help-27

[inner sand]

And it's foiled form

Roots stay -2 and 5

That's what I mean

[rich mason]

my bad

[noble roost]

.

i still dont get it 😦

[inner sand]

Which part

[noble roost]

say im comfortable with putting it straight equal to 0

is it okay?

or

i need to simplify it first

[inner sand]

Sure is, who is stopping you

[noble roost]

okay

[inner sand]

Simplifying makes it easier to some people

[noble roost]

then i get (x+2)(x-5)=0

[inner sand]

Whichever suits you

[inner sand]

Okay

Then?

[noble roost]

then isnt it just (x+2)(x-5) over (x-3)(x+3) <=0?

[inner sand]

No?

What happened with the -2?

[noble roost]

i did quadratic

for -2x^2+6x+20=0

[inner sand]

What you do here is find roots

But it in no way changes our equation which is -2(x+2)(x-5) over (x-3)(x+3)

Since this way you straight up change the equation

[noble roost]

but u said its fine to make it equal to 0

[inner sand]

To find the roots, yeah, that's why we equal it to 0

[noble roost]

then why in x^2+6x-7

we equaled it to 0

and thats the solution

?

like in the other side

how is it different thatn -2x^2+6x+20

i find roots as well in x^2+6x-7

[inner sand]

Yeah

[noble roost]

and for some reason its solution there but not here

[inner sand]

No

Equaling it to zero is just your roots you put on your interval line

You are having an inequality

Not an equation to solve for x

Your answer should be an interval, not a number

[noble roost]

then i think from now on i will just simplify it

because equaling it to 0 is just confusing me

[inner sand]

What do you think equal to zero gives us?

[noble roost]

the qadratic formula so we can find the x

like an easier way to simplify it?

i dont know

[inner sand]

It's all it does yeah

1. Find us roots
2. Give us a more compact way to look at it

[noble roost]

because there is a difference between x^2+6x-7 and x^2+6x-7=0

x^2+6x-7 just simplifies to (x+7)(x-1)

and x^2+6x-7=0 simplifies to (x+7)(x-1)=0

[inner sand]

x^2+6x-7 and -x^2 - 6x + 7 are different equations

But both have same roots

Difference is they are opposite to each other parabolas

As you see have same roots, but have different intervals

When they <= 0 or >= 0

[noble roost]

yes i see here

[inner sand]

Same goes for the right side of your question, you can equal it to 0, find the roots which you put in the interval line, but cannot change the equation in the inequality

Since such a change changes the sign

Do you think you can finish your problem on your own now?

[noble roost]

yes i understand the solution.
but i may sound dumb but whats the difference between simplifying it and equaling it to 0

this is what i still dont get

[inner sand]

Equal to zero means when our equation intersects the x axis, it gives us solutions when our polynomial is equal to 0 which means when it is changing it's sign from + to - or from - to +, but equalling it to 0 doesn't tell us, just tells us "such points exist"

Simplifying it in such problem might just be having -2 infront of brackets

In other problems simplifying might mean take a common term, usually e^x in front of brackets

And when simplifying we can actually see what is going on

-2(x+2)(x-5)/(x-3)(x+3) is easier to make deductions on than -2x^2+6x+20=0/x^2-9

You see both roots from the nominator, both roots from the denominator and more

Unfortunately I'll have to go, but hope you understood, for the solution you have to intersect both intervals as you did

Good luck

[noble roost]

thanks

.close

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[hearty nexus]

I asked that question before but I just want to make sure 😶

[hearty nexus]

is the answer

f(k+4) = -2k^2 - 13k -28?

[polar chasm]

What you wrote was correct

[hearty nexus]

was it the final answer?

[polar chasm]

Yep

[hearty nexus]

(my ocd i hate it sry 😭)

[hearty nexus]

alrrr

thankss

ima close

.close

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[coarse coyote]

Good day. I'm doing this question to solve a problem involving mean value theorem but I don't know how to proceed. I know how to do it with a polynomial with a greatest power of 2 but got stuck in this situation. Sorry if this question sounds dumb but math is not my strong suit

[coarse coyote]

I think it's more of how to get the value of x from the 24x^3-18x

[supple knot]

use $ab = 0$ implies $a=0$ or $b=0$

[woven radish]

riemann

[coarse coyote]

Wait is it for value of a n b for the theorem ?

I think my problem is more on algebraic manipulation ngl

Not sure if I should bring this question to one of the uni channels below not here

[supple knot]

6x(4x^2-3)=0

[supple knot]

no. unfortunate choice of variable names i made tere

[coarse coyote]

Ohh .... How can I simplify it further ? I need to get the value of x to use as my c in getting the mean value result

[supple knot]

that x is your c

[supple knot]

$6c(4c^2 - 3)=0$

solve for c

[woven radish]

riemann

[supple knot]

using this property for all real numbers

[coarse coyote]

Yeah that's what I'm stuck on ... Ayt I'll use the property you mentioned brb I guess

[supple knot]

you can divide both sides by 6 to make this a little simpler

[coarse coyote]

Cant I just divide both sides by 6c instead ? Damn I really to brush up on my algebra notes

[supple knot]

you can only divide by c if it's not 0

but you don't know that

c can be zero

[supple knot]

a = c and b = ?

[coarse coyote]

Ohh dayum

I just assume it ain't 0 ngl

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[charred cove]

I need help haha

[charred cove]

Finding

$integration xlnxdx$

[woven radish]

Menoplay01

Mehdi_Moulati

$\int x\ln(x) \dd x$

[charred cove]

Yes

[real grail]

this one ?

[charred cove]

I need to learn this bot haha

Ges

Yes

[real grail]

use integration by parts

[charred cove]

I'm trying the tabular method, or is that not possible

So would lnx be used for integration or derivative

[crisp fossil]

for tabular you differentiate the x^n term

but by parts I don't think it matters what direction you do it in (for this problem, in terms of how hard it would be to solve) *actually nvm integrating lnx would be the hard way

[charred cove]

Because by parts you're gonna be using both in a way

But I thought so but do we know integration of lnx before integration by parts

[crisp fossil]

yeah

integrate by parts lnx = 1lnx, integrate the 1 differentiate the lnx

you get int(lnxdx)=xlnx-int(x/xdx)=xlnx-x

[charred cove]

Ok

So by tabular method you would go from x to 1 to 0, then integration it'll be lnx xlnx, then x^2/2?

[signal forum]

Am I allowed to share how I get the answer for int xlnx

[charred cove]

^

[signal forum]

I used the regular method

[charred cove]

So for my original

So by tabular method you would go from x to 1 to 0, then integration it'll be lnx xlnx, then x^2/2?

[signal forum]

Do you want the answer with reg method?

[crisp fossil]

you want to let them do the work themselves nasa

[signal forum]

With work shown

[crisp fossil]

don't give out answers, this server is for learning

[signal forum]

Yeah ig ppl learn dif

[crisp fossil]

not quite?

[signal forum]

Alright gl

[crisp fossil]

where did you get x^2/2 from?

your intentions are appreciated though! @signal forum

[charred cove]

Integration of x, but that is wrong

[crisp fossil]

mhm

if you have two columns

on the left is x, 1, 0

on the right is lnx, xlnx, then what?

[charred cove]

Then xlnx will be integration by parts again right

[crisp fossil]

your initial problem is xlnx

[charred cove]

Then I stop

Jee

[crisp fossil]

which means you should be doing it all from scratch by parts, rather than using tabular integration: since as we see here, it leads you in a loop to differentiate the x term

which means we should have approached the problem by differentiating lnx and integrating x

worth pointing out this is a fairly rare case

but lnx does not integrate pretty

do you know how to apply by parts in the opposite direction?

[charred cove]

D I
Lnx. X
1/x X^2/2
-1/x^2 X^3/6

[crisp fossil]

nope nope nope no tabular integration

[charred cove]

Ohhh ok

[crisp fossil]

it only works with x^n because that burns itself out

if you differentiate x^n long enough, it'll end up as 0

you try tabular with any other term, it'll go on forever (since nothing else ends up as 0 after being differentiated endlessly)

you have to do it formally by parts, since tabular is shorthand

does that make sense?

[charred cove]

U=x
Dv=1/xdx

Du=1dx
V=lnx

Yes

?

[crisp fossil]

why are you using dv=1/x?

ok look, your initial problem is xlnx

xlnx=udv when integrating by parts

tabular integration is u=x, dv=lnx. We just showed that doesn't work (since you end up needing to know the integral of xlnx to get xlnx's integral)

[charred cove]

Oh so dv=lnx

[crisp fossil]

that's what you tried earlier, with tabular integration

we want the other direction

xlnx=udv, u=lnx, dv=x

so

[\int{udv}=\int{x\ln{x}}=\frac{x^2}{2}\ln{x}-\int{\frac{x^2}{2}\frac{d}{dx}(\ln{x})}]

[woven radish]

Scythe

[crisp fossil]

integrate x, differentiate lnx

does that make sense?

[charred cove]

Why so many integrations?

[crisp fossil]

there's only really one, note the equals signs

just showing how I'm rewriting the problem

[charred cove]

Ohhhh

I didn't see the 2nd one

[crisp fossil]

ah yeah lol that would be confusing

[charred cove]

So we'd have x^2/2lnx-x^3/6?

[crisp fossil]

pardon? how did you get x^3/6?

d/dx(lnx)=1/x, x^2/2*1/x=x/2, integral of x/2 is x^2/4

so you should have gotten (x^2lnx)/2-x^2/4

[charred cove]

Integration of x^2/2

Isn't that x^3/6

[crisp fossil]

ah ok I see your problem

you are not integrating just x^2/2

[real grail]

did you derivate ln(x) ?

[crisp fossil]

you are integrating (x^2/2 * d/dx(lnx))

as Mehdi said, you forgot to differentiate and multiply by lnx

[charred cove]

Oh I missed the lnx part

[crisp fossil]

;-;

[charred cove]

So it would be x^3/6x which reduced is x^2/6

,w integrate x^2/2lnxdx

[woven radish]

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[crisp fossil]

nope

you queried integral of x^2lnx/2

not x^2(d/dx(lnx))/2

forgot the derivative bit again

[charred cove]

Oh duh

,w integrate not x^2(d/dx(lnx))/2

[woven radish]

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[charred cove]

,w integrate x^2(d/dx(lnx))/2

[woven radish]

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[charred cove]

That looks complicated

So x^2/2lnx-x^2/4+c

Too complicated

[signal forum]

What did you pick for
U, du, v, dv

[charred cove]

xlnx=udv, u=lnx, dv=x

[signal forum]

Close you got u and dv right

So what’s the antiderivative of x?

[charred cove]

X^2/2

+c

[signal forum]

Right since dv is x what would v be?

[charred cove]

x^2/2

[signal forum]

Yeah

So what’s du?

[charred cove]

1/x

Bc v is lnx

Or am I backwards

[signal forum]

Yeah

It is 1/x

[charred cove]

Oh ok

[signal forum]

But remember you just said v is x^2/2

So now plug in dv, v, u, and du into this formula

Hint find constant in x^2/2 and pull it out of the integral

[charred cove]

Lnx(x^2/2)-1/2int(x^2(1/x)dx)

Yes

?

[signal forum]

Well for uv

You are multiplying them

[charred cove]

Xlnx

[signal forum]

Alright now you just got to solve the integral

You have any ideas?

[charred cove]

Which would be x^2/2

[signal forum]

x^2 is over x

[charred cove]

Yes so integration of x?

[signal forum]

How can you simplify it

[charred cove]

X

[signal forum]

Yeah

[charred cove]

Int(x) is x^2/x

2 not x

[signal forum]

So what’s ur final answer

[charred cove]

Xlnx-x^2/2+c

[signal forum]

Ur getting closer

Lnx(x^2/2)-1/2int(x^2(1/x)dx) remember this statement

Now plug the derivative you found and replace it with integral

[charred cove]

Derivative?

[signal forum]

What was the integral for int(x^2(1/x)dx)

[charred cove]

Int(vdu)?

[signal forum]

Yeah

What was it

[charred cove]

X^2/2+c

[signal forum]

(Ln(x)) (x^2/2) - 1/2 [x^2/2]

That’s everything you told me

You can still simplify the very end

[charred cove]

So it's x^2(lnx)/2-x^2/2+c

So lnx/2+x

C not x

[signal forum]

Mo

No

It’s pretty much solved already at this point

(Ln(x)) (x^2/2) - 1/2 [x^2/2]

[charred cove]

Lnx+c

No

What am I missing

No it is lnx+c

[signal forum]

Where r u getting lnx from

[charred cove]

I have no idea at this point

[signal forum]

Ur getting the derivatives and integrals right

Ur just not putting the pieces together

[charred cove]

x^2(lnx)/2-x^2/2+c

That's right right

[signal forum]

Ur missing one thing

[charred cove]

x^2(lnx)/2-x^2/4+c?

[signal forum]

Yeah

That’s right

(x^2(lnx)/2)-(x^2/4) +c
Here is proper format tho

[charred cove]

So it's (x^2(lnx))/4+c

?

[signal forum]

No ur done

No need to do anything else

[charred cove]

(x^2(lnx)/2)-(x^2/4) +c that's the final answer?

[signal forum]

Yes

Do u understand it

[charred cove]

You can't combine 2x^2(lnx)/4-x^2/4

Right

Bc multiply by 2 for first

[signal forum]

Where did the 2 come from

And 4

Ur already done

[charred cove]

Multiply x^2(lnx)/2 by 2/2

[signal forum]

You don’t need to do that

(x^2(lnx)/2)-(x^2/4) +c
Is fine

[charred cove]

Ok

That took way to long haha

I feel like if I had written it down it would've been easier

[signal forum]

I spent 4 hours today on a integral because I missed a distribution

[charred cove]

Haha

[signal forum]

💀

But u get it now right

[charred cove]

I think so

If I were to have written it down I think I would've gotten it faster

Thanks tho

.close

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[signal forum]

For a more clear reference type

Xlnx integration by parts
Into YouTube

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[supple knot]

Find a basis for $V\setminus U$

[woven radish]

riemann

[devout snow]

@wraith roost Has your question been resolved?

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[left veldt]

Why is the x positive shouldn’t it be negative?

[left veldt]

That’s cot(-x) on the right side

I’m not sure if you’re supposed to take the absolute value when you plug in your x and y values

Oh even odd identity

Silly me

.close

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[small raptor]

https://gyazo.com/eebb7cd465693f085fce62cc6d112757

[small raptor]

Why is force the negative derivitive of Potential and not just the derivitive

[pseudo basin]

forces pull you in the direction where potential is lower

[remote meteor]

Cus F = ma i guess

[small raptor]

ahhh this makes sense

Thanks

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[restive river]

Hey

[restive river]

Can anyone tell me the difference between : and | here ?

[wooden veldt]

none!

pick whichever you prefer

[restive river]

Oh really

[wooden veldt]

yeah they mean the exact same thing inside a set

[restive river]

And is this also an alternative ? Or do i need {} ?

[wooden veldt]

thats fine

(-inf,-28) is a set already

[-28,inf) also works

[devout snow]

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Channel closed

Closed due to the original message being deleted

[knotty bolt]

I disagree.

[pastel pasture]

But yes, you'd need to visit Scotland

[restive river]

Unless you consider it to be a homeomorphic transcendental projection, in which case you'd need to use the Riemann-Kanye theorem to solve it

[restive river]

I thought you need the {} after writing a D= |R \

You can also write [) stuff after it?

[hybrid snow]

" im gonna go death con 3 on matrices" - Kanye East

[knotty bolt]

How do you check if an object or array is empty in JS?

[devout snow]

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[north violet]

why is many to one is not a function?

[sonic smelt]

You mean one to many?

[north violet]

yeah one to many mb

[stone stump]

definition

[sonic smelt]

By definition a function should map every element from its domain to only one element from its codomain

Literally contradicting the case when it maps to more than one elements

[restive river]

A function is just a total univalent relation

[north violet]

interesting...

.close

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[teal niche]

in Z_79 what is X here ? can someone explain to me how to solve this

[sonic smelt]

73x = 31
73x = 584
x = 8

I believe

[devout snow]

@teal niche Has your question been resolved?

[restive river]

(use extended euclidean algorithm)

[devout snow]

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[grizzled totem]

I got it to this point and the z variable is wrong bc its supposed to be (2,2,-3) but i cant tell where i went wrong after looking it over, could someone pls help?

<@&286206848099549185>

[upper schooner]

,rccw

[ashen void]

romina

[grizzled totem]

hi

[ashen void]

please send me your problems

I can help you

[grizzled totem]

x-y+9z=-27
2x-4y-z=-1
3x+6y-3z=27

using rref method

for the matrix

[upper schooner]

Check this maybe?

I get 77 rather than 123

[grizzled totem]

omygod thank you im so sorry

thank you so so so so so much

[upper schooner]

You're fine, it happens

[grizzled totem]

i cannot believe i didnt see that

[upper schooner]

Some times it's like that, had a moment like that myself just now

With my own stuff, I was like "how didn't I spot that"

But have a wonderful one! 🙋‍♀️

[grizzled totem]

thank u so much ❤️❤️❤️❤️❤️❤️❤️

‘close

how do i close

[upper schooner]

.close

[devout snow]

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[upper schooner]

Like that

[grizzled totem]

thank you 🙏🙏🙏

[upper schooner]

Catch ya around

[devout snow]

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[surreal steeple]

How do you maximize the value of $\sin(2(\theta + \phi)) - 2\tan(\theta)\cos^2(\theta + \phi)$, where $\phi$ is in terms of $\theta$ (ie. need to find $\phi$ in terms of $\theta$ so that the expression is maximized)

[woven radish]

NotOrz

[surreal steeple]

This is the original question

and I found out that the horizontal distance covered is equal to $\sin(2(\theta + \phi)) - 2\tan(\theta)\cos^2(\theta + \phi)$

[woven radish]

NotOrz

[surreal steeple]

But I don't know how to find the maximum of this expression

assume theta is some angle between 0 radians and pi/2 radians

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[somber rampart]

Hii. My friend says the P-Series Test doesn't work like this. Is this correct or not?

[upper schooner]

You pulled an n right out of the sum when you're supposed to be summing with respect to it(!)

[somber rampart]

so that's not a legal thing to do? c.c

I always thought it was

[upper schooner]

No, very illegal 👮‍♀️

[somber rampart]

finna go to jail

Then I'm ..really at a loss how to check this series for convergence 🙃

[upper schooner]

Like because the n is the summation variable, you can't take it outside of the sum you're doing

[somber rampart]

ohhh

but if it was a constant i could?

dfgdfg

[upper schooner]

Yep, constants are all fair game!

[somber rampart]

i see.. alright. any hints what test i might have to apply for this one? c.c

[upper schooner]

And to me, I think I would try to compare the series from below

[somber rampart]

from below?

[upper schooner]

I think that works out

[somber rampart]

i don't think I know what you mean :l

[upper schooner]

As basically you have that $n^{3} - 1 < n^{3}$, then we have that $\frac{1}{n^{3}} < \frac{1}{n^{3} - 1}$ (noting that $n\geq 2$ of course), and then:
$$
\frac{n}{(n^{3} - 1)^{3/7}} > \frac{n}{(n^{3})^{3/7}}
$$

[woven radish]

chartbit

[upper schooner]

So then check the series of the one of the left for convergence or divergence

[somber rampart]

ooo i see i see

well once again thanks alot for your help, I'll get right back to cramming for my calculus exam haha

[upper schooner]

Aww best of luck for it! Hope it goes amazingly well

And catch ya around of course!

[somber rampart]

.close

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[lusty tapir]

i know the formula for finding the area of the surface

im just not sure how to go about this problem

should i try and factor out before getting the derivative

of y

or do i just find y prime

and then plug that in to the surface area formula

[restive river]

are you in calc 2?

[lusty tapir]

yes

[restive river]

ok so use the disk method

disc*

oh this is surface area nvm

[lusty tapir]

yea

this is the formula im pretty sure i have to use

[somber vault]

Just try integrating it

The formula is mostly right, but it should have limits of integration

[lusty tapir]

oh yes i forgot about that

does this look correct so far

[somber vault]

Is the negative sign on the fraction or just the x in the numerator?

[lusty tapir]

it is for the x

in the numerator

[somber vault]

Looks good

Keep computing and you should get a clean answer at the end

[lusty tapir]

ok

just to make sure my progress is correct

[somber vault]

Check the signs

[lusty tapir]

ok ya in the nominator it shouldve been x^2-2x+1

[somber vault]

Yep

[lusty tapir]

now for this part should rewrite 1 the same as the denominator?

[somber vault]

You could do that

[lusty tapir]

ok i think i see it

[somber vault]

I did not see this before, but you forgot the square in the first root

[lusty tapir]

oh yes u are correct

am i correct so far?

[somber vault]

That's right

[lusty tapir]

awesome, i got the rest from here

thank you so much

for your help

[somber vault]

You're welcome

[lusty tapir]

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[celest fox]

can someone help me with this question pls

[gleaming socket]

a + ar + ar^2 + ... This is now a geometric series goes

So what is Un?

[devout snow]

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[timber narwhal]

Why is this wrong

[weak cove]

whats the derivative of 1/2ln(3+sin^2(x))

?

,, \frac{3+\sin{x}^{2}}{2x}2\sin(x)cos(x)

[hybrid snow]

They have the right antiderivative

[weak cove]

just checking

[hybrid snow]

Just use wolfram for that

[timber narwhal]

Is it to do with the absolute value on the top

[hybrid snow]

I'm also getting 0

Oh there's an absolute value?

They looked like parenthesis lol

[timber narwhal]

Yes

My bad

[hybrid snow]

Yes it makes a difference

[timber narwhal]

How so

[hybrid snow]

The integrand can be negative

[timber narwhal]

Can’t u mean?

[hybrid snow]

The period of the integrand is pi/2, so your integral is equivalent to $2\pi\integrate{\frac{\sin(x)\cos(x)}{3 + \sin^2(x)}}{x}{0}{\frac{\pi}2}$

[woven radish]

Umbraleviathan

[timber narwhal]

I see

Ty

Cus after pi/2 the top becomes negative

[hybrid snow]

Yeah

[timber narwhal]

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[sonic hill]

i dont know where to start

.close

[devout snow]

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[real grail]

[devout snow]

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[paper salmon]

Would the answer for this be a vector?

obviously x = cost

y = sint

z = 4cos^2t

but would the parameterization be a vector or like

r(t) = cost + sint + 4cos^2t

[devout snow]

@paper salmon Has your question been resolved?

[paper salmon]

useless

it's a vector

.close

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[restive river]

Hello i was doing a physics question and this integral came up

[hushed wraith]

A substitution might work

[restive river]

This kinda looked like sin

[pastel pasture]

Is x a constant?

[restive river]

So i was wondering if i could replace it with sin

[restive river]

Yes

[pastel pasture]

You don't need to

$x^2 + y^2 = u$

[woven radish]

NEONPerseus

[hushed wraith]

It is exactly the derivative of sqrt(x²+y²)

[restive river]

[hushed wraith]

Wrt y

[restive river]

Oòoh hmm

[restive river]

But is it equivalent to this?

[hushed wraith]

It shud be equivalent to $\left[\sqrt{x^2+y^2}\right]_0^R$ ig

[woven radish]

SilverSoldier

[restive river]

But isnt the integral of sin=>-cos?

[hushed wraith]

It is, but why is that necessary

How did you convert this to an integral of a sine

[restive river]

So why can not we use that relationship here?

[restive river]

Y/root x²+y² is clearly a trig ratio

So cant i write it as

Sin y

[hushed wraith]

No, not sin y

U can define an angle theta or something such that sintheta = y/sqrt(x²+y²)

[restive river]

Hmm

[hushed wraith]

Theres no reason to say that the angle that has a sine of y/sqrt(x²+y²) is y itself

[restive river]

Oh hmm

I see

[devout snow]

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[devout snow]

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[lime swift]

i counted all the vertices, faces, and edges

if we still had the two segments

and it was 22+30-50

Euler's Polyhedral Formula

[pseudo basin]

you do not need to count all the vertices, faces and edges.

[lime swift]

and if we subtract 1 verticy and 1 face, and 2 edges, we get 21+29-49

and i got 1

so does it decrease by 1?

[pseudo basin]

the singuular of vertices is vertex, not "verticy".

[lime swift]

srry

vertex

so did i make any mistakes?

[pseudo basin]

50 - 2 isn't 49, for a start.

[lime swift]

lol, my mistake,

21+29-48

then it makes no difference?

i still get 2?

nvm, i get it, ty for the help

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[lofty monolith]

if im trying to show two circles touch each other and i have the equations

[lofty monolith]

is the only way to use simultaneous eqns

[lunar harbor]

Definitely not lol, they have many uses, such as allowing you to find unknown quantities

[lofty monolith]

i think i worded my question badly

uh

how do i show that two circles touch each other

[lunar harbor]

You could solve the system and show there's only one intersection

[lofty monolith]

hmm

its only three marks

so maybe a sketch would work

idk

[lunar harbor]

Ig you could also take the distance between the centres?

And show the distance is equal to the sum of the radii

[low holly]

post the original question?

[lofty monolith]

B

[lunar harbor]

Oh then prolly do this

[lofty monolith]

Okay

Thanks

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[solemn mulch]

i got

x^3-3x^2-14x+24

im confused on where i went wrong

[wooden veldt]

show your work

[sonic smelt]

Show your work

[solemn mulch]

kk

question 2

[wooden veldt]

where did you get -14 from?

[solemn mulch]

+8x-6x-12x

i did

+8x-6x = -2x

-2x-12x

=14x

but i see you can do -6x-12x= -18x

then -18x+8x=10x

but is there 2 answers then

...

[wooden veldt]

check this

[solemn mulch]

Oh shit

yueah

im dumb

sorry about that

.close

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[frozen spoke]

hi

[frozen spoke]

im dumb at maths

i'm not sure how to do this

[devout snow]

@frozen spoke Has your question been resolved?

[frozen spoke]

<@&286206848099549185>

[plush sleet]

range is how big the spread of output data is. what's the difference between the highest and lowest scores

the frequency column tells you how many students got each score, so you should be able to tell from that column how many students there are total

[devout snow]

@frozen spoke Has your question been resolved?

[arctic temple]

@frozen spoke

[frozen spoke]

yeah i didnt really understand

[arctic temple]

The range is essentially highest value minus lowest value

Range= 10-6=4

@frozen spoke

[arctic temple]

The way you should be thinking about this table is, other than writing 6,6,6,6,6,7,7,7,7,8,8,8,8… we put them in a table instead

Number of students is $\Sigma f$

[woven radish]

.doc

[arctic temple]

Mean= $\frac{\Sigma fx}{\Sigma f}$

[woven radish]

.doc

[gloomy dawn]

yea the mean is Mean= $\frac{\Sigma fx}{\Sigma f}$

[woven radish]

LilFireBoy

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[jaunty gazelle]

Quick question, am I on the right track here?

[jaunty gazelle]

Just want to know if I’m on the right track

[hollow pollen]

you cant pull x out of the integral

your final answer should be in x

not u

and there shouldnt be du

[jaunty gazelle]

Wait so I shouldn’t have 3x in front of integral?

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[azure widget]

Hello, I have unclear exercise from Geometry.

[azure widget]

Find the coordinates of centre of circle which touches the x orbit and contains point M(-1,2) and it's r=5.

I hope it's clear.

[cosmic trail]

what's the x orbit?

[mellow panther]

x-axis?

[azure widget]

Yes.

X-axis, I meant.

Hello?

[cosmic trail]

ok so call the centre point O: (a,0)

as it's on the x axis so it's y value is 0

then the length OM will be 5

and then you can solve for a

[azure widget]

How do I write root in this server?

In order to ask you.

A question.

[cosmic trail]

sqrt

[supple jackal]

The circle touches the x axis. Its centre does not lie on the x axis

[azure widget]

Like this? sqrt(9)?

[cosmic trail]

ya

[cosmic trail]

it says the centre touches the x axis

[supple jackal]

oh

[azure widget]

So sqrt((p+1)^2+(2)^2))=5^2?

[supple jackal]

I thought the circle touches the x axis

sivalije can you confirm what touches the x axis, the circle or the centre

[cosmic trail]

what's p

yes that's correct

I'm assumign you mean p is a

[azure widget]

determine the coordinates of the center of the circle that touches the x-axis, contains the point M(-1, 2) and whose radius is r =5.

The same exercise.

[supple jackal]

I'm asking what is touching the x axis

[shadow breach]

the circle

[supple jackal]

Yeah I thought so

[azure widget]

Center of the circle.

[supple jackal]

oh

[azure widget]

The exercise says that.

[supple jackal]

ok then what bo luo said is correct

[azure widget]

@cosmic trail if I've done it correctly then I should get a^2+2a-20=0?

@cosmic trail Hello?

Anybody?

[cosmic trail]

yes hellow that is correct

you can divide by 2

oh no you can't lol

ignore that

[azure widget]

I got weird numbers.

A= - 1-sqrt(21) A=-1+sqrt(21).

Well, it isn't correct. I don't blame you.

[devout snow]

@azure widget Has your question been resolved?

[devout snow]

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[frail lake]

So I have to graph the function A * sin (2pi * f1), where A and f1 are all discrete values entered from the user. The thing i am confused about is that I think that this is just a point, not a function

[frail lake]

am i mistaken?

if you want i can send the prompt but i think it's a bit confusing the prompt

[devout snow]

@frail lake Has your question been resolved?

[frail lake]

<@&286206848099549185>

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@frail lake Has your question been resolved?

[frail lake]

.close

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[devout snow]

✅

[knotty bolt]

.close

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[hybrid snow]

.reopen

[devout snow]

✅

[devout snow]

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[frail lake]

what were you guys doing lol

with all the .reopens lol

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[kindred dock]

Geometric proof involving postulates, theorums, and definitions. I'm not allowed to use the definition of a parallelogram. Anyone got advice? Did some based on the provided midpoint but I don't know how to continue.

[dim perch]

triangle congruency?

vertical pair angles is a start

[kindred dock]

I could say angle DQC is congruent to AQB, but where would that get me

[dim perch]

SAS congruency?

[kindred dock]

how would I say AQ is congruent to DQ to get that result?

and if I said tri DQC was congruent to BQA, how could I say that the segments were parallel

[devout snow]

@kindred dock Has your question been resolved?

[kindred dock]

<@&286206848099549185> some advice?

[devout snow]

@kindred dock Has your question been resolved?

[kindred dock]

.close

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[placid rover]

!15m

[devout snow]

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

[weak cove]

please only use the helpers tag once

[placid rover]

[devout snow]

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[placid rover]

<@&268886789983436800>

smh

[wicked rover]

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[simple jackal]

Me and my friends have been stuck on this for awhile.

Translation of the text: The top triangle is uniform with the entire triangle. Calculate the distance x

[sonic smelt]

Could you show your work?

[vast rain]

är du svensk

[simple jackal]

We've figured out a) but b) we just cant figure out even where to begin.

[simple jackal]

Ja

[vast rain]

I think likformig in a mathematical context is translated to similar

[simple jackal]

No clue just used google translate...

[vast rain]

vad kan du säga om sidorna av den liten triangeln

fck my swedish has gone to shit

what do you know about the sides of similar triangles

[simple jackal]

I dont quite get what youre asking. can you clarify maybe?

[vast rain]

like what does it mean for triangles to be similar?

[simple jackal]

I think it means for the measurments of one triangle to correspond to the proportions of the other triangle. Maybe completelly wrong

[vast rain]

basically the ratios have to be the same

[simple jackal]

much simpler way to answer

[vast rain]

so the problem says two triangles are similar

so it would be probably helpful to write some equation as side_of_little_triangle/side_of_big_triangle = other_side_of_little_triangle/other_side_of_big_triangle

more specifically, you probably want one of the sides of the little triangle in that equation to be x

[simple jackal]

Ok, ill try that. Ill get back if i get stuck

Solved it, although not quite through your method i think.

[vast rain]

do tell

[simple jackal]

quite messy

[vast rain]

,w solve x/6 = (21-x)/8

[woven radish]

Results provided by WolframAlpha

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

Requested by Saccharine#3780

[vast rain]

,w solve x/21 = 6/14

[woven radish]

Results provided by WolframAlpha

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

Requested by Saccharine#3780

[vast rain]

hmm guess it works

[simple jackal]

thanks for the help anyways. helped me solve it

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[tough folio]

How to solve this kind of exercise?

[tough folio]

By logic it must be greater than option C, D, E, so just got to choose between 99 and 100.

I'm pretty sure it's 100, but how to actually solve it?

[restive river]

you see... P(1)+P(1^-1), P(2)+P(2^-1), P(3)+P(3^-1).... upto P(100)+P(100^-1), each adds up to 1

[tough folio]

Ohhhh

Thanks

You're cool

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[hoary pond]

what is the representation and equation in the word problem, “Laura invested P12,000 in two bank accounts. One of the accounts pays 6% annual interest, and the other account pays 5% annual interest. If the combined interest earned in both accounts after a year was P700, how much money was invested in each account?”

[copper quail]

Ig simultaneous equations

So 0.06x+0.05y=700
X+y=12000

I think

[restive river]

too much work,just use one variable

x and the other one will be 12000-x

[copper quail]

Yeah that works aswell

[copper quail]

Surely there's hardly any difference between the 2 methods though

[restive river]

well yes, but why bother making another statement

[copper quail]

Ig that makes sense

[restive river]

@hoary pond

[hoary pond]

?

12k - x will be the money invested in the account

that?

[restive river]

uh... no

let money invested be x for 6% and the remaining money, that is (12000-x) for 5%

so, total interest =700

0.06x + 0.05(12000-x)=700

0.01x=100

x=10,000

so invested 10000 at 6% ans 2000 at 5%

[hoary pond]

so, Let x be the 6% money invested and 12000-x be the 5% money invested?

[restive river]

yep

[hoary pond]

alr

so whats the equation

[restive river]

i wrote it above

[hoary pond]

this?

[restive river]

yep

[hoary pond]

alr

why cant 6% also have 12000-x?

[restive river]

you can take what you want

[hoary pond]

huh 😭

[restive river]

12000-x could be going for 6% while x went for 5%, the answer wont change

[hoary pond]

ohhh

alr

[hoary pond]

how do u do its solution?

[restive river]

just solve the equation?

[hoary pond]

i dont get it

can 500/11 be simplified

[restive river]

how do you even get 500/11?

do it part by part...
First, he invested amount x at 6% annually, so interest = (6/100)*x=0.06x

now he invested the remaining amount, 12000-x for 5% annuaally

so interest = 5% of (12000 -x)= (5/100)*(12000-x)

simplify this we get the second interest = 600-0.05x

total interest= first interest + second interest= 0.06x+600-0.05x=600+0.01x

now this is 700 by question, so 600+0.01x=700, and finally 0.01x=100

x=10,000

[devout snow]

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[lament sequoia]

hello

[lament sequoia]

wa

wat

is

.reopen

tf

3+35

[pseudo basin]

3 + 35? is that your question?

[lament sequoia]

what is the formual for finding out the diagonals of a n. number of sides pf a polygon

[lament sequoia]

nah

is

n(n-3)/2

@woven radish

[pseudo basin]

...

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@lament sequoia Has your question been resolved?

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[dusty valley]

Is my second answer, NOT correct? https://i.imgur.com/JJElASw.png

[dusty valley]

I think the website is lying to me.

[fast garden]

your second answer is equivalent to cos

[restive river]

Counter example: when theta = 0 you have sin(pi/2) and sin(0) which are not equivalent

So no the website is not lying to you

[dusty valley]

Wait, if the first sin($\theta$) = -Y, doesn't the equivalent have to be negative also?

[woven radish]

j4w4

[restive river]

Recall the quadrant signs here

[dusty valley]

For Y, positive above X-axis, negative below.

[restive river]

I mean the signs of trig ratios in different quadrants

[dusty valley]

Ah, I see my mistake now. It's answer D. Okay, thank you.

[fast garden]

correct

[dusty valley]

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[devout snow]

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[bronze urchin]

Lets say u have a trapezoid and the ratio between a:c is 5:2 the diagonal of the trapezoid cuts the sharp angle in half and the diameter of the trapezoid is 33cm how do i calculate the height of the trapezoid here

[bronze urchin]

legs of the trapezoid are the same b=b

So i got to 33cm = 7t + 2b

And not much progress from here

Im assuming u have to get something from the diagonal info

But idk how help

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[devout snow]

Please don't occupy multiple help channels.

[devout snow]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[proud nimbus]

.close

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[restive river]

i dont understand exponential sequence lately do you have a video on or can you explain what is an exponential kind of a sequence

[restive river]

in easier words

[polar chasm]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:introduction-to-geometric-sequences/v/geometric-sequences-introduction

[restive river]

i do have an understanding about quadratic and arithmetic/linear sequence dont get the exponential kind of

[polar chasm]

This one is about exponential

[restive river]

thank you @polar chasm, i might check it so that i actually grasp some understanding of what it actually is

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[restive river]

math help the middle term break method isnt workin

[restive river]

2x^2 - 13x + 15

i have made factors of 30

-15 + 2 = -13

when i use this i dont get the right answer

[uncut marsh]

factor top and bottom

[restive river]

i did the top one there is another identity being applied

the second needs middle term

it is not working on it

[restive river]

if you get what i mean by this

to get -13

to do middle term

[mellow panther]

yeah middle term split

[restive river]

it is not working

[mellow panther]

also, -13 = -10 - 3

[restive river]

@mellow panther sorry for the ping does that mean we can check the answer if we are not getting it means you didnt take the right factors?

probably my factors didnt work

[uncut marsh]

what is a middle term break?

[mellow panther]

this will work

[restive river]

it is when you take out some factors in such a way you get the middle number from those two factors

[mellow panther]

cause -10 - 3 = -13 and (-10)(-3) = 30

[uncut marsh]

can you not just do inspection

and top is difference of squares

[restive river]

this one exactly