help-36

[unborn wave]

<@&286206848099549185>

[final saddle]

@unborn wave Has your question been resolved?

[unborn wave]

<@&286206848099549185>

[final saddle]

@unborn wave Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[upper minnow]

I'm trying to take a derivative from e^(x^2) and I'm failing miserably.
(a^x)'=a^x ln a.
therefore it should be something like this:
(e^x)^x = e^(x^2) ln e^x = e^(x^2) x
but wolfram says there's a two from somewhere
what am I doing wrong?

[amber holly]

The first equation works when a is a constant, not a function

So you can't let a = e^x

[upper minnow]

oooh! thanks

how do I derive it then ;_;

[amber holly]

What you need to do is apply the chain rule

Are you familiar with it?

[upper minnow]

yes! thank you <З

.close

[final saddle]

Channel closed

Closed by @upper minnow

Use .reopen if this was a mistake.

[upper minnow]

.reopen

[final saddle]

✅

[upper minnow]

how do I express e^(x^2) as a product of multiplication?

[amber holly]

You mean as a composition?

[upper minnow]

derp, forgot english terminology, though chain rule is the one that's (f g)'=f'g+g'f xD

.close

[final saddle]

Channel closed

Closed by @upper minnow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pastel cedar]

ok this might seem like a really simple problem but I can't find the line through the points (-3, -5), (2, -3)

[fathom walrus]

What have u tried?

[pastel cedar]

just simple m= y2-y1/x2-x1

then sub into eqn to find c

[fathom walrus]

Ok what did u get for m

[pastel cedar]

for reference the question includes non-concentric circles

m=2/5

before we get to that

i have radical axis between the 2 non intersecting circle

does that have anything to do with it?

[fathom walrus]

Uh idrk, what’s the eqn of the line u got

[pastel cedar]

the one through the points?

y=2/5x+19/5

am i trippin?

this seems so easy

but look at desmos

[fathom walrus]

That’s incorrect

Check ur signs

Ur slope is correct

[pastel cedar]

what did you get -31/5?

for c

[fathom walrus]

No

Show ur working for the +c part

[pastel cedar]

ok so we sub in any point into the equation y=mx+c

therefore i'll sub in point 1

-5=+2/5 (-3)+c

correct?

now we find c by rearranging

2/5 * -3 = -2/15

-5 = -2/15

[fathom walrus]

No

[soft zealot]

Stephen

[pastel cedar]

oh wait

i put it in the calc wrong

-6/5

[fathom walrus]

Yes

Now we have

[pastel cedar]

yeah so -5 = -6/5 +c

c= -5 +6/5

[soft zealot]

Stephen

[pastel cedar]

uhuauhhauuhu

i've wasted an hour on this crap

[fathom walrus]

https://tenor.com/view/sonic-sonic-the-hedgehog-sonic-x-vector-vector-the-crocodile-gif-22457028

Rip

[pastel cedar]

i'm not even joking and this is the easiest part

[fathom walrus]

u got this

Keep going

[pastel cedar]

i have 7 hours left

and have a validation for basically all non linear lines

like hyperbolas, asymptotes and stuff

i wasted an hour on this ;-;

[fathom walrus]

Sorry to hear that

Best thing u can do is keep going

👍

[pastel cedar]

facts

wait can i ask for advice

i have to create a moving image in desmos

and it has to include : line, parabola, semi-
circle, hyperbola, square root

what's something easy to make?

that includes these

[fathom walrus]

Honestly I’m not too sure sorry, not too familiar with desmos

[pastel cedar]

damn

basically just a graphing calculator

example

for the thing we just did

it just graphs equations

[fathom walrus]

Ye ik that, but idk how to make it move

Maybe ask in #math-discussion or smth, I’m not too sure

[pastel cedar]

also i need some more help on another question

what comments would i make other than the radical axis and line that goes through the centre of each circles is perpendicular?

i found the radical axis through simultaneous eqns and the quadratic eqn

so talking about the points of intersection with the circumferences, with the radical axis is pointless

only other thing would be finding the points where the lines going through the centres intersect the circumference

[final saddle]

@pastel cedar Has your question been resolved?

[final saddle]

@pastel cedar Has your question been resolved?

Channel closed

Closed by @pastel cedar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[next pagoda]

I'm guessing the reason why I got it wrong is because there's a part where I shouldn't have combined fractions?

But I don't see where

I'm not sure how they got that as a solution

[tulip coyote]

What did you do?

[tulip coyote]

sub in dy/dx = -x/y there

[next pagoda]

OOOOOOOOOOOOOOOOO

I FORGOT ABOUT THAT

wait

so I have (-y + (-x^2 / y)) / y^2
but, how do I proceed without combining fractions

[tulip coyote]

You do combine fractions

[next pagoda]

WAIT

I READ THJE WRONG THING THAT SAID NOT TO

OKAY

TY LMAO

where is 9 coming from

I got -y^2 - x^2 / y^3

[tulip coyote]

[next pagoda]

what is that

i don't recognize that property

[tulip coyote]

[next pagoda]

oh

wait

no

don't recall

[tulip coyote]

Your original question

[next pagoda]

oh

wow

I'm just

making so many mistakes

[tulip coyote]

tbf it's one of those types of questions that are just there to test you and make sure you remember

[next pagoda]

so I just take out a negative 1 from both terms

[next pagoda]

lol yeah

Like

I don't think I would have thought of that if I didn't see the answer

like

if this was a test

I would have stoppped there and thought

oh no

I did something wrong

or

oh look

it's correct Xd

[tulip coyote]

Well luckily it's not a test right now, and you can learn what to look for in these types of questions, for when you do have one

[next pagoda]

❤️

true

ty

[tulip coyote]

Always a pleasure

[next pagoda]

.close

[final saddle]

Channel closed

Closed by @next pagoda

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tranquil flume]

Show that the line x-2=(y+3)/2=(z-1)/4 is parallel with the plane 2y-z=1

[tranquil flume]

I dont know how to proceed

I know that the dot product of the line vector and the normal vector of the plane should be 0 but dont know how to get there

[solar glade]

Can you rewrite in parametric form?

[tranquil flume]

which one?

the line?

[solar glade]

yes

to find the direction of the line

[tranquil flume]

x = t + 2, y = 2t - 3, z = 4t + 1 ?

[solar glade]

why 4t?

[tranquil flume]

I wrote the equation wrong originally, now fixed

[solar glade]

oh ok

[tranquil flume]

so direction vector of the line is i + 2j + 4k?

[solar glade]

yes and the plane is

2y-z = 1

How do you find the normal vector of the plane?

[tranquil flume]

not sure

[solar glade]

with the coefficients

0, 2, -1

[tranquil flume]

oh so 2j - k ?

[solar glade]

now you said before

Two vectors are orthogonal if their dot product is zero

[tranquil flume]

yes, why is it the coefficient though?

is there any explanation?

[solar glade]

Equation of a plane
Ax + By + Cz = D

A, B, and C are the coefficients of x, y, and z, respectively, and D is a constant. The normal vector of the plane is given by the vector <A, B, C>. This is because the normal vector is orthogonal to every vector that lies within the plane

consider two vectors that lie in the plane, u = <x1, y1, z1> and v = <x2, y2, z2>. Their difference, w = u - v, also lies in the plane. The dot product of the normal vector, n = <A, B, C>, and w should be zero, as they are orthogonal:

n · w = (A, B, C) · (x1 - x2, y1 - y2, z1 - z2) = A(x1 - x2) + B(y1 - y2) + C(z1 - z2) = 0

since u and v lie in the plane, they satisfy the plane equation:

Ax1 + By1 + Cz1 = D
Ax2 + By2 + Cz2 = D

substituting these equations into the dot product equation, we get:

A(x1 - x2) + B(y1 - y2) + C(z1 - z2) = (Ax1 + By1 + Cz1) - (Ax2 + By2 + Cz2) = D - D = 0
so, the normal vector <A, B, C> is orthogonal to the difference vector w, which confirms that it is indeed the normal vector to the plane

[tranquil flume]

oh it makes sense

thanks a lot for explaning

[solar glade]

you're welcome

[tranquil flume]

.close

[final saddle]

Channel closed

Closed by @tranquil flume

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spare sky]

@amber holly going back to my question from a few hours ago, is the fuction concave up at (2,inf) and concave down at (-inf,-2)?

[spare sky]

the second derivative of the function i mean

[amber holly]

Concave down on (-2, 2) and concave up on (-inf, -2)U(2, +inf)

Yes

[spare sky]

Is that for the second derivative or the first

[amber holly]

Second

[spare sky]

now where would the original function be concve up and down

[amber holly]

Concavity of a function directly corresponds to the sign of the second derivative, I have already told you the answer

[spare sky]

how would I draw the graph of the original function?

[amber holly]

You can just use a graphing calculator to get the idea of what such type of a function's graph looks like

[final saddle]

@spare sky Has your question been resolved?

Channel closed

Closed by @spare sky

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[random niche]

in the quotient rule, what will my g(x) and g'(x) be?

i understand that exponents in bottom are negative

so 1/t is the same as t^-1

[magic sparrow]

Yes

so if you have just exponentials

[onyx peak]

why quotient rule?

[magic sparrow]

do you even need to do quotient rule?

[onyx peak]

you can apply power rule and sum rule

[magic sparrow]

sum rule

[random niche]

i dont have to that?

[soft zealot]

MathIsAlwaysRight

AustinU

[random niche]

1/t = t^-1 . 1/t^6 = t^-6

[onyx peak]

so you can apply this

[magic sparrow]

https://tenor.com/view/yeah-yes-sir-yes-yess-yes-yes-yes-gif-22592717

[random niche]

and those become -1/t^2 and -6/t^7 ?

[magic sparrow]

be more careful with your positive and negatives

[random niche]

ok i think i fixed it

in the dit

edit

[magic sparrow]

yes looks good

[random niche]

but this will be quotient

[magic sparrow]

Sure

[random niche]

is there a quicker way? is this something you can do in ur head?

[spring haven]

I dont think so

[magic sparrow]

^

I mean derivatives of 8x and of e^x should be fairly simple

but it would be best to still write out your steps

[spring haven]

why the ?

[random niche]

idk what happens when you ^2 e^x

[spring haven]

leave it as it is

it'll cancel partially with the numerator

[random niche]

hmm im not sure wym

one of the e^x on top can "take away" one power from bottom?

[spring haven]

$\frac{e^x(8-8x)}{(e^x)^2} =\frac{8-8x}{e^x}$

[soft zealot]

kheerii

[spring haven]

correct

[random niche]

when distributing we multiply to the front of the term of the ( ) ?

nvm its just confusing seeing exponent there

.close

[final saddle]

Channel closed

Closed by @random niche

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[eager stirrup]

can i get a hint as to how to find the max height?

[final tangle]

vertex of parabola

[final saddle]

@eager stirrup Has your question been resolved?

[eager stirrup]

ah. why would that be the max height?

[final tangle]

what do you know about concave down parabolas

[final saddle]

@eager stirrup Has your question been resolved?

[eager stirrup]

oh right i forgot

thanks

.close

[final saddle]

Channel closed

Closed by @eager stirrup

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Closed due to the original message being deleted

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tranquil pine]

• i have more questions, what needs to be done is in the image itself

[supple mantle]

Hmm

What's troubling you in this question?

[tranquil pine]

im just genuinely confused

[supple mantle]

Hmm

The question seems to be asking about factors

[tranquil pine]

its scientific notations

[supple mantle]

Yeah

Did you attempt it or did you not start yet?

[tranquil pine]

i have ive been doding well for most bcs its a review so its a mix of stuff

[supple mantle]

Okay

Let's look at the first one

It says $9 \times 10^{-2}$

[soft zealot]

VulcanSeven

[supple mantle]

And $2 \times 10^{-3}$

[soft zealot]

VulcanSeven

[supple mantle]

Now let's see

What does 10^{-3} mean to you?

[tranquil pine]

0.001?

since we arent multiply anything there with it

[supple mantle]

Yeah, but could you show it in a fraction?

[tranquil pine]

1/1000

[supple mantle]

Okay

And 10^{-2}?

[tranquil pine]

1/100

[supple mantle]

Nice

Okay

So 1/100 is bigger than 1/1000 or not?

[tranquil pine]

it is

[supple mantle]

Okay, by a factor of what?

[tranquil pine]

10^1 greater?

[supple mantle]

Yep

Or just 10 times greater

So that means that 9 * 10^{-2} is greater than 2 * 10^{-3} by more than just 4.5 times right?

[tranquil pine]

it is

oki perfect i think do can do the rest now <3

[supple mantle]

[tranquil pine]

[supple mantle]

[tranquil pine]

ok so 2nd is correct right?

[supple mantle]

Yep

[tranquil pine]

and 3rd is also

[supple mantle]

Yep

[tranquil pine]

and 4th is also

[supple mantle]

Yep

[tranquil pine]

Yes omg tysvm

☺️ tyty

.close

[final saddle]

Channel closed

Closed by @frozen talon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cloud zephyr]

Look at the definitions of corresponding, alternate interior angles, alternate exterior angle

You should be able to answer

[fickle crater]

and opposite angles

[final saddle]

@tranquil pine Has your question been resolved?

Channel closed

Closed by @hushed canyon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[long tendon]

Let $f$ be a bijection. If there is a real number $a$ such that $f(a) = f^{-1}(a)$, does that always imply that $f(a) = f^{-1}(a) = a$? In other words, they intersect at $y = x$ where $x = a$

[soft zealot]

Amarinya

[hybrid heath]

Hint: by definition $f^{-1}(a)$ is some value $b$ that satisfies $f(b)=a$

[soft zealot]

SWR

[sturdy cypress]

hold on
f(x) = 1−x
f(6) = −5
f^-1(6) = −5

it doesn't follow

[hybrid heath]

Good old self-inverse functions

[final saddle]

@long tendon Has your question been resolved?

[long tendon]

then what conditions are needed for it to be true?

take for example $f(x) = e^{x-1}$. Its inverse is $f^{-1}(x) = \ln(x) + 1$ and they meet at $f(1) = f^{-1}(1) = 1$

[soft zealot]

Amarinya

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[final saddle]

Channel closed

Closed by @obsidian geode

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[simple lotus]

Hey! Question: a^2 -5a + 6
Solve by splitting the middle term

[simple lotus]

a x c = 6
6 = 3*2

[fathom walrus]

Ur trying to factor correct?

[simple lotus]

Correct

[fathom walrus]

so ac = 6

[simple lotus]

Yes.

[fathom walrus]

Now we need factors of 6 that add to -5

[simple lotus]

right

But if I want -5 then I need 3 * -2 right

but 3 * -2 is not equal to 6

[hybrid heath]

3+(-2)=1

[simple lotus]

hm

So how do I solve this

[fathom walrus]

List out all the factor pairs of 6

Positive and negative

This will help u see

[simple lotus]

Factor pairs?

what

I'm just being taught splitting the middle term

so

[solar glade]

6 = 3 * 3, 6 * 1, etc, etc

[simple lotus]

I don't know :/

oh wait

6 + -1 is also 5

[fathom walrus]

Right but 6* -1 isn’t 6

[simple lotus]

right.

[fathom walrus]

Some factor pairs of 10 would be 5,2 and -2,-5 for example

Try doing that for 6

[simple lotus]

32,
61
thats about it If im not wrong

[solar glade]

You have 4 pairs of integers.

[simple lotus]

and the other way around too, 2*3, 1 x 6

[solar glade]

You're missing the negative ones

[simple lotus]

hmm

3 x 2
-3 x -2

like that?

[solar glade]

ye

[simple lotus]

right

[fathom walrus]

Yep and 6 * 1 and -6 * -1

[simple lotus]

so -3 x -2 is oh crap

-3 x -2 = +6

and -3 + -2 = -5

sick

[fathom walrus]

Yep

[simple lotus]

so end equation is (a^2 -3x -2x + 6)

[fathom walrus]

not x, It’s a

[simple lotus]

right, A

Thanks a lot chat

.close

[final saddle]

Channel closed

Closed by @simple lotus

Use .reopen if this was a mistake.

[fathom walrus]

u didn’t factor yet tho

[simple lotus]

.reopen

oh lmao

[final saddle]

✅

[simple lotus]

right, factor.

[fathom walrus]

Is that what u have to do or no?

[simple lotus]

Yeah I have to factorize it

I believe I have to take commons?

[fathom walrus]

Ye

I think ikwym but yea go ahead

[soft zealot]

Stephen

[simple lotus]

$?

o

[simple lotus]

Answer is coming

(a-3) (-a-3)

Which I have a feeling is incorrect.

[fathom walrus]

Show how u got that

[simple lotus]

how

[fathom walrus]

What “commons” did u get

[fathom walrus]

Where did this come from im asking, what was ur thought process

[simple lotus]

Sending

[fathom walrus]

,rotate

[fathom walrus]

The stuff inside the parentheses should be the same

Manipulate plus and minus signs to do so

[simple lotus]

For example?

[fathom walrus]

If I gave u: x^2 - 4x - 2x + 8, I’d factor that to be x(x-4) -2(x-4)

[simple lotus]

If I un-factorize/open the brackets of what ive done

[fathom walrus]

See how the stuff inside the parentheses is the same

[simple lotus]

its a^2 -3a -2a +6

which is exactly like the equation

correct?

[fathom walrus]

My equation?

[simple lotus]

the image I sent

[fathom walrus]

Yes it exactly is

However, we cannot factor in that form

The general form we want to get it into is:

z(x) + b(x) = (z+b)(x)

The stuff inside the parentheses should be the same

[simple lotus]

Right

[fathom walrus]

So try getting an “a-3” in both parentheses instead

[simple lotus]

I get it now

a(a-3) -2 (a-3)

$a(a-3) -2 (a-3)$

[soft zealot]

Shady1

[simple lotus]

There

[fathom walrus]

Nice

[simple lotus]

But the end part, I don't understand.

[fathom walrus]

Now finish it up

z(x) + b(x) = (z+b)(x)

[simple lotus]

I know answer will be (a-3) (a-2)

But don't know why

Why do we skip the second term

[fathom walrus]

It’s just distributive property

[simple lotus]

Alright

[fathom walrus]

Wdym by skip?

[simple lotus]

(a-3) (a-2)

Lemme check that

Bingo

[fathom walrus]

Wdym by this

[simple lotus]

like

a-3 is first term

a-2 is second term

where does the third a-3 go

[fathom walrus]

Which third a-3?

[simple lotus]

$a(a-3) -2 (a-3)$

[soft zealot]

Shady1

[simple lotus]

The third one

a(a-3) -2(a-3)

Do we take as a common and it just cancels out to one?

[fathom walrus]

Each individual term in a-2 (which is “a” and “-2”) is individually multiplied to a-3 as u see. To fully factor we combine the a and -2 because of the common factor, and yes it “cancels” out to one

[simple lotus]

Oh alright

t h x a l o t

[fathom walrus]

Np

[simple lotus]

.close

[final saddle]

Channel closed

Closed by @simple lotus

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[heavy laurel]

Can someone help me with this problem?

[heavy laurel]

Anyone? I can show the steps to how I got here.

[final saddle]

@heavy laurel Has your question been resolved?

[heavy laurel]

.close

[final saddle]

Channel closed

Closed by @heavy laurel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unborn hill]

i dont understand these solutions

can someone help me understand them pls

[final saddle]

@unborn hill Has your question been resolved?

[unborn hill]

<@&286206848099549185>

[final saddle]

@unborn hill Has your question been resolved?

[unborn hill]

<@&286206848099549185>

[little coral]

@unborn hill what part do you not understand?

[unborn hill]

i get it now

it was the values they sub in for x

but i can pull any number

.close

[final saddle]

Channel closed

Closed by @unborn hill

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sly rover]

I have a question, I was watching a video tutorial on vector calculus. I was wondering how do you compute this. In what other do you multiply and combine like terms?

[sly rover]

This is a little bit beyond my calculus level (1-2) but I’m researching it to write a paper on how the math behind the formula for surface area of a 3D is obtained.

It looks like matrixes but if it is I forgot the order on which you multiply.

[lethal estuary]

look up the vector cross product

[sly rover]

I will, thank you for the information.

.close

[final saddle]

Channel closed

Closed by @sly rover

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slender tapir]

help

[slender tapir]

I found f(-1)

it is

$\sum_{n=2}^{\infty} \frac{(-1)^n}{n^3-n}$

[soft zealot]

MHuseyin

[slender tapir]

how to proceed

c.lose

.close

[final saddle]

Channel closed

Closed by @slender tapir

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[final saddle]

Channel closed

Closed due to the original message being deleted

[old coyote]

.close

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brave jewel]

Hello, I am not sure how to approach or answer this question. Any help is much appreciated

[final saddle]

@brave jewel Has your question been resolved?

[final saddle]

@brave jewel Has your question been resolved?

[final saddle]

@brave jewel Has your question been resolved?

[brave jewel]

.close

[final saddle]

Channel closed

Closed by @brave jewel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[real mango]

kinda more physics question

[tranquil pine]

the area under the graph is impulse

(change in momentum)

[real mango]

momentm = mass x velocity

do i take whole area under graph of just first half

[tranquil pine]

i'm guessing the entire area

[sturdy cypress]

just first half presumably

the ball is stopped, and then thrown backwards

[tranquil pine]

the ball is still in contact

[sturdy cypress]

yeah

[real mango]

yeah thanks guys

it is the whole area

get the area then divide by the mass

0.044kg

[tranquil pine]

you got it

[real mango]

thanks u lot

.close

[final saddle]

Channel closed

Closed by @real mango

Use .reopen if this was a mistake.

[sturdy cypress]

what

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[valid berry]

In the 2 alike 2 alike case why doesn't 4C1 x 3C1 work?

[gritty solar]

Generally speaking, you need to make the selection at once

You can list out the cases by hand if you wish, there aren't that many

[primal star]

but that wont work in the long run

[valid berry]

why is that though

isnt "I choose 1 out of 4 AND choose 1 out of the 3 remaning three" the same as "I choose 2 out of 4"

[gritty solar]

The thing is

You're inadvertently ordering the items when you make the selection like this

So selecting S first and A second, and A first and S second become two different cases

While in reality they're the same

Notice how you're getting exactly double the answer you're meant to

[valid berry]

AH I get it

Okkkk thx

.close

[final saddle]

Channel closed

Closed by @valid berry

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[buoyant linden]

<@&286206848099549185>

[final saddle]

Channel closed

Closed due to the original message being deleted

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[half forum]

I need help

[zenith sierra]

you need me?

srry gotta do that

[half forum]

yep haha

[zenith sierra]

haven't learned it tho, so ima just go back to my help channel

[half forum]

summon @rustic sequoia

https://tenor.com/view/kuchiyose-no-jutsu-summoning-gif-13501965

[iron perch]

what have you tried thus far?

[half forum]

lemme send

disregard the last line

idk I feel it is kinda wrong

[iron perch]

Ok, there's good stuff going on. I'm glad you sketched the region of integration, it will make it slightly easier to explain.

The problem is that the regular old change to polar coordinates (x=r cos(theta), y=r sin(theta)) is really good for problems with circular symmetry about the origin. We do have circular symmetry so polar is still the right move here, but because it's not symmetric about the origin r will change as a function of theta as we integrate. What this means is that the upper bound on your r integral is not correct (I think the theta bound is also problematic, should be pi instead of pi/2 but that's a smaller issue), I believe it should be 2sin(theta) and we can get into that if you like

[iron perch]

I think the factor of 2 out front is misplaced, but otherwise this should be headed in the right direction

[half forum]

IIgot it

ty

https://tenor.com/view/okay-ok-thumbs-up-got-it-gif-14071545

[iron perch]

np 👍

[half forum]

.close

[final saddle]

Channel closed

Closed by @half forum

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[astral hedge]

Where does this come from

[vocal forge]

<@&286206848099549185>

[magic sparrow]

Okay this isn't even your channel but

!15mins

[final saddle]

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.

[magic sparrow]

A differential equation is said to be homogeneous if every nonzero term of the linear ODE depends on the unknown function or some variable of it

Basically saying that, since you are solving for y as a function of "x" here, every term must involve a y, or a y', etc... or be zero, else it is inhomogeneous

The reasoning behind this is being able to set the equation equal to 0, with only containing terms of the unknown variable on the left hand side

this is kind of a normal use of homogeneous in math is if the equation is equal to 0

well, you could always make a diffeq equal to zero by subtracting all the terms to one side

so that wouldn't really be special, to call that the definition of a homogeneous ODE

it is more special if the left hand side only contains terms involving the unknown variable and its derivatives, and that is equal to 0

you will see this become especially useful as you go into higher order ODEs

[soft zealot]

AustinU

[magic sparrow]

it would be inhomogeneous

because the "x" is hanging out by itself

@astral hedge

[final saddle]

@astral hedge Has your question been resolved?

[astral hedge]

Yea but where does that rule above come from

[magic sparrow]

Which rule?

[astral hedge]

The image above i sent

[magic sparrow]

Did my explanation not suffice?

[astral hedge]

Well it just says how to determine if something is homogeneous

But where does that come from

[magic sparrow]

I'm a little confused. That is just the definition of what it means for a first-order ODE to be homogenous. I tried to explain the motivations behind such a definition in my response

could you be more clear what you are asking?

[astral hedge]

How is that a definition cuz homogeneous is when you can say like t^n f(x,y) = f(tx,yx)

[magic sparrow]

Where are you getting that from?

[astral hedge]

The definition of a homogeneous function

[magic sparrow]

This is saying that the ODE is a homogeneous ODE

and that is the definition of what that means

A homogeneous ODE is different than a homogeneous function

they use the same word, but they have different definitions and implications

[astral hedge]

So then what does homogeneous mean

[magic sparrow]

In different places it means different things and it depends on the context, I could give you a dictionary definition but I am sure that wouldn't be helpful

a lot of times, homogeneous means the equation can be set equal to 0

but that isn't very useful for ODEs

so a little more specificity is involved

[astral hedge]

So if this is a definition what does homogeneous mean because at this point it seems like it has no meaning

[magic sparrow]

A definition of homogeneous could be "consisting of parts all of the same kind." The reason that word is used here, is because every term in that differential equation involves a "y" or a "y' "

So the ODE is homogeneous because it consists of parts "y's" of the same kind

every term involves a y, or a y'

so we call it homogeneous

[astral hedge]

Yea for that definition i can see where homogeneous comes from but that one above just says you can express it as y/x

[magic sparrow]

if you can express it as y/x

that means every "x" can be connected to a "y"

think of it as y * 1/x

so that means every thing in the equation can be connected to a y

so it's homogeneous

[astral hedge]

mm

[magic sparrow]

anything I could do to help clarify?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[magic sparrow]

.reopen

[final saddle]

✅

[astral hedge]

what about the definition m dx = n dx is homogeneous if m and n are the same degree homogeneous

[magic sparrow]

Could you be more specific or send me a picture of the definition you are talking about please

[astral hedge]

$M(x,y) , dx = N(x,y) , dy$

[soft zealot]

4321

AustinU

[astral hedge]

Same degree homogeneous

[magic sparrow]

?

[astral hedge]

So is like a function being homogeneous unrelated to homogenous ode

[magic sparrow]

A function being homogeneous is completely unrelated to what a homogeneous ODE is

yes

other than that they use the same word to describe two different things

[astral hedge]

Ok

That makes sense now

Thanks

[magic sparrow]

you'll see that homogeneous equations are much more useful when the ODEs are higher order

like 2nd degree

[astral hedge]

I have been trying to connect them to each other

[magic sparrow]

no problem!

[astral hedge]

Wait how can this definition and the other one with m and n work because rewriting a function as f(y/x) means f(tx,ty) = f(x,y) but if m and n are not homogeneous degree 0 that doesnt apply

[magic sparrow]

you are mixing up the two definitions

What do you mean by, "if m and n are not homogeneous degree 0"

[astral hedge]

Well homogeneous degree 0 means $f(tx,ty)= t^0 f(x,y)= f(x,y)$

[soft zealot]

4321

[magic sparrow]

You are mixing up the two definitions

they are completely unrelated

you keep bringing up homogeneous functions

homogeneous functions have nothing to do with homogeneous ODE

[astral hedge]

No here homogeneous refers to a homogeneous function

The functions m and n

[magic sparrow]

if m and n are homogeneous "not degree 0" say they are degree 1

you can rewrite the ODE of the form dy/dx= F(y/x)

which fits the definition

same if they are degree 2, 3, 4, or degree 100000

[astral hedge]

But f(y/x) means f tx ty = f x y but if its degree 1 f tx ty would be t f(x,y)

[magic sparrow]

where "t" is a scalar constant

so you can write that as F(y/x) still

[astral hedge]

ic

[final saddle]

@astral hedge Has your question been resolved?

[robust sedge]

They can be degree zero too. A condition for the D.E. having homogenous coefficients of the same order is in dy/dx = F(y/x), F is homogenous of degree zero.

[magic sparrow]

I was just responding that because he made the distinction in his question

[robust sedge]

I may have repeated something already stated there’s a lot of text. 🙂

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[loud gust]

Can someone help me determine how to find a connected subset of R2?

[tired walrus]

just any connected subset of R^2?

or are there some requirements for it

[loud gust]

Yeah, any connected subset of R^2. Would {(0, y} in R^2 | y is in R} be connected?

I think it would.

[sinful folio]

indeed it would

[loud gust]

Right. Now, what if you considered {(x, y} | x <= 0, y < = 0}?

Would this be nonconnected?

@sinful folio

[sinful folio]

that would also be connected

[loud gust]

Is it because graphically, you can connect x <= 0 with y <= 0 since (0, 0) is in the set?

[sinful folio]

well if you pick any two random points in the set

i.e. (a,b) and (x,y) you can draw a straight line between them

an example of a nonconnected set would be something like

$\left{(x,y) \in \Bbb R^2 | y \neq 0\right}$

[soft zealot]

Shell

[sinful folio]

this set is the lower left quadrant

[sinful folio]

this set is the entire plane but with no x axis

so for instance, if you pick (0,-1) and (0,1) you wouldn't be able to connect them

[loud gust]

Oh, I see. So, that's how you think of it.

Because you would have to go through y = 0 right?

which technically "breaks the straight line"

[sinful folio]

yeah in that case you really cant draw a line without going outside of the set

for instance

$\Bbb R^2 \setminus { (0,0)}$ is connected

even though you cannot draw a straight line from (0,-1) to (0,1)

but you can draw a half circle

[soft zealot]

Shell

[loud gust]

Interesting because you're "going around" (0, 0)?

[sinful folio]

yeah

[loud gust]

Makes sense. Okay, thanks.

.closed

.close

[final saddle]

Channel closed

Closed by @loud gust

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hard mist]

Given $f = x+y^2-3xy+5y-1$ In what direction in the point p(1,1) does the function value change the most?

[soft zealot]

rainy

[hard mist]

I calculated the gradient, and got {-2,4}

But the answer is {1.-2} and I don't know why

[tranquil pine]

To find the direction in which the function $f(x,y)=x+y^2-3xy+5y-1$ changes the most at the point $p(1,1)$, we can use the gradient vector. The gradient vector points in the direction of the steepest increase in the function, and its magnitude gives the rate of change in that direction. Therefore, we need to find the gradient vector at point $p(1,1)$ and then determine its direction.

The gradient vector of $f$ is given by:

∇
�

(
∂
�
∂
�
∂
�
∂
�
)

(
1
−
3
�
2
�
−
3
�
+
5
)
∇f=(
∂x
∂f
​

∂y
∂f
​

​
)=(
1−3y
2y−3x+5
​
)
At point $p(1,1)$, the gradient vector is:

∇
�
(
1
,
1
)

(
1
−
3
(
1
)
2
(
1
)
−
3
(
1
)
+
5
)

(
−
2
4
)
∇f(1,1)=(
1−3(1)
2(1)−3(1)+5
​
)=(
−2
4
​
)
The magnitude of the gradient vector is:

∥
∇
�
(
1
,
1
)
∥

(
−
2
)
2
+
4
2

2
5
∥∇f(1,1)∥=
(−2)
2
+4
2

​
=2
5
​

Therefore, the direction in which the function changes the most at point $p(1,1)$ is the direction of the gradient vector $\nabla f(1,1)$, which is $\begin{pmatrix} -2 \ 4 \end{pmatrix}$.

We can also verify that the function changes the most in this direction by computing the directional derivative in the direction of the gradient vector:

�
∇
�
(
1
,
1
)
�
(
1
,
1
)

∇
�
(
1
,
1
)
⋅
∇
�
(
1
,
1
)
∥
∇
�
(
1
,
1
)
∥

(
−
2
4
)
⋅
1
2
5
(
−
2
4
)

4
5
D
∇f(1,1)
​
f(1,1)=∇f(1,1)⋅
∥∇f(1,1)∥
∇f(1,1)
​
😦
−2
4
​
)⋅
2
5
​

1
​
(
−2
4
​
)=4
5
​

This means that the function changes at a rate of $4\sqrt{5}$ in the direction of the gradient vector.

[soft zealot]

IronNugget

[hard mist]

bro what

[final saddle]

@hard mist Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[modest wigeon]

The sum of roots was asked; -2 was repeated twice but was only added once; why?

[urban coyote]

you do not take it twice, when you plug -2 it ensures the equation

so it is "a" root

we looked for roots on x for x>=3 or x<=-2 first

then we looked for x>=-2 or x <=3

so we looked for roots on x=-2 and x=3 twice

-2 is a root so we just found it twice

[modest wigeon]

Right; so we could've excluded -2 and 3 from the domain of one of the two cases to've avoided this redundancy right?

[urban coyote]

absolutely

you got it

we didnt have to look for x=-2 and x=3 on the second case

because we looked for it on the first case already

[modest wigeon]

Right. Thank you for your time and assistance.

[urban coyote]

you are welcome

[modest wigeon]

.close

[final saddle]

Channel closed

Closed by @modest wigeon

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[storm anchor]

how do i find the answer for number 2?

[sweet summit]

what have you tried so far?

[fickle crater]

either plugin values to each equation and try who fits

or you see how each y changes for each x change

[storm anchor]

is it 3 because 3 x 3 is nine and the rest is multiplied by three

[fickle crater]

there you go you noticed the trend each y follows for each x

[storm anchor]

OHHH

I UNDERSTAND THATS SUPER EASY, SORRY!

[fickle crater]

you're fine do .close if you are done

[storm anchor]

.close

[final saddle]

Channel closed

Closed by @storm anchor

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jovial stone]

help

[stable fossil]

mm yes

[jovial stone]

[hybrid heath]

[jovial stone]

I don't know WHY we have to do the steps

[hybrid heath]

Which steps?

[jovial stone]

this is the contest I'm referring to: https://www.cemc.uwaterloo.ca/contests/past_contests/1997/1997CayleyContest.pdf

these are the solutions: https://www.cemc.uwaterloo.ca/contests/past_contests/1997/1997CayleySolution.pdf

I'm stuck on number 21

and I can't understand the simplification part

[hybrid heath]

What does the spade mean

[jovial stone]

I have no idea, don't mind it

why did it become (ab+ac+bc)/bc?

wait i understand it now

.close

[final saddle]

Channel closed

Closed by @jovial stone

Use .reopen if this was a mistake.

[grim badger]

Another word for shovel

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cedar beacon]

can someone help me

[stable fossil]

on..........?

[cedar beacon]

wait 1 sec

sry

the question above

[lethal estuary]

what have you tried

[cedar beacon]

so i got this but i dunno what to do now liek where to start with this

[lethal estuary]

try separating the two terms of the LHS instead

[cedar beacon]

what lhs

[lethal estuary]

lefthand side of the equation

[cedar beacon]

like this?

[lethal estuary]

yes but don't write cot as 1/tan

and then get rid of those messy fractions

[cedar beacon]

did that but i still ahve no idea what to do

[lethal estuary]

then show me

[lethal estuary]

you can change cotangent to its fraction, and same w/ tangent, but don't leave it as a fraction in the numerator. combine w/ the denominator

[cedar beacon]

i dont get it

[lethal estuary]

how else can you write $\frac{\frac{a}{b}}{c}$?

[soft zealot]

cwatson

[cedar beacon]

so 1/sinxcosx/cot?

[lethal estuary]

you didn't answer my question...

[cedar beacon]

i tried to understand 😭 i dont get it or mabye im over thinking

i tried to answer

[lethal estuary]

you may want to review this if you're not understanding: https://www.khanacademy.org/math/arithmetic-home/negative-numbers/mult-divide-negatives/v/making-sense-of-hairy-fractions

[cedar beacon]

alr

.close

[final saddle]

Channel closed

Closed by @cedar beacon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gritty raptor]

Can someone help me on this question. Please and Thank you!

[celest crane]

What have you tried?

[gritty raptor]

yes

but I don't know where to start

so

what I know is

x on tuesday is x + 3

and also

the successive rings was one more point on monday

so

[celest crane]

So what would the value of the inner white ring be on Tuesday?

[gritty raptor]

X + 3

[celest crane]

The white ring.

[gritty raptor]

oh sorry

[gritty raptor]

2x - d?

[celest crane]

What is the value of the inner white ring on Monday?

[gritty raptor]

x - d

[celest crane]

And the value of the outer rings on Tuesday is one more than the respective rings on Monday.

[gritty raptor]

yes

[celest crane]

So what is the value of the inner white ring on Tuesday?

[gritty raptor]

(x - d) + 1?

[celest crane]

Correct.

[gritty raptor]

sorry be right back in a minute

[celest crane]

You are graphically presented with where the arrows landed on Monday and Tuesday. Given the abstract representation of the scores, you can make an equation from the given information.

[gritty raptor]

hmm

[celest crane]

On Monday, how many times did James score (x-d) points?

[gritty raptor]

2

[celest crane]

And (x-2d) points?

[gritty raptor]

(x - d) x 2?

[celest crane]

So what was James total score on Monday?

[gritty raptor]

Total score on (x - d)?

[celest crane]

You want to make an expression in terms of x and d.

2(x - d) + 2(x - 2d)

[gritty raptor]

ah

alright alright

[celest crane]

Now do the same for Tuesday using the adjusted scoring method.

[gritty raptor]

1(x - d) + 3(x - 2d)?

so

wait

[gritty raptor]

yes

so

1((x - d) + 1) + 3((x - 2d) + 1)?

[gritty raptor]

that was wrong mb

[celest crane]

Now the problem states that James had the same score on both days.

[gritty raptor]

yes

[celest crane]

Which means you can set the two expressions you found equal to each other.

[gritty raptor]

hmm

explain further?

[celest crane]

What was the expression for the score on Monday?

[gritty raptor]

its 2(x - d) + 2(x - 2d)

right?

[celest crane]

And for Tuesday, it was 1(x-d + 1) + 3(x - 2d +1).

[gritty raptor]

yes

but his total scores were the same on both days

[celest crane]

Now, we don't know what x and d are but it doesn't matter. The problem states the score was the same on both days.

[gritty raptor]

yes.

[celest crane]

So the expression you found for each day are equal.

[gritty raptor]

indeed

so how do I find out the value of d?

[celest crane]

Make an equation by setting the two expressions equal to each other and solve for d.

[gritty raptor]

so

The total of Monday is 2(x - d) + 2(x - 2d) = 4x - 3d

[celest crane]

4x - 6d

[gritty raptor]

what did I do wrong?

[celest crane]

2(x-d) + 2(x-2d) = 2x - 2d + 2x - 4d

[gritty raptor]

$2(x-d) + 2(x-2d) = 2x - 2d + 2x - 4d$

[soft zealot]

Techroz

[celest crane]

You wrote that it equalled 4x - 3d.

[gritty raptor]

so what did I do wrong?

like in the solving

[celest crane]

-2d - 4d = -6d

Not -3d

[gritty raptor]

hold on

[gritty raptor]

yeah thats the part where i'm wrong

i'm trying to correct myself

[gritty raptor]

yes

you are right

and tuesday is

[gritty raptor]

1(x-d + 1) + 3(x - 2d +1) = (x - d + 1) + (3x - 6d +1) = (4x - 7d + 2)?

[gritty raptor]

yeah

[gritty raptor]

hmm

$1(x-d + 1) + 3(x - 2d +1)$

[soft zealot]

Techroz

[celest crane]

You mathed incorrectly somewhere. The x terms should cancel out.

[gritty raptor]

yeah I probably did

[gritty raptor]

like there will be now x term in the answer

[celest crane]

It will cancel out.

[gritty raptor]

alright

I got it

then what is the next step?

[celest crane]

Did you solve for d?

[gritty raptor]

no

[celest crane]

Solve for d. That's what the question asked you to solve for.

[gritty raptor]

yeah

So we've already found out the total score for both Monday and Tuesday

how so?

[rich ferry]

find out

answer is b tho

[gritty raptor]

but how do I solve for d?

[rich ferry]

lol

[gritty raptor]

I'm not understanding sorry

[rich ferry]

bruh

[gritty raptor]

i'm stuck

[rich ferry]

4x cancels

[celest crane]

Be nice.

[rich ferry]

oops

[celest crane]

So you want to start by combining terms.

[gritty raptor]

4x - 7d + 4?

[celest crane]

ie. With the x terms, you want to get them on one side.

[gritty raptor]

so d is 4?

[celest crane]

Yes.

[gritty raptor]

(I'm not cheating) I took a look at the answer sheet to check and it tells us that its 5

[rich ferry]

Combine like terms on both sides of the equation:
4x - 6d = 4x - 7d + 4

Subtract 4x from both sides to isolate the variable term:
-6d = -7d + 4

Add 7d to both sides to isolate the variable d:
d = 4

Therefore, the solution for d is d = 4.

[celest crane]

So when combining terms from either side of an equation, what you do to one side must be done to the other side.

[gritty raptor]

alright

[celest crane]

Correct.

[gritty raptor]

thank you for helping

[celest crane]

yw

[gritty raptor]

i appreciate it

[rich ferry]

WELCOME

[gritty raptor]

enjoy the rest of your day guys

[rich ferry]

lol u 2

[gritty raptor]

chill bro thanks too

lol

.close

[final saddle]

Channel closed

Closed by @gritty raptor

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gritty raptor]

Can someone please help me with this question? These shapes have equal perimeters. A circle with the radius of 4cm and a Rectangle with a length of x + 2 cm and a Width of x cm. What of these answers is the value of x?
A π −1
B 2π −1
C 2π −4
D 4π −1

[gritty raptor]

thank you

[craggy plume]

can you tell me how far you've gotten

!status

[final saddle]

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

[gritty raptor]

step 2

[craggy plume]

where are you stuck?

[gritty raptor]

I have started finding the perimeter of the circle

which is 8pi

[craggy plume]

correct

[gritty raptor]

but what do I do next to find out the perimeter of the rectangle?

[craggy plume]

if i told you a rectangle has height 4 and width 10, what would the rectangle's perimeter be?

[gritty raptor]

here is the screenshot to make it easier to read

[gritty raptor]

28

[craggy plume]

yes

and you see what you did to do that

you did 2(length)+2(width)

[gritty raptor]

yes

indeed

[craggy plume]

so, now apply this to our rectangle

you have height x and width (x+2)

what is the perimeter, in terms of x?

[gritty raptor]

(2x + 2)?

no

[craggy plume]

can you show me your working?

[gritty raptor]

sorry

[craggy plume]

no worries

[gritty raptor]

(4x + 4)?

[craggy plume]

Yes

do you know how to solve the problem from here, now that you have the perimeter of both shapes?

[gritty raptor]

no

[craggy plume]

"these shapes have equal perimeters"

not a trick question, but what does this actually mean?

[gritty raptor]

so the rectangle and the circle both have a perimeter of 8pi

[craggy plume]

Yes

or, more algebraically, you can say

(perimeter of rectangle) = (perimeter of circle)

[gritty raptor]

yes indeed

[craggy plume]

and you have just previously figured out these