.

[timid silo]

oh sorry i thought he finished

[scarlet gale]

To ask, just go to one of the #help channels under the "Math Help (Available)" channels section.

They don't have #help-x | person-name as the channel name, they just have #help-x.

[obtuse pebble]

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[fervent cradle]

apply trig formulae

do you know what cos(2t) can be rewritten as

[zinc drum]

cos^2theta-sin^2theta

or 2cos^2theta-1

[unique solstice]

https://tenor.com/view/yoda-there-is-another-star-wars-jedi-gif-5140031

[zinc drum]

hmm

1-2sin^2theta

[unique solstice]

Yes

[zinc drum]

okay I think I did something wrong, I end up with 19sin^2t-6=0?

[unique solstice]

Uhh

Did you use the sin^2 formula

[zinc drum]

yeah so I'm trying it again, but I changed cos and here is what it looks like before I multiply the 6, 7sin^2t-6(1-2sin^2t)=0

[unique solstice]

That looks right to me

[zinc drum]

okay then I get 7sin^2t-6+12sin^2t=0

[unique solstice]

Yes

[zinc drum]

do I combine 12sin^2t and 7sin^2t?

or can I lol

[unique solstice]

Ye

It's just like combining a variable

[fervent cradle]

this is right

your answers are just gonna be depressing

[unique solstice]

Yeah I think it's right also

[zinc drum]

right ok so now 19sin^2t-6=0

I'm stuck here, no idea where to go next

[unique solstice]

Just isolate the sin^2 as a first step ig

[zinc drum]

oh wait, yeah okay let me do that

[unique solstice]

Or actually isolate just the sin

[zinc drum]

sin(t)=rad6/19 ?

[mild ocean]

not exactly

remember it could be negative

[zinc drum]

+/- k

[unique solstice]

Can you use a calculator

[zinc drum]

professor says we shouldn't have too but the prompt says too. So I'm going to

[unique solstice]

[zinc drum]

He's the worst, you guys are helping me more than he has all semester

ty

[unique solstice]

Ask your professor to solve arcsin(37/618)

[zinc drum]

yeah I know, hes crazy

[unique solstice]

Maybe he wants you to put it in exact form with the arcsin?

Then check your exact form with the calculator

[zinc drum]

this prompt wants the degrees

[unique solstice]

Hmm

[zinc drum]

Where did 37 and 618 come from?

[unique solstice]

I was just joking

[zinc drum]

oh lmao

[unique solstice]

But yeah uhhh

You'd just arcsin it

Just remember arcsin can have multiple solutions on top of the +-

Well arcsin can't but he would want you to give both

[zinc drum]

ok thank you!

[unique solstice]

Np

[obtuse pebble]

@zinc drum Has your question been resolved?

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[hot oxide]

guys help please

[short spruce]

with?

that's not a test, is it?

[hot oxide]

nope

i promise

[short spruce]

alrighty

what do you need help with

[hot oxide]

how to solve for x in each case

[short spruce]

well, for the first one, do you recognize anything about 27 in relation to 3?

[hot oxide]

27 to base 3 is 3 cube

[short spruce]

precisely

so if you rewrite 27 as $3^3$, and $3^3=3^{x^2}$, what can you say about those exponents?

[warm shale]

a disappointing son

[hot oxide]

ohh yeaah thats what i did but i was not sure about it okii

so i now take the powers?

[short spruce]

and do what with them?

[hot oxide]

3=x^2

[short spruce]

correct

[hot oxide]

🙂

[short spruce]

and that's an easy solve for ya

[hot oxide]

i think i love maths

haha

how about (iii)

?

[obtuse pebble]

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[austere crest]

What's the error here?

[austere crest]

I know it lies in step 3

Just not sure what it is

Sure if you try to evaluate the limit directly you get 0/0

But you can remove the discontinuity

So why don't we

oh wait

it's not in indeterminate form in the first one

?XD

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[obtuse pebble]

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[onyx spoke]

when doing partial derivatives, can you assume the terms that are held constant are any constant that is convenient?

[obtuse pebble]

@onyx spoke Has your question been resolved?

[onyx spoke]

<@&286206848099549185>

[slow sonnet]

what do you mean exactly?

[onyx spoke]

so let's say

i need to take the derivative of b³/a³ respect to a

can i "hold" b at whatever constant value i need to prove something

[slow sonnet]

well

you can but then you need to resubstitute again as b

and that might get messy

so just assume it's a constant

so for example if you have the function ax^2

and you take the normal derivative with respect to x

it's 2ax

[onyx spoke]

yeah

[slow sonnet]

a is constant

same here

b^3 is constant

so it's b^3 . 1/a^3

imagine b^3 as a constant and the answer will be b^3 times the derivative of 1/a^3

[onyx spoke]

the problem is
depending on how large b is in that example
the parity of the whole expression i have in general changes

actually nvm

thanks

you've helped

.close

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[supple prairie]

A negative angle greater than -720° that is coterminal to -301° is (?)°

[supple prairie]

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[timid silo]

√2x = 2h, how can I find h and x? Is h = 2/√2x?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

you rearrange the equation

so is my answer correct? Im having a brainfart rn

h is close just you did the division the wrong way round

√2x/2?

why?

because you divide both sides by 2 to get h by itself

that sounds like basic math 😆 Thanks for explaining, have a good day!

.close

[obtuse pebble]

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[timid silo]

thanks, you too and stream the feels 🙇

[obtuse pebble]

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[vivid oxide]

#linear-algebra

[vivid oxide]

how can I further simplify this, in order to find the characteristic polynomial of A?

hello, is there anyone there?

[fervent cradle]

you already got the characteristic polynomial, it's -L^3 + 7L^2 + 17L + 9

notice that L = -1 is a root

[obtuse pebble]

@vivid oxide Has your question been resolved?

[vivid oxide]

oh i see but dont i still need to factor it in order to find the zeros?

[fervent cradle]

i gave you one root

so that's one factor

when you factor that out, it's just a quadratic, which is easy to factor

i got that factor by staring at it really hard and trying small values

[vivid oxide]

is there an easy way to factor that out?

you mean to factor out 1+L right?

how would I factor that out of such a long equation?

are you still there? is there some kind of method i could use to factor that out?

im trying to do it manually just by thinking about it but it seems there must be a simpler way than that, because that requires you to predict how the lamba and the 1 will multiply and add with everything ahead of time which is extremely complicated

[fervent cradle]

algebraic long division

look it up

it's actually simpler than regular long division

[obtuse pebble]

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[versed bobcat]

How to calculate area?

[obtuse pebble]

@versed bobcat Has your question been resolved?

[mild ocean]

what are you trying to get the area of

wait i can’t even help why am i asking

[versed bobcat]

area of the shape

[mild ocean]

so the width at the bottom is 8cm, and the width at the top is 5cm

i’d say you can just pretend this is a rectangle of height 13 and width 8 and just subtract the area of two triangles that both have a height of 13 and a base of 1.5

you want the area of the whole shape right? @versed bobcat

just making sure because i don’t know why that triangle is in there

[versed bobcat]

oh yeah ill minus the triangle area

but you said 1.5 of the traiangles at the side

2 of them

[mild ocean]

yes

[versed bobcat]

but how d u get 1.5?

[mild ocean]

the difference between the width of the top and bottom is 3

half of that is 1.5

[short spruce]

or just do area of trapezoid minus area of triangle

[mild ocean]

i need a triangle on both sides

to be fair i wasn’t thinking of area of a trapezoid

mainly because i don’t know the formula

[versed bobcat]

oh yeah 8-5 = 3

and 3 divide by 2

= 1.5

but in the picture the base

says 2

and 4

but the 2 has a line on it

[mild ocean]

the other side is 2

2+4+2 = 8

[versed bobcat]

and the other side does not doesnt that mean its not the same length?>

[mild ocean]

wow that’s a lot of double negatives

wait i read it wrong lol

[mild ocean]

i’m not sure

it definitely looks the same length

[versed bobcat]

yeah...

if it wasnt i dont think there is anyway to find it out right?

so it must be?

[mild ocean]

probably

[versed bobcat]

mmmm''

thanjks

but can u help me with one more thing>

[mild ocean]

i can try

[versed bobcat]

Thanks

so

[mild ocean]

no clue lol

[versed bobcat]

ive found the area of the semicircles by using the diameter

[mild ocean]

oh wait that’s a good idea

[versed bobcat]

and that equals 10053.09

times 2 because theres 2 semicircles

=

20106.19

and thats the semicricles done

[mild ocean]

it’s actually the area of the whole circle with that radius divided by 2

[versed bobcat]

but now i need to find the rectangle in them iddle

[mild ocean]

if you didn’t know

wanna make sure you got it right

well they both have a radius of 40

170-2*40 = 90

[versed bobcat]

wait what

[mild ocean]

huh

[versed bobcat]

170-2*40 = 90

this is the area of the rectangle?

[mild ocean]

no

the width of the rectangle

[versed bobcat]

and then its just 90 x 80 right?

[mild ocean]

yes

[versed bobcat]

which is 17000

1700

[mild ocean]

no

[versed bobcat]

oh

[mild ocean]

7200

[versed bobcat]

oh yah

[mild ocean]

what’s with the little box in the center

[versed bobcat]

oh i just have to minus that arae

area

[mild ocean]

lol

[versed bobcat]

from the whole thing

[mild ocean]

why even put that there if it’s that easy

[versed bobcat]

idk lol school

[mild ocean]

you already did the hard work why put something easy in there

weird

[versed bobcat]

mmmyah

ok ok

so we have the area of the rectangle

which is 7200

cm2

and the area of the semicircle which is 20106.19

wait wtf

[mild ocean]

the area of the rectangle can’t be that much smaller than the circle

[versed bobcat]

that doesnt sound right

yeah...

[mild ocean]

it can’t be right

[versed bobcat]

ok ok

so the rectangle iscorrect

7200

[mild ocean]

so you have two semicircles

so just think of it as one circle

a whole circle

with radius 40

pi*r^2 gives us 1600pi

or probably approximately 5000

[versed bobcat]

ive put in calc

5026.54

[mild ocean]

oh yeah

[versed bobcat]

PI x 40r2 right?

[mild ocean]

pi*r^2

with r = 40

[versed bobcat]

mmmm

perfect

[mild ocean]

probably leave it as 1600pi since they probably want an exact answer

[versed bobcat]

mm

oh wait

thats it rtight?

1600pi x 7200

pluis io mean

[mild ocean]

well add all the stuff together and subtract the one thing

[versed bobcat]

plus

[mild ocean]

yeah

[versed bobcat]

yah

[mild ocean]

-60

so 1600pi+7140

they probably want meters squared

so (1600pi+7140)m^2

[versed bobcat]

12166.54

[mild ocean]

did they say if they wanted an exact answer

[versed bobcat]

Anddddd that is the correct answer

[mild ocean]

oh ok

[versed bobcat]

wow thank you quantam

[mild ocean]

nice

[versed bobcat]

for this help

[mild ocean]

no problem

[versed bobcat]

@mild ocean

ONE MORE THING PLEASEEE

Ive calculated the triangle by 9*12

Divide by 2

Times 3 because theres 3 of them

Which is 162

So thats 162 cm2

Now i need to calculate the area of the circle

And then minus the triangle areas

But how do i find the area of the circle

?

[spiral maple]

find the radius

[versed bobcat]

yaeh

[versed bobcat]

how do i find the radiustho?

[spiral maple]

assume the triangles are isoceles

then apply pythagorean appropriately

[versed bobcat]

so i was thinking that the the side angle of the triangle is the radius

[spiral maple]

it is

[versed bobcat]

mm

and how do i find that?

[spiral maple]

read what I just said

[versed bobcat]

yeah like how do i use that

with only the base and height

@spiral maple

[spiral maple]

you know half the base is 4.5

so... you have a right triangle

[versed bobcat]

oh ok

and so

the height is still 12

and base is4.5

[spiral maple]

the other leg is 4.5, yeah

[versed bobcat]

and so with that

how doi find the side length, the (slanted one) ?

[spiral maple]

you have a right triangle...

and know 2 of the sides.

[versed bobcat]

sorry?

So like if i split the triangle in half

Its now 4.5 x 12

Which is a right triangle

[spiral maple]

yes.

and?

[spiral maple]

yeah

[versed bobcat]

Like thaat

[spiral maple]

yes

[versed bobcat]

And so how do i find the slanted angle?

[spiral maple]

you're not asked for angles

and I've already said how to

[spiral maple]

.

[versed bobcat]

Sorry i mean how do i find the side length

Not angle sry

Side length i mean

@spiral maple

[spiral maple]

are you reading what I put...?

[spiral maple]

.

[versed bobcat]

we use pythagorean to findthe side length?

[spiral maple]

Yes.

[versed bobcat]

can u help use that..??

in this problem?

[spiral maple]

Attempt it first.

[versed bobcat]

ok

so

i have a right angle which is 90degre

i dont know what to do from here on😦 pls

@spiral maple

[spiral maple]

do you know pythagorean theorem Y or N?

[versed bobcat]

i learnt it but i forgot it

[spiral maple]

so google it

[versed bobcat]

ive tried

but i cant find anything that is the same as this problem

[spiral maple]

????

Google "Pythagorean Theorem"

You will get... the pythagorean theorem

[versed bobcat]

but maybe i will learn better if u teach me how to apply it to this problem 🙂

i think thats agood idea 👍🏽

[spiral maple]

You need to know what it is to begin with, and I don't plan on googling stuff for you

So google it yourself, plus learning how to effectively find stuff out yourself is frankly more important

[versed bobcat]

can u just walk me thru the steps from here on? just this one time

with having a base of 4.5

a height of 12

[spiral maple]

Do you know what pythagorean theorem is?

[versed bobcat]

and a right angle

of90 degrees

[spiral maple]

yes, the 2 legs are 4.5 and 12.

[versed bobcat]

and they both have a 90degree angle

[spiral maple]

???

There's only 1 right angle in the triangle

[versed bobcat]

Like

each side has a right angle right?

[spiral maple]

sure if you consider the whole isoceles triangle

[versed bobcat]

mm

but each one only has 1 right angle

so we only need one leg tho

to find the side length

[spiral maple]

...........

[versed bobcat]

maybe its called the hypotenuse

[spiral maple]

You have both legs

[versed bobcat]

mm but we only need one right ?

[spiral maple]

????????

You need 2 sides to find the 3rd

[versed bobcat]

what dou mean the 3rd?

[spiral maple]

wdym

do you not know what a triangle is?

[versed bobcat]

ok i understand now

if we split the triangle in half

it has 2 legs

and a hypotenuse

which is opposite to the right angle

and so one leg is 12

and the other is 4.5

and we have a right angle

[spiral maple]

yes.

[versed bobcat]

and pythagoream

is

c2 = b2 + a2

and c2 is the hypotenuse

and b2 and a2 is the 2 legs

12r2 + 4.5r2

is

164.25

which is the hypotenuse

right?

actually

164.25r2

[spiral maple]

r^2=164.25, yes

[versed bobcat]

and so the hypotenuse is

26978.06

cm

which is also our radius

correect?

@spiral maple

and usign the radius

[spiral maple]

no

[versed bobcat]

we do

oh

[mild ocean]

you squared it

[spiral maple]

how did you get a bigger number from taking a square root

[mild ocean]

you were supposed to square root it

[versed bobcat]

ohh

im getting confused

back to the triangle

hypotenuse^2 = leg1^2 + leg2^2

otherwise known as

c2 = b2 + a2

b2 = 4.5^2

a2 = 12^2

4.5^2 + 12^2

=

[spiral maple]

657/4.

[versed bobcat]

164.25

yah

and so

164.25^2

is the hypotenuse right?

@spiral maple

@mild ocean

[mild ocean]

no

sqrt164.25

[versed bobcat]

which is 12.81?

ahh

ive done it

thank you @spiral maple

and @mild ocean

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

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[wispy parrot]

Can someone explain how to solve this type of problem step by step? This isn't covered in my lecture notes and I'm not sure how to even approach this type of problem.

[wispy parrot]

I tried to ask for help last night but no one responded

[tired shell]

a) one thing you always know is the probability of anything happening at all is 1, so summing all the p(x)'s should give 1, which will let you solve a

b) this is all the p(x)'s where x>3, or just p(4)+p(5)

c) E(X) = sum of xp(x), so p(1)+2p(2)+3p(3)+4p(4)+5p(5)
E(X)^2 is the same but with sum of x^2 * p(x)

[obtuse pebble]

@wispy parrot Has your question been resolved?

[wispy parrot]

thank you

I'll try to work off of what you sent

and ask if I get stuck

[obtuse pebble]

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[wispy parrot]

@tired shell I'm confused about your explanation for a.). Are you saying to plug each x value into the p(x) equation and then sum that to get a?

[tired shell]

sum up p(x) for all x, and set that equal to 1

[wispy parrot]

does this make sense?

and im supposed to solve for a from this?

[lethal crest]

you can factor out 1/a. then use the formula for sum of square of natural numbers

[obtuse pebble]

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[timid silo]

I need help determining whether this is true or false

[tired shell]

uh, I might need context on if the log is in base b

[timid silo]

thats the whole problem

no other context

[tired shell]

ah, I couldn't say then

[timid silo]

wdym by context though

there isnt a value given for b or for x

[tired shell]

like is it log_b(2x)

or just log base 10 like usual

[timid silo]

i am assuming it has a base of 10

since no other base is listed

[tired shell]

cool

so there's only 1 thing we can do to an equation with an exponent like this, take the log of both sides

to get rid of the b, it'll be log_b

that turns it into log(2x) = log_b(2x)

that should be false right? since 10 and b are different

[timid silo]

i got to the same point actually but was wondering if b is 10

so i thought i had to solve for b