help-26

[topaz sinew]

Please don't occupy multiple help channels.

[molten vine]

!status

[topaz sinew]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[verbal bison]

1

[topaz sinew]

@verbal bison Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[verbal bison]

.reopen

[topaz sinew]

✅

[novel echo]

do those arrows mean approaching from the left/right?

haven’t seen that notation before

[gray storm]

Its my first time seeing these types of symbols

[topaz sinew]

@verbal bison Has your question been resolved?

[topaz sinew]

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.

[hollow mountain]

hello i need help wtih this question

[hollow mountain]

i dont know how to find the function of f and function of g

[vale furnace]

There's no g here.

[hollow mountain]

oh..

[pastel oracle]

and you're given f

[topaz sinew]

@hollow mountain Has your question been resolved?

Channel closed

Closed by @hollow mountain

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.

[cinder owl]

howo did they get the matrix of 1's in a)

[pastel oracle]

by multiplying v by its transpose

[cinder owl]

ohh lol bruh that. was a bad mistke

ty

.close

[topaz sinew]

Channel closed

Closed by @cinder owl

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.

[inner drum]

In words, what are the steps involved in changing 0.2 1/6 to a percent?

[verbal bison]

yes it means left/right

[sinful pumice]

What is that number

0.21/6?

[inner drum]

Problem Number 25

[neon iron]

First, convert the fraction 1/6 to a decimal. Divide 1 by 6 to get 0.1667 (rounded to four decimal places).

Second, add the decimal part to the whole number. 0.2 + 0.1667 = 0.3667.

Lastly, multiply the decimal by 100 to convert it to a percentage.

Then you have the answer!

[inner drum]

This was exactly what I needed. THANK YOU

You guys are frikkin wizzards!

but my book is saying the answer is 21 2/3

[pastel oracle]

that's terrible notation

[neon iron]

You said in percent

Why 21 2/3?

[inner drum]

% right. my fault. it says the answer is 21 2/3%

[pastel oracle]

it must mean 0.216666666, converted to percent is 21.66666 --> 21 2/3

[neon iron]

36.67%

Huh?

Seriously?

[pastel oracle]

assuming the book answer is correct, it must be

[inner drum]

Where did the 0.2166... come from?

[pastel oracle]

1/6 in decimal form is 0.166666, so that stupid notation must indicate that it is not 0.2 + 0.16666, but 0.21666666

[neon iron]

Yes

[pastel oracle]

either look earlier in the book to see if they define that notation, or ask your teacher

[neon iron]

So it's book error

[inner drum]

I've searched the whole book and I dont have a teacher, Im trying to catch up on basic math stuff before I start college.

But I'm not crazy right?

This is wonky?

[pastel oracle]

yes. i've never seen it written like that before

i'd move on

if I were you

[inner drum]

Thank You!

Frikkin baffled over here.

Angels you people are.

.close

[topaz sinew]

Channel closed

Closed by @inner drum

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.

[silk comet]

I always end up somewhere where nor x nor y are solved

[vale furnace]

!show

[topaz sinew]

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

[silk comet]

the picture is not here?

[vale furnace]

I only see the question.

[silk comet]

oh, I will try to upload it again

and now?

[vale furnace]

It's still just the question?

Can you show what you've tried?

[silk comet]

If I express log(x) from the first equation, I get 6^2 = √54

Do I think correctly?

[vale furnace]

no

[silk comet]

why?

[vale furnace]

clearly, 6^2 isnt sqrt(54)

[silk comet]

I know

[vale furnace]

How did you get to 6^2?

,,\expolaws

[thorny flame]

Pure

[silk comet]

because I did: logx = 2 - logy

then I used in in second equation

[vale furnace]

[2^{2-\log y}\cd3^{\log y} = \s {54}]

[thorny flame]

Pure

[vale furnace]

Like this?

[silk comet]

so it looked like: 2^(2-logy)*3^(logy)=√54

yes

exactly

and (-logy)+logy is zero

right?

[vale furnace]

You can't do that

[silk comet]

I need to log all the equation?

[vale furnace]

,,\loglaws

[thorny flame]

Pure

[vale furnace]

This is wrong. You have to take log of the whole product, and what's happening on he LHS?

[silk comet]

but the ypsilons aren't supposed to be shortened. Where is the mistake, please?

I´m not sure if I can multiply the logarithms on second line by their exponents (I know I can do it, but if it is correct here)

<@&286206848099549185>

I'm totally clueless

<@&286206848099549185> guys, please I need your help

.close

[topaz sinew]

Channel closed

Closed by @silk comet

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.

[drifting briar]

I think i can help you

okay in order to find the time we need to use the standard energy approach

$E_{kin}=E_{L}+E_{F}$

[thorny flame]

Jill ♡

[drifting briar]

oh then you just have to find the normal force and solve from there

yea

and you have to multiply it by the friction coefficient as well

$R=m\cdot g\cdot\cos\left(\theta\right)\cdotmu$

[thorny flame]

Jill ♡
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[drifting briar]

then you need this formula

do you know the formula for kinetic energy?

oh yea i got it i think

[drifting briar]

basically we want to make use of this formula

and that we know E=F*d

also you probably know that v=d/t

wait

okay let me explain

we know that the kinetic energy is equal to the energy lost by carrying the particle up that slope

so we can use this approach

$E_{K}=E_{R}$

[thorny flame]

Jill ♡

[drifting briar]

now we just have to substitute our formulas

$\frac{1}{2}mu^{2}=g\cdot m\cdot d\cdot\cos\left(\theta\right)\cdot\left(1-mu\right)$

and you can solve for d

and by using the law of velocity, you can solve for t

also (mu) means μ here because it wouldnt let me use the letter here

@muted fjord

[thorny flame]

Jill ♡

[drifting briar]

yw

[topaz sinew]

@muted fjord Has your question been resolved?

Channel closed

Closed by @muted fjord

Use .reopen if this was a mistake.

[topaz sinew]

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.

[strange quartz]

hey

[strange quartz]

how does it go from this step to the next?

[acoustic pecan]

$$\frac{ax(x-2)}{x-2}+\frac{(2a+b)x+c}{x-2}$$
$$ax+\frac{(2a+b)x-2(2a+b)+2(2a+b)+c}{x-2}$$
$$ax+\frac{(2a+b)(x-2)+2(2a+b)+c}{x-2}$$

[thorny flame]

AℤØ

[strange quartz]

where is 2(2a+b) coming from

second step

[acoustic pecan]

well, i added (2(2a+b)-2(2a+b)) which is 0

so nothing changed

[strange quartz]

but why though

what’s the thought process behind adding that

[strange quartz]

why not just leave it as it is

[acoustic pecan]

whats this question actually answering

[topaz sinew]

@strange quartz Has your question been resolved?

[topaz sinew]

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.

[undone dragon]

completely lost

[topaz sinew]

@undone dragon Has your question been resolved?

Channel closed

Closed by @undone dragon

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.

[neon iron]

asked to give an exact answer

I am unsure what to do

[pseudo bear]

First, use the double angle formula.

[neon iron]

cool, 1/cos2x

$\theta$

$\tan \theta + \frac{1}{\cos 2\theta}=1$

[pseudo bear]

Well, theta on the bottom.

[thorny flame]

mj

[neon iron]

$\frac{\sin \theta}{\cos \theta}+ \frac{1}{\cos 2\theta}=1$

[thorny flame]

mj

[pseudo bear]

You can't do that.

[neon iron]

why not

[pseudo bear]

You need the denominators to be the same to add the tops like that.

[neon iron]

they are

[pseudo bear]

cos(theta) is not cos(2 theta).

[neon iron]

I skipped a few steps butessentially yes

[pseudo bear]

You need to cross multiply.

It should be sin(theta) cos(2 theta) + cos(theta) on top.

[thorny flame]

mj

Chai T. Rex

[pseudo bear]

This is getting too complicated, though.

[neon iron]

mhm

we could factor

a cos

from top and bottom

but we'd have to simplify the double angle

so not sure if we could do that

[pseudo bear]

[\frac{\sin(\theta)}{\cos(\theta)} + \frac1{\cos(2\theta)} = 1]
[\frac{\sin(\theta)}{\cos(\theta)} + \frac1{\cos^2(\theta) - \sin^2(\theta)} = 1]

[thorny flame]

Chai T. Rex

[neon iron]

we're going back steps?

oh I see

you went back a step

and you changed cos2theta

into it's identity

cos2theta-sin2theta

^

hm, but what can we do from here

re cross multiply?

$\frac{\sin(\theta)\cdot (\cos^2(\theta) - \sin^2(\theta))+\cos(\theta)}{\cos(\theta)(\cos^2(\theta) - \sin^2(\theta))} = 1$

what could we weven do with this though

we could move the denom to the otehr side

but we can't solve for theta

yet

[pseudo bear]

The cross multiplication was done incorrectly.

[neon iron]

without eliminating sins or cos

[pseudo bear]

But, instead, try to get rid of the denominators.

[neon iron]

what was it supposed to be?

[thorny flame]

mj

[pseudo bear]

[\frac{\sin(\theta)}{\cos(\theta)} + \frac1{\cos(2\theta)} = 1]
[\frac{\sin(\theta)}{\cos(\theta)} + \frac1{\cos^2(\theta) - \sin^2(\theta)} = 1]
[\sin(\theta) + \frac{\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \cos(\theta)]

[thorny flame]

Chai T. Rex

[neon iron]

wait whaaatt

[pseudo bear]

You multiply everything by cos(theta).

[neon iron]

okay

ah this math is the annoying kind

(the kind I don't understand)

[pseudo bear]

[\sin(\theta)(\cos^2(\theta) - \sin^2(\theta)) + \cos(\theta) = \cos(\theta)(\cos^2(\theta) - \sin^2(\theta))]

[thorny flame]

Chai T. Rex

[neon iron]

okay fair enough

[pseudo bear]

Well, you can make it a bit easier.

Do substitution where s = sin(theta) and c = cos(theta).

[s(c^2 - s^2) + c = c(c^2 - s^2)]

[neon iron]

should've done that from the start then

[thorny flame]

Chai T. Rex

[neon iron]

there's too many things here lol

[pseudo bear]

Now you expand everything.

First, we did the double angle stuff.

Then we got rid of the denominators.

Now we get rid of the parentheses.

[sc^2 - s^3 + c = c^3 - s^2c]

[thorny flame]

Chai T. Rex

[neon iron]

okay

hm

you could probably factor c

wait nvm

that would lead you to the previous step

[pseudo bear]

Now, you want to get s^2 + c^2.

To use the Pythagorean identity.

[neon iron]

pythagorean identity?

[pseudo bear]

Yes, s^2 + c^2 = 1.

[neon iron]

oh you mean

1

ok

ahh how owuld we

get about to doing that

[pseudo bear]

Get all the things with an odd s power to one side and all the things with an odd c power to the other side:[sc^2 - s^3 = c^3 - s^2c - c]
[s(c^2 - s^2) = c(c^2 - s^2 - 1)]

[thorny flame]

Chai T. Rex

[pseudo bear]

Then, you can factor out one from the odd powers.

Now, c^2 - 1 = -(1 - c^2) = -s^2.

Actually, no, that's too complicated.

Let's go back.

[sc^2 - s^3 + c = c^3 - s^2c]

[thorny flame]

Chai T. Rex

[pseudo bear]

Get it all in terms of one variable.

Let's change c to s.

[neon iron]

this question gave me a headache

and I'm not even solving it rn

[pseudo bear]

s(1 - s^2) - s^3 + sqrt(1 - s^2) = (1 - s^2) sqrt(1 - s^2) - s^2 sqrt(1 - s^2).

[neon iron]

$s(1 - s^2) - s^3 + \sqrt{(1 - s^2)} = (1 - s^2) \sqrt{(1 - s^2)} - s^2 \sqrt{(1 - s^2)}.$

[pseudo bear]

You need \sqrt{inside}.

With the curly braces.

[thorny flame]

mj

[pseudo bear]

[s(1 - s^2) - s^3 + \sqrt{1 - s^2} = (1 - s^2) \sqrt{1 - s^2} - s^2 \sqrt{1 - s^2}]

[thorny flame]

Chai T. Rex

[pseudo bear]

Now, move the square roots to one side.

[neon iron]

this has to be the hardest way possible to solve it

no shot it should take this long

[pseudo bear]

Well, Wolfram Alpha is saying you should use the Weierstrass substitution, which looks pretty complex.

[neon iron]

dude what 😭

[pastel salmon]

i do not want to disturb but:

$\frac{\sin\theta}{\cos\theta}+\frac{1}{\cos2\theta}=1\Leftrightarrow \sin\theta\cdot \cos2\theta+\cos\theta=\cos\theta\cdot \cos2\theta\Leftrightarrow\\sin\theta\cdot \cos\theta\cdot \cos2\theta=\cos^{2}\theta\left( \cos2\theta-1 \right)=-2\sin^{2}\theta\cdot \cos^{2}\theta\Leftrightarrow \\frac{1}{2}\sin2\theta\cdot \cos2\theta=-\frac{1}{2}\sin^{2}2\theta\Leftrightarrow \\sin2\theta\left( \sin2\theta+\cos2\theta \right)=0$

[neon iron]

wait a minute

that makes life a bit easier

[thorny flame]

Joanna Angel

[neon iron]

so answers would be sin2 theta = 0

[pseudo bear]

It looks like that gives the correct solutions.

Well, you use the zero product property.

[neon iron]

yeah, so sintheta=0

costheta=0

[pseudo bear]

Either sin(2 theta) = 0 or sin(2 theta) + cos(2 theta) = 0.

[neon iron]

hm

2sinxcosx=0

sin^2x-cos^2x=0

[pseudo bear]

No, don't do it that way.

sin(2 theta) = 0 can be solved by figuring out when sine gives zero. Divide those angles by 2 to get theta.

[neon iron]

sine gives 0 at 2pi, pi, and 0

[pseudo bear]

sin(2 theta) = -cos(2 theta) can be solved by figuring out when sine is negative cosine, then dividing those angles by 2.

[pastel salmon]

$\sin2\theta=0\Leftrightarrow 2\theta=k\pi\Leftrightarrow \theta=\frac{k\pi}{2}$

[thorny flame]

Joanna Angel

[neon iron]

oh the answer has to be

from 0<=x<=theta

[pseudo bear]

Hmm, that's not included in the list of solutions Wolfram Alpha gives.

[neon iron]

so 2pi is excluded

pi, and 0

[pastel salmon]

and

$\cos\theta\neq 0\text{ }\wedge \text{ }\cos2\theta\neq 0$

[thorny flame]

Joanna Angel

[pseudo bear]

Yeah, the tangent would be undefined if cosine is zero.

Same with the secant.

[pastel salmon]

taking into account the reservations, we obtain that, if it comes to the first factor:

$x=k\pi$

[thorny flame]

Joanna Angel

[pastel salmon]

next, it should be considered the second factor

$\sin2\theta+\cos2\theta=0\Leftrightarrow \sin2\theta+\sin\left( \frac{\pi}{2}-2\theta \right)=0\Leftrightarrow \\2\sin\frac{\frac{\pi}{2}}{2}\cos\frac{4\theta-\frac{\pi}{2}}{2}=0\Leftrightarrow \\\cos\left( 2\theta -\frac{\pi}{4}\right)=0\Leftrightarrow 2\theta-\frac{\pi}{4}=\frac{\pi}{2}+k\pi$

[thorny flame]

Joanna Angel

[pastel salmon]

etc

Anyway, I agree, it was a tricky equation.

[topaz sinew]

@neon iron Has your question been resolved?

Channel closed

Closed by @neat cosmos

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.

[amber ibex]

how would i approach this

[pastel salmon]

you have compute the limit:

$\lim_{x \to 5} f\left( x \right)=_{\cdots }$

[thorny flame]

Joanna Angel

[pastel salmon]

and then conclude about continuity or discontinuity

[amber ibex]

its 0/0 tho

do i use l'hopitals?

[pastel salmon]

no, it is too simplle for such method

[amber ibex]

how would i approach this then

[pastel salmon]

you should use such formula to reach the limit:

$\frac{a-b}{c}=\frac{a^{2}-b^{2}}{c\left( a+b \right)}$

[thorny flame]

Joanna Angel

[amber ibex]

.close thank you

[topaz sinew]

Channel closed

Closed by @amber ibex

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.

[south phoenix]

im stuck with the 2/3

is it 2/3e^ln(10)?

[pastel salmon]

hint:

$g\left( 2 \right)=\frac{2}{3}\ln10$

[thorny flame]

Joanna Angel

[south phoenix]

yes

do i set equal to 0?

[pastel salmon]

no

why ?

you do not have any equation there

next you must compute: f(g(2)) = ...

means:

[south phoenix]

oh bruh

[pastel salmon]

$f\left( \frac{2}{3}\ln10 \right)=_{\cdots }$

[thorny flame]

Joanna Angel

[pastel salmon]

try it

[south phoenix]

i have 10e^2(ln(10))

to

10e^ln(10)^2

[pastel salmon]

yes

so 10e^ln100 = ?

[south phoenix]

oh no

i forgot it doesnt stay squared

[pastel salmon]

finally you have to use this:

$pe^{blna}=p\cdot a^{b}$

[thorny flame]

Joanna Angel

[south phoenix]

10e^3(2/3 ln(10))

= 10e^2ln(10)

= 10e^ln(10^2)

10*10^2

= 1000

.close

[topaz sinew]

Channel closed

Closed by @south phoenix

Use .reopen if this was a mistake.

[south phoenix]

this is just setting the denominator equal to 0 right?

so v.a at x=-3

[topaz sinew]

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.

[ivory tulip]

Hi, I need to graph a trig function with already given points. In particular, I am stuck on making sure my asymptote doesnt cross the x intercept, as well as continue infinitely if that is possible. I have to do this for 2 graphs, here they are. I also need to identify the amplitude, period, phase shift, and vertical translation. For the first graph, the function I have so far is y= 0.3973cos(pi/08)(X).
https://www.desmos.com/calculator/uuklva52zw
https://www.desmos.com/calculator/g3dqjkrtpz

[ivory tulip]

I already have the amplitude on the first graph as the highest point, but the amplitude also goes to the inverse of the y value. How can I prevent this? As well as is there something else missing from my function?

[topaz sinew]

@ivory tulip Has your question been resolved?

[ivory tulip]

<@&286206848099549185>

[topaz sinew]

@ivory tulip Has your question been resolved?

[topaz sinew]

@ivory tulip Has your question been resolved?

Channel closed

Closed by @ivory tulip

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.

[umbral ruin]

i need help solving this

[hard crown]

what have you done

[topaz sinew]

@umbral ruin Has your question been resolved?

[topaz sinew]

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.

[fresh lance]

Can I get help with this problem

[acoustic pecan]

sure

what are your thoughts

[fresh lance]

I am a little rusty on this section

but from what I remember

I have to calculate the areas with triangles and cirles

*circles

[acoustic pecan]

i wouldnt say you have to actually calculate the areas, you can judge by eye really

just keep in mind that the sections below the x-axis have negative values

[fresh lance]

Ohh yeah

signed areas

ok for sure o to 8

largest i assume

[acoustic pecan]

im not sure i agree with that

[fresh lance]

hmm

oh

0 to 4

[acoustic pecan]

indeed

[fresh lance]

ok I kinda understand

5 to 8 smalles

smallest

[acoustic pecan]

yup

[fresh lance]

ok I think I got the order

[acoustic pecan]

what did you end up with

[fresh lance]

B,C,A,D

I couldn't assume what was larger than B or smaller

I mean not B

0 to 8

[acoustic pecan]

id say thats correct

[fresh lance]

So I just did all the other values around it

Yessir it's correct

Thank you very much

Could I get your help on this one as well

.close

[topaz sinew]

Channel closed

Closed by @fresh lance

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.

[drowsy drum]

I need help with these 2 practice problems, they focus on sin cos tan

[drowsy drum]

Pre-calculus

[stable relic]

For the second one, do you by definition what sine and cos are?

[drowsy drum]

Not entirely, I know that sin is y, and cos is x

[flat kindle]

that's when the triangle is in unit circle

sin = opoosite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

[drowsy drum]

Oh yeah I know that part

And tan is also x/y

[flat kindle]

substitute the values in

can you identify which sides are opposite, adjacent and hypotenuse

[drowsy drum]

13 is opposite, 14 is hypotenuse, and square root of 27 is adjacent

[flat kindle]

yep

[drowsy drum]

Im not sure how to get sin cos and tan from the sides

[flat kindle]

for example sin(theta)=opposite/hypotenuse

plug in opposite=13 and hypotenuse=sqrt(27)

so sin(theta)=13/sqrt(27)

[drowsy drum]

I thought 14 was hypotenuse

[flat kindle]

oops my bad

13/14

[drowsy drum]

Ah ok

Well I got #5 answered then

Are you able to help with #4?

[flat kindle]

yes

draw a right triangle

since tan(theta)=4/3 we can let opposite=4 and adjacent=3

[drowsy drum]

Oh ok yeah that makes sense

Does it matter where I put the angle in the right triangle?

Figured it out myself, channel is free

[topaz sinew]

@drowsy drum Has your question been resolved?

Channel closed

Closed by @drowsy drum

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.

[fallen crescent]

could someone help? it says: Define a function 𝑓( 𝑥 ) = sin 𝑥 + cos 𝑥
maximum and minimum value inbetween

[drifting swift]

this is not enough by itself

you'll get that cos(x)+sin(x) lies between -2 and 2 but neither of those values can actually be achieved

the actual min and max values are closer together than that

@fallen crescent still here?

[fallen crescent]

ooh sorry lmao

i dont know though answer says sqrt of -2

and -1

like max and lowest

[drifting swift]

sqrt(-2)?

???

[fallen crescent]

yeah

[drifting swift]

that's only half correct

also that's sqrt(2), not sqrt(-2)

the minimum value is actually -sqrt(2)

which is NOT the same thing as sqrt(-2) at all

what the hell is up with your homework system? why does it give you wrong answers?

[topaz sinew]

@fallen crescent Has your question been resolved?

[fallen crescent]

I mean it was created by real authors

not a machine so I assume they want the most basic answer

[drifting swift]

the most basic != wrong

[fallen crescent]

also yeah mb no idea where I got the -

[drifting swift]

the answer is objectively wrong, the min value isn't -1

[fallen crescent]

T_T

why do you come to that conclusion

[drifting swift]

f(3pi/4) = -sqrt(2)

which is lower than the claimed minimum -1

[topaz sinew]

@fallen crescent Has your question been resolved?

[topaz sinew]

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.

[coral kraken]

claim

[coral kraken]

can someone explain this as like if theres any easier way to think of it as or shortcuts

<@&286206848099549185>

[topaz sinew]

@coral kraken Has your question been resolved?

[marble gate]

what..specifically about it

like, an easier way to plot these sorts of graphs?

if it's linear (i.e. it doesn't have x^2 or x^10 or whatever) then you can do it with just two points but the idea is the same

doing it for 5 values is a bit much but it's just to make sure you get the concept

[coral kraken]

oh alr

[marble gate]

and also I imagine if they only asked you to do it for 2 values, many people would do x=0, x=1, and then freehand draw the line for x=2+

by making you plot more x values, it means you have to draw a straight line

[coral kraken]

so i do it for those and then place them then what after that

[marble gate]

you...draw a line through the points

[coral kraken]

and then after that what

[marble gate]

you're done. congrats

you've graphed the function

lol

[coral kraken]

oh fr?

so what would i do for #2

just graph them draw line then im done

?

[marble gate]

so pick some values for n

like n=1, n=3, n=4. doesn't matter what. nice easy numbers

work out what f(1), f(3), f(4) are and plot those points

then draw the line through them

et voila, a graph of f(n)

[coral kraken]

okay

and then i do the math and put the answer where it says x

[marble gate]

yeah

you pick the n, and then the f(n) you calculate

[coral kraken]

okay

thanks ima try this out

[topaz sinew]

@coral kraken Has your question been resolved?

Channel closed

Closed by @coral kraken

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.

[fast plover]

Maybe a bit stupid but the gain in the first inv opamp is -1 right?

So how would I calculate the voltage input at the second amp, which is the important one

[topaz sinew]

@fast plover Has your question been resolved?

[fast plover]

<@&286206848099549185> Anyone that can give me a lead? I tried myself but I could not solve this atm

[topaz sinew]

@fast plover Has your question been resolved?

[topaz sinew]

@fast plover Has your question been resolved?

[valid marsh]

Can you send your working?

[topaz sinew]

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.

[coral fog]

Please how is (d) and (f) the same

I'm not really good using polar coordinates

[restive inlet]

converting polar to cartesian
(r,t) → (r * cos(t), r * sin(t))

oh. its actually simpler than that here

[valid marsh]

going around the origin 7π/3 radians is the same as going around it π/3 radians

[restive inlet]

^

[valid marsh]

because 2π radians is a full τurn

[coral fog]

[coral fog]

I'm getting there

[coral fog]

so if I split it I get 2pi + pi/3

2pi+pi/3 = pi/3?

[valid marsh]

they are not equal

it’s just that doing both of them results in the same point

[topaz sinew]

@coral fog Has your question been resolved?

[topaz sinew]

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.

[waxen field]

can i get help on this please

[marble gate]

!status

[topaz sinew]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[waxen field]

3/4

[marble gate]

alright, it seems like the Q is "draw and label a venn diagram and then use that to give a set theory description of the wanted part"

[waxen field]

yeah

[topaz sinew]

@waxen field Has your question been resolved?

[waxen field]

no

[topaz sinew]

Channel closed

Closed by @waxen field

Use .reopen if this was a mistake.

[waxen field]

.reopen

[topaz sinew]

✅

[marble gate]

so...where are you stuck?

what have you tried?

[waxen field]

i have an answer its the the set notation part that makes me not sure if my answers are correct

[marble gate]

alright

so..?

[waxen field]

you want to see ?

[marble gate]

I mean, do you want help?

It's very hard to help if you go "I have a problem" and then don't elaborate lmao

[waxen field]

fair point

well number 1)∣N∩W∩¬B∣=270−113=157

the notation looks terrible i apologise

2. it states 558 in the question so i thought that was more actually ptoving it

proving it

558=B+N+W−2×(B∩N)−2×(B∩W)−2×(N∩W)+3×(B∩N∩W).

[marble gate]

well for 2), that includes e.g. B n N

but it wants the hills which are only in 1 set

so it's going to be less than 558

[waxen field]

ah yes

damn

i didnt see the key word

[marble gate]

I'm also not too sure what notation it wants you to use

[waxen field]

set theory

[marble gate]

like if it's asking you to describe what the set of hills is as a union/intersection/difference, or if it's asking for you to use {x | x \in A, x \not in B} etc notation, or if it wants \exists x s.t. x \in A and x \notin B

[waxen field]

like intersections and unions

i think the second is the most acceptable

thats all the info i got which is in the question

[marble gate]

because for 1, it could be:
the set of hills: (N n W) / B
whether there is a hill: \exists x \in (N n W) / B or (N n W) / B \neq \empty

though you could also avoid using set difference if you wanted: (N n W n B^c) but using a complement feels weirder

I think it wants the second one for 1), but that only makes sense if it has introduced existentials (\forall and \exists)

[topaz sinew]

@waxen field Has your question been resolved?

Channel closed

Closed by @waxen field

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.

[mellow talon]

What does X equal

[mellow talon]

Soo im on page in math… and it say to what do X equal.. sound easy right.. wrong because it has no value………..

[topaz sinew]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[mellow talon]

(8 + 8) - X = 12 it’s impossible…

[vale furnace]

why is it impossible?

[neon iron]

What?

[willow stump]

bro is yapping lmao

-x = -4

x = 4

[topaz sinew]

@mellow talon Has your question been resolved?

[topaz sinew]

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.

[topaz sinew]

Please don't occupy multiple help channels.

[paper urchin]

Is this correct?

[topaz sinew]

@paper urchin Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[fallow dagger]

lim((e^(2x)-c)/x); x tends to -0

[fallow dagger]

this is not the full problem

can t figure it out how to continue

is it -infinite?

[thorny flame]

jan Niku

[fallow dagger]

this is it except the minus is in front of 0 i guess

[vernal vale]

no value for c?\

[fallow dagger]

no, c is 1 when x0=0 here x0<0

[vernal vale]

what? so c is a function of x?

[fallow dagger]

so there a s system function with parameters and i have to find when the function is a derivate, i have found the left and right limit and now i am trying to find the left derivate

the function is f(x)=e^(2x) when x<0

and f(x)=ax^2+bx+c when x>=0

[vernal vale]

okay, so what were really looking at is a and b not mattering here because you are taking the limit near 0

but the value of this limit will depend on c

can you place any conditions on it?

[fallow dagger]

no, i dont think so

[vernal vale]

okay, then you have to split it into cases

[fallow dagger]

well

isn t it -infinite or +infinite

[vernal vale]

well no

i think c=1 makes it exist

[fallow dagger]

and when i calculate the right derivate i get b and i don t think b can be equal to infinite

[vernal vale]

you can use lh there

[fallow dagger]

lh?

[vernal vale]

lhopital

basically you have e^(2x) - 1 which goes to 1 as x->0

[fallow dagger]

we didn t pass it yet though

[vernal vale]

so even though the 1/x is driving it to infinity

well, negative infinity

the exponential goes to 0 fast enough to make the limit finite

but i think for any other c this ... explodes? right

[fallow dagger]

mann, i am confused asf

aight

[vernal vale]

lol

sorry

[fallow dagger]

i think i am going to ask my teacher tmr

[vernal vale]

i think the limit doesnt exist

[fallow dagger]

thx for helping

[vernal vale]

except for c=1

,w Limit[(Exp(2x) - c)/x, x->0, Assumptions -> x<0]

[thorny flame]

Results provided by WolframAlpha

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

Requested by janniku

[fallow dagger]

exp is e right?

[vernal vale]

yea

theres some command to let it check around c

[fallow dagger]

i think i messed it up when calculating the limit

wait a few sec

[vernal vale]

,w Limit[(Exp(2x) - c)/x, x->0, Direction -> -1]

[thorny flame]

Results provided by WolframAlpha

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

Requested by janniku

[vernal vale]

oh, well

i guess thats helpful

what a weird way to report that result

[fallow dagger]

welp, f(x0)=c=1, cus the function is continue, does it mean that i can write c as 1 here?

[vernal vale]

idk i dont understand your whole f(x) thing tbh

[fallow dagger]

should i write it again? sorry can t take a pic

wait i am going to use a whiteboard

[vernal vale]

i get the limit i just dont understand what you are talking about with the function

[fallow dagger]

i have to find the parameters when the function is a derivate in x0=0

[vernal vale]

$\lim _{x \to x_0} \qty( \frac{e^{2x} - f(x_0) }{ x })$

like this?

[thorny flame]

jan Niku

[fallow dagger]

yes

[vernal vale]

can you share the original text here? is it in another language? its not clear what this means

[fallow dagger]

it is in romanian

[vernal vale]

[fallow dagger]

wait

Find the values of real variables a,b,c so the function is a derivate in the point x0=0

does this help

this the function

[vernal vale]

oh, wait, am i just being dumb

can we just solve the derivative directly?

[fallow dagger]

can we?

[vernal vale]

wait

okay so clearly b=0 right

[fallow dagger]

dont u need to calculate the left and right limits and f(x0)

[fallow dagger]

why

[vernal vale]

well were gonna need the right hand limit to be 0

thats along the polynomial

so itll need to be a min or a max there

[fallow dagger]

this is what i got when calculating limits

s is left

d is right

[vernal vale]

https://www.desmos.com/calculator/a8dzrtfxvw

i think we actually need uhh

[vernal vale]

i dont think using limits here so directly is gona help

instead you need to make x=0 a critical point of functions

this is equivalent to making the left and right hand limits 0 of both functions

but thats fine, this gives us the right hand of the polynomial and the lefthand of the exponential, right?

im not sure this is possible

because its not possible to make the derivative of e^2x 0 anywhere but at infinity

if we could set it e^0 then itd be okay

[fallow dagger]

isn t it e^0?

[vernal vale]

@fallow dagger are you sure the problem isnt "make the function differentiable at 0?

[vernal vale]

i mean, everywhere

if you make the exponential a constant, say, M, you can use a=whatever and b=0 and c=M

and it will have a 0 derivative at 0

but otherwise this isnt possible

unless the problem is "make the function differentiable at x=0"

[fallow dagger]

differentiable?, idek if i translated it corect, derivate means f'(x) right?

[vernal vale]

differentiable would be like, make it so f doesnt have a sharp corner at x=0

so we can take the derivative f'(0) and it exists and is finite

[fallow dagger]

no, we didn t learn that yet

[vernal vale]

the problem as I'm understanding youve said it so far is impossible

[vernal vale]

there is no way to make this have a 0 derivative at 0

but you can make it have a derivative there

it just wont be 0

[fallow dagger]

yes

u have to make it a derivate

in point = 0

that s what i meant

[vernal vale]

alright

so i dont think using limits is totally necessary here, at least this directly

[fallow dagger]

i mean u have to find a,b,c so the function is a derivate in point x0=0

[vernal vale]

what I would do is try to make $$\dv x e^{2x} = \dv x (ax^2+bx+c)$$

[thorny flame]

jan Niku

[vernal vale]

can you take the derivative of these functions?

[fallow dagger]

sorry but what s d and dx

[vernal vale]

its a derivative

[fallow dagger]

so (d/dx)e^2x is f'(e^2x)?

[vernal vale]

it just means take the derivative with respect to x

[fallow dagger]

aha

[vernal vale]

can you take derivatives?

[fallow dagger]

yeah, that should not be complicated

thank u for your time

[vernal vale]

nono its not so bad

[fallow dagger]

should not*

[vernal vale]

,w D[Exp(2x),x]

[thorny flame]

Results provided by WolframAlpha

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

Requested by janniku

[fallow dagger]

yeah i misstyped

[vernal vale]

,w D[a x^2 + b x + c, x]

[thorny flame]

Results provided by WolframAlpha

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

Requested by janniku

[vernal vale]

so $$2e^{2x} = 2ax+b$$ at $x=0$

[thorny flame]

jan Niku

[fallow dagger]

so then i put instead of x, 0

and then i have b=2?

[vernal vale]

yea

[fallow dagger]

how do i find a and c tho

[vernal vale]

well, the functions have to meet, too

so you have $$e^{2x} = ax^2+bx +c$$ at $x=0$

[thorny flame]

jan Niku

[fallow dagger]

aha

and c=1

and then finding a should be easy

[vernal vale]

its actually impossible

[fallow dagger]

how

[vernal vale]

you have no additional information

[fallow dagger]

isn t it an exponential equation

oh

[vernal vale]

well what you know is this

the derivatives match at x=0

and the functions match at x=0

thats enough to determine 2 constants

and to make the function differentiable there

so, it's undetermined.

but its fine, you just have infinitely many solutions

actually, any a will work

[fallow dagger]

aight

[vernal vale]

https://www.desmos.com/calculator/k0kunrpivg

[fallow dagger]

aha

thank you

[vernal vale]

[fallow dagger]

much love

.close

[topaz sinew]

Channel closed

Closed by @fallow dagger

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.

[upper monolith]

hi

[upper monolith]

im doing trig functions but im trying to understand where numbers are coming from

in the minimum, why is pi/2?

and 3pi/2 for the maximum

these numbers seem random to me

[topaz sinew]

@upper monolith Has your question been resolved?

Channel closed

Closed by @upper monolith

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.

[turbid dawn]

One person rolls a die until 1 comes out, a second person rolls a coin until 3 tails are rolled. 1) How many throws will each one make on average?
2)What is the probability that they will stop at the same instant, i.e. find P(X=Y).

Answer 1)We denote X = 1st (die) and Y = 2nd (piece). X ~ G(1/6)(geometric distribution) with expectancy EX=6 and variance V(X) =30, Y ~BN(1/2; 3)(negative binomial) with expectancy EX=6 and variance V(Y) = 6
Answer 2) The 3 in the picture is P(X=Y) but my teacher says to me that i need to find 25/343

[topaz sinew]

@turbid dawn Has your question been resolved?

[turbid dawn]

<@&286206848099549185>

[topaz sinew]

@turbid dawn Has your question been resolved?

[turbid dawn]

<@&286206848099549185>

[topaz sinew]

@turbid dawn Has your question been resolved?

[topaz sinew]

@turbid dawn Has your question been resolved?

[topaz sinew]

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.

[potent venture]

Calculate the distance between the points N=(3,-2) adn L= 8,-6) in the coordinate plane. In the exact answer not a deciamal approx

[potent venture]

is it 6?

<@&286206848099549185>

[sweet shard]

!15m

[topaz sinew]

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.

[sweet shard]

And read this

[potent venture]

.close

[topaz sinew]

Channel closed

Closed by @potent venture

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.

[silent hull]

How would I go about solving this?

[silent hull]

I don't really know where to start

[tough nest]

Can you rewrite $4n$ and $n$ in a way similar to $c_n$

[thorny flame]

Katharine

[mint flicker]

N means all natural numbers to start

[silent hull]

I'm not sure, but I don't think I even understand the sequence. Would the sequence look like {1, 2, 3, 4, 1, 2, 3, 4, 1, ...}?

Where n is the index

[tough nest]

no

not necessarily

[silent hull]

then what would b_n look like?

[tough nest]

we don't know

not precisely

we know that all $b_n$ are 1, 2, 3, or 4

[thorny flame]

Katharine

[tough nest]

so $b_0 = 1$ or $b_0 = 2$ or $b_0 = 3$ or $b_0 = 4$

[thorny flame]

Katharine

[silent hull]

ah alright

[tough nest]

and similarly for $b_1$

[thorny flame]

Katharine

[tough nest]

etc

oh actually they don't include 0 in the indices

the point i'm making is that we know vaguely what b_n looks like but not precisely

we know all the ways b_n CAN look

but not exactly what it does look like

does that make sense?

[silent hull]

ah alright, yeah i understand that

[tough nest]

but with that we have enough information for the given problem

[silent hull]

i know that intuitively then that n <= c_n <= 4n

i just dont know how i would write it on paper

because the lowest it could be is 1 + 1 + 1 + ...

which would always = n

[tough nest]

exactly

[silent hull]

and never go below n

[tough nest]

exactly

[silent hull]

and the logic is similar for the c_n <= 4n

i just dont know how to write it

[tough nest]

you can first show the smallest element of the set that all b_n are part of

as in you can show that the smallest any b_n can be is 1

and similarly for the biggest

and then show that with that

if b_n is the smallest always

[silent hull]

could i just write it similarly to how i explained it?

or is there a certain proof or method i need to use

[tough nest]

have you done any classes about proving in mathematics?

[silent hull]

yeah, i know proof by induction, strong induction, etc

im 2nd year in a uk university if that gives any gauge to proof knowledge

[tough nest]

that helps

in my uni proofs in mathematics is the first course mathematics students do but obviously in other universities it can be later on

so knowing you're in second year of university

[silent hull]

yeah, we had a lot in set theory last year

[tough nest]

means you know what language is used in proofs

[silent hull]

yeah

[tough nest]

you can use what you wrote

you show that c_n can at its smallest be 1 + 1 + 1 + ... + 1

and at maximum 4 + 4 + ... + 4

and that those are equal to n and 4n respectively

[silent hull]

just say something like "We shall first assume the smallest case of c_n to be 1 + 1 + 1 + ... + 1, meaning that n will always be equal to c_n, satisfying n <= c_n" etc

?

[tough nest]

well you have to prove that the smallest case of c_n is 1 + 1 + .. + 1

assuming it would be assuming the thing you are trying to prove basically

so you would show that all b_n can at minimum be 1

and then you say

let us take b_n = 1 for all n

and so c_n = 1 + 1 + ... + 1

etc etc

😛

i

[silent hull]

ahhh alright

[tough nest]

i'm lazy

[silent hull]

alright, i understand now

thank u so much for ur help

[tough nest]

np 😄

[silent hull]

.close

[topaz sinew]

Channel closed

Closed by @silent hull

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.

[daring swan]

Whats the formula to solve this type of integral?

[daring swan]

Just need the formula that’s all. Ik (ax+b)^n = 1/a 1/n+1 (ax+b)^n+1 + c but I’m not sure what it would be when it’s x/(ax+b)^n

[raven sparrow]

Let u = x+1

Fairly easy to do from there.

[daring swan]

My professor was weird in not wanting to teach us u-substitution

[pseudo bear]

u-substitution is basically the inverse of the chain rule, so it's important.

[raven sparrow]

You can also just add 1 and subtract 1

[daring swan]

Ex.?

[raven sparrow]

like (x+1 - 1) / (x+1)^2 = 1/(x+1) - 1/(x+1)^2

[daring swan]

Like this?

[daring swan]

Im confused on how this works

[raven sparrow]

They are separate, not in the denominator.

With the first two terms in the numerator, you get (x+1)/(x+1)^2 which is just 1/(1+x)

Then the remaining -1 gives -1/(x+1)^2.

[daring swan]

My friend just replied with how she approached it

Just dragged the x+1 up

I thought you could only drag the denominator up if the numerator was a 1

[raven sparrow]

That's not the same case though.

x in the numerator changes things considerably

[raven sparrow]

It's just that if the numerator is not constant (like x or something) you can't distribute it inside the negative exponent binomial. Hence you need the numerator to be constant for it to help in any way.

[daring swan]

So is it legal or illegal to drag the denominator up in this way?

[raven sparrow]

You can do, but that isn't the problem you asked help for to begin with. It's another problem entirely.

At the end of the day it's just writing the denominator as a negative exponent.

Again this will not help if the numerator is x because you can't just distribute x over (x+1)^(-2).

[daring swan]

Wdym it’s the same problem

Oh wait

I see the confusion

I just automatically translated K into X as I wrote it down

My fault

[raven sparrow]

Yeah it's different then. You can just bring the denominator up by changing the sign of its exponent and power rule it

[daring swan]

Okie dokie

Thanks for the explanation

🙏

.close

[topaz sinew]

Channel closed

Closed by @daring swan

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.

[neon iron]

how would i go about doing these two questions?

[neon iron]

for 8, its nPr = 55440, and nCr = 462

[topaz sinew]

@neon iron Has your question been resolved?

[keen raptor]

For 8, use the formula for nPr and nCr

[long stirrup]

for 7, i don't know a combinatorial approach, but you can add up paths from top to bottom manually, it's very easy

like with a pencil

it's like a pascal triangle so it's probably the intended way

[keen raptor]

In general you think about permutations of, in this case, 7 down moves and one right move

so, rearrangements of DDDDDDDR

[long stirrup]

but that's not the solution

[keen raptor]

?

[long stirrup]

that's wrong

[keen raptor]

Oh wait

Same principle though

[long stirrup]

you can go more R, it's not backwards

[keen raptor]

LLLRRRR

[long stirrup]

There's no fixed amount of L and R, it's not the intention and it doesn't follow from the rules

[keen raptor]

There is

7 moves must be made

And there has to be one more right then left

[long stirrup]

you;re right thanks

it's not too close to the edge that this fails

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[fathom void]

so would i just factor this first and then use the negative for everything that was factored or negative this stuff first and then factor

[craggy haven]

it's already factored

[fathom void]

well like the whats it called form

x^2+3x+2 kinda form

forgot name

im guessing do -(x^2+10x+25)

[jagged sparrow]

Yes

[fathom void]

kk thx

.close

[topaz sinew]

Channel closed

Closed by @fathom void

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.

[sweet shard]

Try drawing some pictures

[wooden holly]

hmmm?

but the max number is 96

...

<@&286206848099549185>

[sweet shard]

Well draw 3 circles first

Find that max first

Then see where you can draw a fourth circle to intersect the other three the most

[wooden holly]

ok..

[warped thistle]

@wooden holly any 2 circles will have 2 points of intersection

[wooden holly]

ye

[warped thistle]

So nC2 is the number of ways of choosing 2 circles
And multiply that by 2

[wooden holly]

okay

[warped thistle]

Do u get it