help-28

[glossy valve]

Chromium

[full thicket]

triangle 1 has area of $\frac{1}{2} bh$

[glossy valve]

Chromium

[full thicket]

so ratio of areas = $\frac{1}{2} bh : \frac{1}{2} bh k^2 = 1 : k^2$

[glossy valve]

Chromium

[torn jolt]

ok

ty

.close

[full forum]

Channel closed

Closed by @copper oasis

Use .reopen if this was a mistake.

[full forum]

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.

[torn jolt]

How do I solve this

[hollow spire]

Can you post the text associated with the problem as well?

[torn jolt]

"Find the value of x"

[hollow spire]

I dont know if there is enough information to solve the problem. I would say that you should assume the ratios between the line and its arc are linear and solve it that way.

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[full forum]

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.

[carmine arch]

A group of 25 individuals is to be involved in a small-scale clinical trial of a
promising new cancer drug. All individuals will be given pills to be taken regularly, but
they will be split into groups with some individuals receiving the actual drug and others a
placebo.

[carmine arch]

Instead of just one cancer drug, the scientists decide to test two different drugs.
If they want to choose 10 individuals to receive drug A, 8 individuals to receive drug B, and
7 individuals to be in the control group and get the placebo, how many different ways can
they accomplish this?

[full forum]

@carmine arch Has your question been resolved?

[carmine arch]

<@&286206848099549185>

[carmine arch]

<@&286206848099549185>

.close

[full forum]

Channel closed

Closed by @carmine arch

Use .reopen if this was a mistake.

[full forum]

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

[full forum]

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.

[molten mountain]

could someone double check my math?

[molten mountain]

Two bags have 4 white and 5 black balls. At random we take 2 balls from 1st bag to the second one.
What is the probability that we'll take 1 ball from the 2nd bag and it will be white?
Let's say we have pulled a white ball. What are the probability that in the second bag we put 1 white and 1 back ball?

so for the first question I got 120/1331

and for the second I got 5/18

are they correct?

[full forum]

@molten mountain Has your question been resolved?

[molten mountain]

<@&286206848099549185>

[molten mountain]

<@&286206848099549185>

[molten mountain]

<@&286206848099549185>

[molten mountain]

<@&286206848099549185>

<@&286206848099549185>

[molten mountain]

<@&286206848099549185>

.close

[full forum]

Channel closed

Closed by @molten mountain

Use .reopen if this was a mistake.

[full forum]

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

[full forum]

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.

[molten wadi]

Dose some one know how to find the length of AD when CB is 10 and CD is 8

I got stuck on a test

[full thicket]

ah

[full thicket]

is the test over?

[molten wadi]

Yes, 10 mins ago

[full thicket]

alright

ever heard of inverse pythagorean theorem?

[molten wadi]

You mean C^2 - a^2 = b^2

?

[full thicket]

no

look it up

[molten wadi]

Then I don't know

Ok

I see it now but I don't get how it'll find the solution

[fathom saddle]

Do you know any of the angles?

[molten wadi]

No

But on the test I did

[fathom saddle]

What does that mean?

[molten wadi]

I mean the test had a version of this problem, the triangle was in a rectangle and had angles but this only has the 90 degree symbols

[fathom saddle]

I'm going to say the presented problem doesn't have enough information. You can use pythag to get every side of the right triangle, but then you have no information about the left triangle, other than one side.

[molten wadi]

That's what I was stuck on

[fathom saddle]

Is it possible these triangles are similar?

[molten wadi]

They are

[mighty thorn]

BD=6 from pythagorean theorem, AB:BC=BC:CD as ABC and CBD are similar so AB*8=100->AB=25/2
AD=25/2-6=13/2

[fathom saddle]

Okay, well, going ahead with the assumption these are similar, then you can get the rest

[molten wadi]

So BD is 6, AB:10 =BC:8 but I don't get why AB * 8 = 100

[fathom saddle]

Maybe I'm missing something. How is it known that AB:BC = BC:CD?

[molten wadi]

I think it's because sides are proportional to each other

[fathom saddle]

That's what I'm asking. How do we know that?

[molten wadi]

Cause their
Similar

1/CD^2 = 1/AC^2 + 1/BC^2, using this formula would I be able to find AD if I solve for AC then use pythagorean theorem on CDA

<@&286206848099549185>

.close

[full forum]

Channel closed

Closed by @molten wadi

Use .reopen if this was a mistake.

[full forum]

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.

[hollow moat]

hey

[hollow moat]

is there some analytical way to think of this?

[full forum]

@hollow moat Has your question been resolved?

Channel closed

Closed by @hollow moat

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.

[sly path]

this the solution to the question if t grows 5 times then r grows with the same amount each time what is that amount

im struggling with how to understand In and how to differentiation

[hollow spire]

So it probably comes down to using something like $R(t)=a+bln(t), R(5t)=a+bln(5t)$ and expanding the ln in the second equation to get two values that you can compare

[glossy valve]

opfromthestart

[hollow spire]

Can you post the original problem as well?

[hollow spire]

Can you post the question associated with this as well, this is just another equation.

[sly path]

oh sorry yea the question is in dutch

[hollow spire]

Ah ok.

[sly path]

if t grows by 5 then r keeps growing with the same amount

what is that number

do you understand the question like that

[hollow spire]

So yeah, you would want to do something like $R(5t)-R(t)$ to find the amount that it grows when t grows by five, since you would be seeing what the growth is when t is pentupled.

[glossy valve]

opfromthestart

[sly path]

hmm could you show me how we get too 7.500

sorry if im being annyoing

[hollow spire]

If you plug in 5t to R, what do you get?

[sly path]

1.4999

[hollow spire]

your answer should still have a t in it. Dont just plug it into your calculator.

[sly path]

when i put 1.34+4.66*in(5)+4.66

[hollow spire]

You should still have the ln(t) in the answer

[sly path]

r(t)* 13.4999

[hollow spire]

Not quite. $R(5t)=1.34+4.66*ln(5t)$, so what would you do from here?

[glossy valve]

opfromthestart

[sly path]

split $Rln(5t)in to in(50 and in(t)$,

[glossy valve]

mr.bubzz

[sly path]

oh that doesnt really work so well never used this before

[hollow spire]

you should hav individual $$ around every expression, and not have any around text

So $1.34+4.66ln(5t)=1.34+4.66(ln(5)+ln(t))$, and then simplify this a bit.

[glossy valve]

opfromthestart

[sly path]

ooooooh

i finally see a misstake i made

i kept seeing 4.66 as number on its on and not with the in

aaah i just dont understand

i see now where we get the 7.5 from

4.66*in(5)

but i dont know what that says or how to use it

[full forum]

@sly path Has your question been resolved?

[hollow spire]

So you want to use what you get from R(5t) and subtract R(t), which cancels out the 1.34 and the 4.66ln(t)

[full forum]

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.

[torn jolt]

Find a 10 digit number that uses each of the digits 0 to 9 exactly once and where the number formed by the first n digits of the number is divisible by n. For example, the number made by the first digit is divisible by 1, the number made by the first two digits is divisible by 2, etc.

[torn jolt]

soo far i have We know that each number in an even position must be even. Let's denote each digit with a letter to make it easier to know which digit we are referring to: abcdefghi. From this we know that b is divisible by 2, cd is divisible by 4, abcdef is divisible by 2 and 3, and fgh is divisible by 8.

is there anything i am missing, that makes this question super easy?

[hollow spire]

Maybe working backwards would be better, I think you could probably figure out i from the last two extensions

Let abcdefg=$a_8$, and expand the last two algebraically, you can solve for i

[glossy valve]

opfromthestart

[hollow spire]

And you can probably do it workign backwards from there

[wise wyvern]

abcdefgh*

Right?

[hollow spire]

Yeah, too many letters

[wise wyvern]

We know the last digit is zero already.

[hollow spire]

No
Oh wait I thought there were 9 digits nvm

[wise wyvern]

That is the only way which ensures $a_{10}$ is divisible by 10.

[wise wyvern]

Alright alright.

[glossy valve]

Sakata Yaksha

[wise wyvern]

Fifth digit also must be 5.

[hollow spire]

Let the number be $d_1d_2d_3...d_{10}$, and let $a_n=d_1d_2...d_n$

[glossy valve]

opfromthestart

[wise wyvern]

$d_5=5$

[glossy valve]

Sakata Yaksha

[hollow spire]

$d_4+d_5+d_6$ must be divisible by 3

[glossy valve]

opfromthestart

[wise wyvern]

$d_6$ must be even

[hollow spire]

all of the triples ending in 3k must be divisible by 3

[glossy valve]

Sakata Yaksha

[wise wyvern]

Right.

[torn jolt]

woah

a lot of stuff

[torn jolt]

that is true!

[hollow spire]

What class is this for? it doesnt seem like a school problem

[torn jolt]

this is probably all i need

[torn jolt]

logic and proofs

[wise wyvern]

Odd and evens must come alternatively. That's something very basic but yeah.

Starting from odd.

[hollow spire]

Also, already siad in different form, $8|4d_6+2d_7+d_8$, $4|2d_3+d_4$, and $2|d_2$

[glossy valve]

opfromthestart

[hollow spire]

And, also just formally, $2|k \Leftrightarrow 2|d_k$

[glossy valve]

opfromthestart

[hollow spire]

Does the question require uniqueness or just existance?

[wise wyvern]

I believe anything works.

Even then, I believe it is having a unique answer.

[hollow spire]

Cause id think there could be probably 6-12 answers based on combinatorics

But maybe not

Generally, $a_k=10a_{k-1}+d_k=kn_k$, where $n_k$ is an integer

[glossy valve]

opfromthestart

[full forum]

@torn jolt Has your question been resolved?

[hollow spire]

So, I just wrote a program to find the number, and it is unique I think. 3816547290

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

Program lol

Which language

[hollow spire]

I mean, it works

Python

import itertools


def sat_tree(num, odd_digits, even_digits):
    if num == 0:
        for i in odd_digits:
            new_odd = [d for d in odd_digits if d != i]
            s = sat_tree(i, new_odd, even_digits)
            if s:
                return s
    d = len(str(num))
    #print(num, d)
    if num % d != 0:
        return None

    if len(odd_digits)==len(even_digits)==0:
        print(num)
    if len(str(num)) % 2 == 0:
        for i in odd_digits:
            new_odd = [d for d in odd_digits if d != i]
            s = sat_tree(10 * num + i, new_odd, even_digits)
            if s:
                return s
    else:
        for i in even_digits:
            new_even = [d for d in even_digits if d != i]
            s = sat_tree(10 * num + i, odd_digits, new_even)
            if s:
                return s


if __name__ == "__main__":
    print(sat_tree(0, [1, 3, 5, 7, 9], [2, 4, 6, 8, 0]))

It reduces the number of choices to (5!)^2 and then weeds out those which arent true, it runs faster than I expected

[gritty rose]

FYI
```python
<your_code>
```

[hollow spire]

oh yeah i forgot

[torn jolt]

how can i go on from this:

We know that each number in an even position must be even. Let's denote each digit with a letter to make it easier to know which digit we are referring to: abcdefghi.  From this we know that b is divisible by 2, cd is divisible by 4, abcdef is divisible by 2 and 3, and fgh is divisible by 8.  We also know that e has to be 5.

[hollow spire]

well, the number is wrong, it should be abcdefghij.

[torn jolt]

ah

still, what do i do next?

<@&286206848099549185>

anyone plsss

<@&286206848099549185>

[torn jolt]

i dont know what to dooo

[torn jolt]

there are 43 helpers

[hollow spire]

Its a hard question

[torn jolt]

im not disagreeing

but surely someone knows the answer and can give hints

.close

[full forum]

Channel closed

Closed by @slender hare

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.

[open isle]

how would i find the 21b i forogt

i go 21a

[hollow geode]

tend h to 0

[open isle]

huh

[hollow geode]

huh

[open isle]

?

[hollow geode]

?

[open isle]

why tend h to 0

[hollow geode]

Cause that's how you make AROCs into IROCs...?

[open isle]

whats aroc and iroc

[hollow geode]

average rate of change
instantaneous

[open isle]

oh

is plugging 0 into h in the formula ?

how would i put that in work tho

[hollow geode]

you'd... plug h=0 into the formula

and write that down...

[open isle]

wait what

for 21 a i used jus this f(final)-f(initial)/(final) - initial

[hollow geode]

yeah...

but yeah

you get $\frac{(10+h)^2+24(10+h)-10^2-24(10)}{h}$

[glossy valve]

Mosh

[hollow geode]

then you simplify that.

[open isle]

yes

i get h + 44

wait no

actually yes

its h + 44

[hollow geode]

ok

so... evaluate at h=0..

[open isle]

its 44

[hollow geode]

yes

[open isle]

!

so it doesnt matter what the value of t is???? we jus plug in h for 0

[hollow geode]

wdym t value?

the t value is 10

the IROC always happen when h=0 from the AROC

[open isle]

ok

so what would the ans be if 21b was t = 5?

[hollow geode]

well you'd have to redo a

[full forum]

@open isle Has your question been resolved?

Channel closed

Closed by @open isle

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.

[light sonnet]

You posted this like 10 times and people tried to help you. I'm pretty sure they gave sufficient hints to solve that

Do what exactly?

Because it's a piecewise function

You have to limit the function between certain domain

[full forum]

Channel closed

Closed by @dense pier

Use .reopen if this was a mistake.

[full forum]

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.

[drowsy lynx]

Need help with number 3

[velvet spoke]

@drowsy lynx Note that the outer and inner triangle are similar

[drowsy lynx]

Yea

[velvet spoke]

So they have the same angles

[drowsy lynx]

Ok

I drew them both separate

Alright uh what were you saying

[velvet spoke]

The inner triangle is just a scaled down version of the bigger, enclosing triangle. So if you can find the interior angles of the outer triangle, they're the same for the inner one

[drowsy lynx]

Oh ok

So uh how would I do that

[velvet spoke]

The angles sum up to 180 and you know two of them already, right?

[drowsy lynx]

Yea

[velvet spoke]

So can you calculate the last one using that?

[drowsy lynx]

Is it like 55 + 60 +x =180

[velvet spoke]

The angle at point C

yes

[drowsy lynx]

Ok

I got 65

@velvet spoke

[velvet spoke]

Yup

[drowsy lynx]

Oh that's the answer?

[velvet spoke]

Should be

[drowsy lynx]

Alright

Ty ty

.close

[full forum]

Channel closed

Closed by @drowsy lynx

Use .reopen if this was a mistake.

[full forum]

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.

[plush egret]

so how the heck

i mean ive tried expanding out (cos theta + i sin theta)^4

something tells me that is really wrong

whats the trick

something is telling me using some other obscure identity is probably not the method

should i pick some theta in general terms that makes sin theta go away?

[tulip marlin]

binomial expansion

[tulip marlin]

.

You equate imaginary parts together

real parts together

So the cos(n theta)

The thing that's relevat will be the real parts

[tulip marlin]

So you just pay attention to the real part this thing spits out

Thats whenever there is an even power of i(sin t)

[plush egret]

oh hmm

okay so i expand out

well lemme write

,w i^4

[glossy valve]

Results provided by WolframAlpha

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

Requested by jan Niku#2119

[plush egret]

that kinda day

okay so I'm getting out

\begin{align*}
\cos 4 \theta + i \sin \theta
&= (\cos \theta + i \sin \theta )^4 \
&= \cos ^4 \theta + 4 i \cos ^4 \theta \sin \theta - 6 \cos ^2 \theta \sin ^2 \theta - 4 i \cos \theta \sin ^3 \theta + 4 \sin ^4 \theta
\end{align*}

[glossy valve]

jan Niku

[tulip marlin]

yh.

[plush egret]

so whats the uhh

well

okay why is it okay to just chuck the entire imaginary part

[tulip marlin]

you dont just chuck it

The real part on the LHS has to equal the real part on the RHS

The imaginary part on the LHS has to equal the imaginary part on the RHS

a + bi = c + di

means a = c, b = d

So you are equating real parts.

[plush egret]

then uhh

11 cos ^4 theta - 14 cos ^2 theta + 4

[tulip marlin]

?????

where are 11 and - 14 coming from

[plush egret]

its wrong

well i pulled out the real part

[tulip marlin]

The next step is to equate the real parts of the equation together

[plush egret]

im gonna forego theta

the real part of the expansion

i have as cos^4 - 6 cos^2 sin^2 + 4sin^4

[tulip marlin]

ok, but i dont understand where the 14 and 11 come from

yes.

[plush egret]

i replace using pythagorean

[tulip marlin]

and this is equal to the left

[plush egret]

cos^4 - 6 cos^2 ( 1 - cos^2) + 4 ( 1 - cos^2 ) ^2

[tulip marlin]

no

yes

[plush egret]

we get

[tulip marlin]

yes

[plush egret]

1 + 6 + 4 cos^4 terms

-6 - 8 cos^2 terms

and a lone plus 4

but its wrong

[tulip marlin]

oh

Doesn't sound right to me yes........... let me have a look

[plush egret]

oh

sign error maybe

that should be

no its right

1 + 6 + 4

i think A = B has to be true

otherwise you get weird harmonics

[tulip marlin]

are u sure it is wrong

[plush egret]

yea

i mean it wont look like a cos(4 theta) if A != B

[tulip marlin]

$$\cos 4\theta = \cos^4\theta - 6\cos^2\theta(1-\cos^2\theta) + 4(1-\cos^2\theta)^2$$

[glossy valve]

Shuri2060

[plush egret]

youll get stuff like this

i think it should be 8, 8, and 1

[tulip marlin]

$$\cos 4\theta = \cos^4\theta - 6\cos^2\theta + 6\cos^4\theta + 4 - 8\cos^2\theta + 4\cos^4\theta$$

[glossy valve]

Shuri2060

[tulip marlin]

$$\cos 4\theta = 11\cos^4\theta - 14\cos^2\theta + 4$$

[glossy valve]

Shuri2060

[plush egret]

yea

its wrong

[tulip marlin]

im not convinced it is

[plush egret]

but were on the same page 😄

so thats good

[tulip marlin]

,w identity cos(4theta)

[plush egret]

well try graphing any Acos^4 + b cos ^2

with A!=b

and neither 0

[glossy valve]

Results provided by WolframAlpha

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

Requested by Shuri2060#9525

[plush egret]

yea

oh

same magnitude

not same number

8, -8, 1

it doesnt matter

theyre equivalent i think

you can eat the -1

wait no you cant

i typed it wrong

8, -8, 1 is the answer i have from just guessing

[tulip marlin]

checking desmos......

[plush egret]

and checking desmos, yea

maybe itd be easier to do cos(2(2theta))

im guess thats how you get to the first one

[tulip marlin]

Oh ok

I see 2 errors here

one doesn't matter (it's in the imaginary term), the other does.

[plush egret]

oh

where the heck that four come from

whats the other error

[tulip marlin]

powers

[plush egret]

huh? where

[tulip marlin]

2nd term

[plush egret]

oh, yea

thats a smol typo

theres another typo

i was hoping you wouldnt notice

in the very beginning

and you didnt

lemme see if its right now fixing that error

[tulip marlin]

yh ok lol

anyways yh

[plush egret]

thank you shuri

🙇‍♂️

its right

ur a genius

.close

[full forum]

Channel closed

Closed by @plush egret

Use .reopen if this was a mistake.

[full forum]

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.

[hollow geode]

What do you have entry wise if A is symmetric?

@torn jolt

[full forum]

@torn jolt Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[full forum]

Channel closed

Closed due to the original message being deleted

[urban ferry]

Can someone help me rq?

[weak coral]

Is the graphing correct?

[polar mica]

go ask in the help channels

[polar mica]

the one on the left looks a little thick, it wopuld look smth more like this

same with your right one actually

you can see the pdf is basically 0 at -2.58

BUT if your teacher isnt picky it should be fine ig

[full forum]

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.

[regal orchid]

Hi everyone i have to find the interval of x that fit the remainder’s value

can someone help me ?

I tried the taylor’s inequality but i got stuck here

[fading steeple]

so you have |error| <= some expression in the second line

[regal orchid]

Yes

[fading steeple]

what you need is |error| <= 0.01, for say, qn 27

[fading steeple]

the idea is to bound the right-hand side of the second line by the value that you need

that is to say

0.01 <= some expression doesn't guarantee |error| <= 0.01

[regal orchid]

How do i bind it

[fading steeple]

but some expression <= 0.01 guarantees it (why?)

[regal orchid]

Idk

[fading steeple]

if you have a < b and b < c, what can you say about a and c?

[regal orchid]

a<c

[fading steeple]

right!

so in this picture, a is your |error|, b is your big expression, and c is your 0.01

so if you have expression <= 0.01, it guarantees |error| <= 0.01

[regal orchid]

Like this ?

[fading steeple]

yes, something along those lines (i'm ignoring the third line)

[regal orchid]

What do i do with lambda?

Greek symbol*

[fading steeple]

what is lambda in this case?

[regal orchid]

it’s supposed to be a value between a and x

we usually take the value that will increase the max value of f^3

[fading steeple]

right, so you want to replace that whole numerator with M instead

where M is the maximum of the (n+1)th derivative on the interval

https://www.mathopenref.com/calclagrange.html

[regal orchid]

3=n+1

[fading steeple]

see the link i sent

sorry, but something cropped up and i have to go

[regal orchid]

Oh no :c

[fading steeple]

someone else will come by!

[regal orchid]

<@&286206848099549185>

My exam is tomorrow plzz help me

[full forum]

@regal orchid Has your question been resolved?

[full forum]

@regal orchid Has your question been resolved?

Channel closed

Closed by @regal orchid

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.

[pale quarry]

okay i know like the first 3 statements but from there on im at a lost

[pale quarry]

wouldnt the the 4th one be alt. interior angles thrm?

cause i got

the first two as given then third is def of parallelogram for reasons

<@&286206848099549185>

[full forum]

@pale quarry Has your question been resolved?

[pale quarry]

<@&286206848099549185>

[torn jolt]

Ok this is a parallelogram…so
Ang1= ang4
Ang2= ang3

Now can u find it

Oh wait what was ur question…?

[pale quarry]

what comes after line 3

would it be alternate interior angles theorem?

[torn jolt]

And then this…thru alt int angles

So hence they are equal

[pale quarry]

and then thats it? no more lines?

[torn jolt]

Idk, I’ve never done these type of questions…so…

Ig add…as 1 and 2 are equal, 3 and 4 will be equal too

I think that completes it

[pale quarry]

really? that proves that angle 3 is congruent to angle 4?

[torn jolt]

Yes obv…
If x=y and a=b and x=a
Obv y=b

Did u understand

[pale quarry]

yeaaaaa

i think

[torn jolt]

Be sure

Make it clear and go ahead

What is confusing

[pale quarry]

i feel like there should be one more property to say under reasons

but the problem my mind is so blank rn

is it reflexive?

[torn jolt]

There shld be 5?

[pale quarry]

it doesnt matter how many as long as it proves ∠3≅∠4 according to my teacher

[torn jolt]

Yes it does

Just make sure u understand how it proves…

And then submit it

[pale quarry]

i think i understand it now

thank you

.close

[full forum]

Channel closed

Closed by @pale quarry

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.

[wet robin]

if nul(A) is two dimensional but a subspace of r^5, does it mean its like a plane inside the subspace of r^5? Is that how I could understand it?

then why does my book say this? since null(A) has dimension n it has to be space R^2 no?

[full forum]

@wet robin Has your question been resolved?

[zenith kernel]

No it means in the end you managed to transform the origin system of linear equations into

The form Ix+Ay=0

For some matrix A and I is the identity matrix of order k where A has k pivot columns

x=(x_j1,x_j2,…,j_k)^T where the pivot columns of A is column j1,j2,…,jk

y=( other x s)^T is a column vector with ( N=(number of columns of A) - k) components

So whatever y you choose to be you can always let x=-Ay so that x+Ay=0

in other word, y is free, you can make it be any N column vector, that’s why the dimension of NulA=N

In this case N=5-3=2

[full forum]

@wet robin Has your question been resolved?

Channel closed

Closed by @wet robin

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.

[full forum]

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.

[torn jolt]

hi! i’m doing a practice test to prepare for my upcoming tests, and i’m not sure if the calculations i’ve done for this question are correct. i struggled a lot doing this and i’m not confident that i’ve done this correctly

[full forum]

@torn jolt Has your question been resolved?

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

<@&286206848099549185>

[full forum]

@torn jolt Has your question been resolved?

[terse meadow]

So for a trapezium, do you know the area formula $A = h \frac{a+b}{2}$ ?

[glossy valve]

Mango

[terse meadow]

You did get the longer side length right, but it would be more helpful if you used that function

[torn jolt]

oh, right!

i see what you mean

is that all i need to fix?

[terse meadow]

You'll start from there, then call the length of the newly drawn blue line y. Given two variables, you can now set up two different equations

I'll try labeling them, a sec

[terse meadow]

Would you be able to figure out your two equations from there?

[torn jolt]

uhh, i’m not really sure which equations to use

i’m a bit lost

[terse meadow]

This one

Because the blue line devides the area into half, you now have two new trapeziums that have the same area, 6m^2

As in upper half area formula should give you 6, as well as the lower should

[torn jolt]

ohhh!!

yeah okay that makes sense

i understand what i need to do now

thank you so much!!

[terse meadow]

If you get stuck with this one again, feel free to ask me

[torn jolt]

i’m busy working on the next question and i’ll come back to this one after that, so i’ll let you know!

for the upper half, which quantities do i substitute into the formula?

i have 6=x (5+?)/2

idk what to put in the ?

[terse meadow]

Just have y as a placeholder for now, you'll be able to substitute later

[terse meadow]

Also could you elaborate on why 5 is there?

[torn jolt]

i looked at the trapezium wrong :/

i have no idea which values to use now lmao, i’m trying to calculate the upper trapezium

[terse meadow]

Could you give me a, b and h for each trapezium?

[torn jolt]

T1
a= 1
b= 5
h= 4

T2
a=y
b=5
h=4-x

[terse meadow]

T1's h seems off

[torn jolt]

ohhh wait

i see it now

LMAO

i struggled picturing it in my head

T1’s h is x

[terse meadow]

Yup

Now would these two equations make sense?

[torn jolt]

yes!!

but how do i find y’s value?

i can calculate for x but idk y

[terse meadow]

Oh after solving those two equations, you'll get something like y = something and then you can substitute that back into one of the two equations we have to solve for x

[torn jolt]

alright

solving for y gives me

y=12-x/x

[terse meadow]

Hm

Could you show me your work?

Oh wait

Did you derive that solely from equation 1?

[torn jolt]

yes

[terse meadow]

So you got x+xy = 12 right, then try equation 2 and see if they add up to cancel anything

I wouldn't divide anything just yet

[torn jolt]

equation 2 gives me x=4y+8/y+5, is that correct?

solving for y gives me y=8-5x/-4+x

[terse meadow]

So before trying to solve for anything, what did you get for equation 2? Could you show me your work?

[terse meadow]

This does look right, it's just that it's not in the form I was looking for

[terse meadow]

Nvm, where did that 8 come from?

Also from step 3 to 4, 12 suddenly seems to be missing

So $12 = (4-x)(5+y)$ right?

[glossy valve]

Mango

[torn jolt]

i didn’t write all the steps down (i do it in my head), but if i use foil and multiply 4 by 5, i got 20, then subtracted 12 to isolate x on the left, which gave me 8

[terse meadow]

Gotcha, cause number was right but then both 12 and 8 sitting there kinda confused me

[torn jolt]

sorryyy, i should have thought about that lmao

[glossy valve]

Mango

Mango

Mango

[terse meadow]

I'd say you can solve for y from there

[torn jolt]

y=x+1

please let that be right LMAO

[terse meadow]

Yep, plug that right back into the equation we derived from 1, x+xy = 1

[terse meadow]

You are correct lol

[torn jolt]

okay so if i plug that into the equations now

then X is 2.61 (rounded up)

[terse meadow]

Oh does the question say you can round em up?

[torn jolt]

that’s just the standard here

only with your answer though

[terse meadow]

Or do you need to use square roots, oo ok

I was gonna say, good ol' quad formula but sure that works too

[torn jolt]

it says on the front page to leave only 2 decimal places unless asked to do otherwise

[terse meadow]

Gotcha. So yes you're right, after getting $x^2 + 2x - 12 = 0$, using quad formula yields us $x = -1 \pm \sqrt{13}$ but since x is a length it cannot be negative hence $x = -1 + \sqrt{13} \approx 2.61$

[glossy valve]

Mango

[torn jolt]

thank you so much for helping me, that was a lot harder than i thought it would be

[terse meadow]

And from there you can get y value

Yeah it's quite a trouble to go through lol but no problem

[torn jolt]

.close

[full forum]

Channel closed

Closed by @tender marsh

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.

[arctic iron]

why do we do that last line i dont get it

[hollow herald]

._.

which line exactly did you not understand?

[arctic iron]

the last one

as in

why do u find the sqrt of the squares of the sums

[hollow herald]

Because

https://youtu.be/krPI0NTlT8w

[arctic iron]

thanks : )))

.close

[full forum]

Channel closed

Closed by @arctic iron

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.

[clear marlin]

I have solved (a) (i) and (ii)

But not sure how to solve b, since it’s like the combination of an arithmetic series and geometric series

[tender rain]

Do you know limits?

[median trellis]

can someone help me?

[tender rain]

#❓how-to-get-help

[clear marlin]

I know the concept, but not sure how to apply it

The idea of limits was briefly mentioned in the lessons

My only use of limits has been providing the formula for a perpetual geometric series where abs(r)<1

[tender rain]

Alrighty. So first you need to derive the formula in b

Which is basically putting the task's description into an equation

[clear marlin]

Sorry for late reply, I went away for something

I’m working on it now

I think it would be something like those

But need to convert it

Wait no that’s not correct

So essentially for every year, the term from previous year is times 0.9 and 350 is added

[tender rain]

Looks correct, after some manipulation you should get the expression in the task

[clear marlin]

Thanks, I’m trying that now

Got it

Do you know if the first statement is correct? I am not sure if the notation would be acceptable

[tender rain]

just a note: 4000 - 3500 is 500, not -500

[clear marlin]

Oh right, thanks for pointing it out, careless mistake

[tender rain]

I personally would just write .. x 0.9, so you can see what operation is performed with the .9

Alrighty, now the interesting part

[clear marlin]

Understood

[tender rain]

in (c), we need to investigate how this expression behaves as N grows

[clear marlin]

(c) is pretty, simple, just not sure how to prove it

[tender rain]

Oh pretty simple

What do we use to investigate the behavior of a function as the argument goes to infinity?

[tender rain]

And there is your proof.

[clear marlin]

That’s it?

So we can just take the first limit as common knowledge

[tender rain]

You could, or you can prove it.

For example with the definition of the limit

But that would be overkill imo

[clear marlin]

True, just gotta see how many marks a question is worth later on

[tender rain]

It's pretty obvious that $\lim_{x\to+\infty} \alpha^x = 0$ if $\alpha < 1$

[glossy valve]

Remavas

[clear marlin]

Ok, thanks

.close

[full forum]

Channel closed

Closed by @clear marlin

Use .reopen if this was a mistake.

[full forum]

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.

[humble carbon]

As tanx=sinx/cosx, is it possible that I write tan^2x=sin^2x/cos^2x or tan^3=sin^3x/cos^3x?

[humble carbon]

and respectively with all other power number?

[vast fossil]

Yes

(a/b)^n = a^n/b^n

[humble carbon]

ok thanks that's all

.close

[full forum]

Channel closed

Closed by @humble carbon

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.

[arctic iron]

many questions

[arctic iron]

where does 2^n-1 come frmo

why do we divide $11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 3$ by $12$

[glossy valve]

Reinhard von Lohenngram

[arctic iron]

and where does the $ e^x = ...$ come from?

[inland mesa]

You mean the .... ?

[arctic iron]

$e^x = 1 + {x \over 1!}+{x^2 \over 2!}+ \ldots$

[glossy valve]

Reinhard von Lohenngram

[inland mesa]

This is the maclaurin series of e^x

[torn jolt]

maclaurin

never heard of it

its just the taylor series

approximation

@arctic iron

u know taylor series approximation

$f(x) = f(0) + f'(0) x + \frac{f''(0) x^2}{2!} + \frac{f'''(0) x^3}{3!}+...$

[glossy valve]

CatHashira

[arctic iron]

Idk what that is actually

[torn jolt]

well

ig u have to learn it

[arctic iron]

Seems like it

[inland mesa]

Maclaurin series is just the Taylor series when the a=0 in (x-a)^n

[torn jolt]

oh

so the taylor series approx at 0

*around 0

[torn jolt]

this is the taylor series thing @arctic iron

if u apply it to e^x

u will have it

[arctic iron]

I see

[torn jolt]

but u need to look up and understand the basics of taylor series to get where that comes from

[arctic iron]

okok thank u

[torn jolt]

https://www.youtube.com/watch?v=3d6DsjIBzJ4

u can see this awesome video if ur familiar with higher order derivatives

[inland mesa]

3blue1brown, classic

[full forum]

@arctic iron Has your question been resolved?

[arctic iron]

<@&286206848099549185>

[full forum]

@arctic iron Has your question been resolved?

[full forum]

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.

[spice heart]

can any1 help with this?

.open

[full forum]

@spice heart Has your question been resolved?

[full forum]

@spice heart Has your question been resolved?

[full forum]

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.

[wind zephyr]

How would I solve this problem?

[eager violet]

First, you need to remove that 2

How would you solve, say, 10^x = 1?

[wind zephyr]

make x 0?

cuz anything to the power of 0 = 1

[vast fossil]

Use logs?

[eager violet]

What about 10^x = 5? You can't use inspection anymore

[wind zephyr]

yea so i have to use logs

how would I do that

[vast fossil]

Just say that 3x = log_2(11)

[wind zephyr]

why?

[eager violet]

If you have a^b = c, then b = log_a(c)

To get rid of the 2, you have to take the log base 2

[wind zephyr]

so log_2(3x) = log(2(11)

[eager violet]

Why did 2^(3x) become just 3x?

[vast fossil]

That would imply that 3x = 11

[eager violet]

If you were gonna remove the 2, there's no reason to keep the log. √(x²) isn't √x

[wind zephyr]

im confused

[eager violet]

You should have log_2(2^3x) = log_2(11)

For some reason, you just had log_2(3x), foregoing the 2

[wind zephyr]

Ohh

Ok so log_2(2^3x) = log(2(11)?

[eager violet]

If you mean log_2(11) by log(2(11), then yes

[wind zephyr]

Ye

so what would I do after that

cancel out the logs?

im not sure

[eager violet]

Let's say you were solving x² = 4. Your first step is to take the square root: √(x²) = √4. Then what?

[wind zephyr]

then u know x = 2 and x = -2

[eager violet]

But algebraically, you'd cancel out the inverses, right? √(x²) becomes just x, right?

[wind zephyr]

Yea

[eager violet]

Well, 2^x and log_2(x) are inverse too. log_2(2^x) = x

[wind zephyr]

So I cancel out the log_2 and the 2?

[eager violet]

Yes

[wind zephyr]

so 3x = log_2^11

[eager violet]

*log_2(11), not log_2^11

[wind zephyr]

Ye

Then divide both sides by 3

so x = log_2(11)/3

[eager violet]

Yep

[wind zephyr]

Ok thank you!

.close

[full forum]

Channel closed

Closed by @wind zephyr

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.

[hoary ridge]

sum i=1 ^ n 3i=198 Find the value of n

[dawn torrent]

do you know how the sum looks like?

maybe write down the first few terms

[hoary ridge]

Okay

[dawn torrent]

i dont know what you mean by that

[dawn torrent]

try doing that

[hoary ridge]

Do you mean like this?

[dawn torrent]

yeah thats correct but let me give you a hint

$1\cdot 3+2\cdot 3+3\cdot 3+4\cdot 3+...$

[glossy valve]

Enoo58

[dawn torrent]

can you simplify this?

[hoary ridge]

Wdym by simplify?

[dawn torrent]

maybe factoring something out

[hoary ridge]

Is this correct?

[dawn torrent]

no

but i think you got the right idea

[hoary ridge]

I’m confused where did I go wrong?

[dawn torrent]

did you have $3\cdot \sum_i^n i=198$?

[glossy valve]

Enoo58

[hoary ridge]

That was the problem

[dawn torrent]

yes

[dawn torrent]

but if you look at that

you can see that you can factor out 3

so you get $3\cdot \sum_i^n i=198$

[glossy valve]

Enoo58

[hoary ridge]

Ok thanks

.close

[full forum]

Channel closed

Closed by @hoary ridge

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

[hearty ice]

Can someone explain why we only subtract 10T from x component?

Why not y component

Wind can blow vertically cant it?

[thin flint]

yes but here what they mean is 10 ft/sec horizontally

they don't really specify

[tender rain]

Sometimes

But here you assume it doesn't

[hearty ice]

Why do we just assume it is horizontal?

[tender rain]

Because most of the time, approximately, the wind is blowing horizontally

And that is what people usually mean

We measure wind direction on a plane

not a sphere

for that reason

[thin flint]

it's simpler

is basically why

[hearty ice]

Hm really? So wind rarely blows diagonally as well then?

[thin flint]

it's easier to work with and still teaches the same things

wind is super complex in the real world

barely ever constant

[full forum]

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.

[ashen elk]

you're asking for the circumference of an arc with a radius of 4 and an angle of 40 degrees, right?

alright, let's try the formula!

$\frac{40}{360} \times 2 \pi \times r$

[glossy valve]

ALIAS

[ashen elk]

in this case, r is 4

so...

$\frac{40}{360} \times 2 \pi \times 4$

[glossy valve]

ALIAS

[ashen elk]

at this point, you can put this in your calculator

is your arc's angle 320 degrees?

nope

you have to work out how much your angle is first

is it 320 degrees or 40 degrees?

alright, then put it in your calculator like this

[full forum]

@torn jolt Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[lapis robin]

Hi, I'm stuck on how to setup the following problem: find the volume if the region enclosing y = x^2, y=0, x=2 is rotated around the x-axis. I just learned about washers and discs so I'm assuming it probably relates to that in some way?

[fossil stump]

Yup - you’re right in your suspicion

Start by drawing the region

[lapis robin]

Ye, I was able to do that

I'm just confused because of the parabola bc all the problems I did before only had straight lines

[fossil stump]

^^

Maybe graphing it helps

[lapis robin]

I did, I just don't know how to find the expression for the radius of each circle

[velvet spoke]

if you draw it, you'll see that the lines x=2 and y=0 simply set the bounds of your integral and the other function determines the rest

[lapis robin]

so the radius would just be x^2?

[velvet spoke]

indeed

[lapis robin]

oh

Thanks :P

.close

[full forum]

Channel closed

Closed by @lapis robin

Use .reopen if this was a mistake.

[full forum]

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.

[mighty arch]

Hello, I just had an Analysis lecture that I found really confusing.

the question is as follows

"is there any set of numbers $S\subset \mathbb{R}^2$ , which edge is the entire $\mathbb{R}^2$"

and apparently $\left{(x,y)\in\mathbb{R}^2 \bigg| x,y\in\mathbb{Z}\right}=\mathbb{Z}^2$ satisfies this requirement, but that doesnt make any sense to me

[glossy valve]

Luca

[full forum]

@mighty arch Has your question been resolved?

[full forum]

@mighty arch Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

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.

[torn jolt]

We call S(n) the sum of the whole digits of n. For example, S(102) = 1 + 0 + 2 = 3. Find the value of A = S(1) + S(2) + S(3) + ⋯ + S(2014)

[zenith kernel]

Take sum in terms of digits I think.like how many of them are of the form (10^(k+1))a+(10^k)b+c where a , b,c are integer, c is smaller than 10^k, then you add how many b

For example 42, 347, 1045,… how many of them are of the form 100a+40+b then you add how many 4

Range over all k, and b

[torn jolt]

still confused a little bit

[zenith kernel]

Then. You get your result

[torn jolt]

wdym by form of 100a + 40 + b

[zenith kernel]

For any k, and b , if there are N(b,k) numbers x from 1 to 2014 such that there exists a and c such that x=(10^(k+1)a+(10^k)b+c then you have N(b,k)b

The answer is ΣN(b,k)b I think

[torn jolt]

I don’t have the correct answer to it so I can’t really say it’s that

[zenith kernel]

This is just one example, when k=2, b=4

I didn’t say it’s the final result, I haven’t calculated it

[torn jolt]

oh I got it damn

[zenith kernel]

Great

[torn jolt]

ty

[zenith kernel]

And I think N(b,k) is not hard to calculate

N(4,2)=30 for example

Oh you only need to calculate 20 of them

[torn jolt]

i thought of something, see if I can do this

[zenith kernel]

N(b,1) b from 1 to 9, N(b,0) b from 1 to 9, N(b,3) b=1 or 2

[torn jolt]

I want the sum of S(1) + S(2) + till + S(2014)

I think I made a critical mistake

could you calcule and see if its any of these answers?

[zenith kernel]

Sure

Wait 10 minutes

[torn jolt]

I think it's actually multiplied by S(2014)

if its one of these, I think it may be letter D

but lets see what you get

[zenith kernel]

Something must be wrong in my approach, I got way bigger result…

I need to check what I got wrong

[torn jolt]

I actually think the question made a mistake

[zenith kernel]

(I got 20110 btw… must be wrong)

[torn jolt]

so look at the way I did

let me tell you

lets consider the sum of S(1) + S(2) + S(3) + S(4) + S(5) + S(6) + S(7) + S(8) + S(90

this is equal to 45

which we can do it by using the formula to sum the y1 to n

Sum of 1 to 9 = 9(1 + 9) / 2

as well, equals to 45

and if we do the same with 1 to 2014

[zenith kernel]

What no

You can’t

[torn jolt]

really?

[zenith kernel]

2014 is greater than 10

You assumed S(n)=n which isn’t the case at all

[torn jolt]

but see, if I can do the same with 1 to 2014 = 2.029.105

2 + 0 + 2 + 9 + 1 + 0 + 5

= 19

ooh

yeah I can't do that

[zenith kernel]

What are you doing . You are calculating Σs(n) not s(Σn)

I still got 20110…

[torn jolt]

like I said, you're probably correct

the question is mostly likely wrong

[zenith kernel]

Okay I show my steps you can check whether it makes sense

[torn jolt]

alright

[zenith kernel]

The answer is Σb(N(b,k) where when k=0 or 1, b is from 1 to 9, when k=3 b=1 or 2

N(b,0)=202 so first I got 202(1+…+9)=9090

N(1,1)=205, N(b,1)=200 when b>1 so next I got 205+200(2+…+9)=9005

N(1,3)=1000 , N(2,3)=15 so finally I got 1030

[torn jolt]

yes

[zenith kernel]

So add them up I got 19125

Sorry 19125 not 20110

Way greater than any option

[torn jolt]

yes

that's what it's weird for me

[zenith kernel]

It makes sense? N(b,k) is actually how many numbers from 1 to 2014 whose k th digit is b

[torn jolt]

I don't know if that point there means to be multiplied or just a mistake

yeah

but apparently either way we dont get near to the answer

[zenith kernel]

Anyway my final answer is 19125, if I eventually can’t find any mistake in my steps

[torn jolt]

no worries

I'll have to ask a teacher later

I don't think you're wrong

.close

[full forum]

Channel closed

Closed by @misty aspen

Use .reopen if this was a mistake.

[full forum]

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.

[plush eagle]

can someone help with complex numbers and polynomials? it's regarding the fundamental theorem of algebra

[hollow geode]

dont ask to ask.

[fleet zodiac]

post problem and someone will help

[plush eagle]

i dont understand how to factor the zeros with imaginary numbers