help-28

[eager violet]

You could use x + 0.5, but it would be a bit uglier

[torn jolt]

ok what about the second equation they have

at the bottom

how do they get that if

when they did sythentic division

they shouldve got 2x^2-4x+34

[eager violet]

It would be if you did (x + 1/2)

[crisp siren]

by rrt, all roots of the polynomial should be in the form of +-p/+-q

[eager violet]

But remember, they used (2x + 1)

[crisp siren]

where p is the last term and q is the first

[eager violet]

That extra (1/2) at the outside goes into the 2x² - 4x + 34

[torn jolt]

so if i did this

how do i solve the second equation

[eager violet]

What second equation

[torn jolt]

next to x+.5

[eager violet]

It's a quadratic

Use normal quadratic stuff

[torn jolt]

ok

a times b

and find 2 numbers that are sum of b

a times b is 68

[eager violet]

To save you trouble, it doesn't factor

[torn jolt]

so how to solve this one

[eager violet]

Quadratic formula

[torn jolt]

oh ok

thank you v ery much for helpiong

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[rich chasm]

How would I be able to start this

I’m studying for my semester exam and I’ve forgotten how to start this problem, so far I tried using the x-mean/stdev

But that’s not the thing I’m supposed to do I think

Also the answer is circled but I wanna understand how to get to it

[cosmic canopy]

ok

so you assume the probability is distributed normally

obviously

then you use the given standard deviation and mean

to find the z-score of the time (35 minutes)

then you use a z-score table or memorised values and you get the answer

ping me when you get back

[rich chasm]

Mb @cosmic canopy I was eating

So w the mean being 30 and stdev being 5 I do the formula

But what do I replace x with

[cosmic canopy]

can you specify

what formula you're using

[rich chasm]

That’s the formula I can remember using mean and standard deviation with

[cosmic canopy]

ok good

what is x?

well x is 35 minutes

because 35 minutes after 8:25 is 9 right

[rich chasm]

Yeah

I figured so I tried doing it

But this pops out with one

[cosmic canopy]

yeah

the z-score should be one

wdy

[rich chasm]

Ohhhh wait

[cosmic canopy]

$P(Z>1)=0.16$

[rich chasm]

So I use the z score right to find the answer

[glossy valve]

ed

[rich chasm]

So

I subtract .84 from 1

@cosmic canopy thank you so much bro🙏

[cosmic canopy]

correct

yes because $P(Z>1)=1-P(Z<1)$

[glossy valve]

ed

[cosmic canopy]

😄

[rich chasm]

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[ancient geyser]

try simplify

[frank grail]

Hm?

[ancient geyser]

you see the relation on the text above?

what rule did you see?

[frank grail]

That its related to temperature? I'm confused

[ancient geyser]

the higher the temperature the higher the rate of chirps per minute

[frank grail]

oh okay

[ancient geyser]

ill give you this

Tm+c=N

and

||(y2-y1)/(x2-x1)||

[frank grail]

Wait, I got it

Now I just need help on this one

[ancient geyser]

wait

are you in an exam

?

[frank grail]

No

This is a mix of two different sections for hw

[ancient geyser]

25^tx=y

[frank grail]

is that what p(t) equals?

[ancient geyser]

i gave you a rough idea of an exponential equation

[frank grail]

Hmm, alright

[frank grail]

Wait

How about this

<@&286206848099549185>

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[wide sundial]

What have you tried

[slow zodiac]

I'm not really sure where to start

[wide sundial]

What do you know about hyperbolas

[slow zodiac]

a is larger than b

[wide sundial]

What about a general form

Do you know if all the options are equations of hyperbolas?

They all look like conics but are there any that aren’t hyperbolas

[slow zodiac]

I'm pretty sure 2 of them aren't because a is bigger than b which makes it another shape but I'm not sure which ones are ruled out

because I don't know if 25 or 9 is a

[wide sundial]

Hmm

Do you know about eccentricity

[slow zodiac]

It's like the amount of curve right

[wide sundial]

https://en.m.wikipedia.org/wiki/Eccentricity_(mathematics)

Using the definition of eccentricity you should be able to figure out which are hyperbolas and which aren’t

[slow zodiac]

I'm pretty sure a and c are hyperbolas

[wide sundial]

What makes you say that

[slow zodiac]

the eccentricity of them is greater than 1

[wide sundial]

What the eccentricity of b

[slow zodiac]

actually I think the b and d are hyperbolas because the eccentricity of b is root20/2 making it greater than 1 therefore it's a hyperbola

and the same goes with d

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[slow zodiac]

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[sullen crater]

Hello

[deft zodiac]

hi

[sullen crater]

(1-r)^6=0.584

How do I get r

[pearl ocean]

$(1-r)^6 = 0.584$

[glossy valve]

Potet

[sullen crater]

Yes

[pearl ocean]

Any thoughts?

[pearl ocean]

Would you mind taking over?

[torn jolt]

take the 6th degree root of both sides @sullen crater

[onyx glen]

it's not "6th degree square root", it's just "6th root"

[torn jolt]

oh apologies

thanks for pointing it out

[sullen crater]

FML

I don't have calc that can do that

[torn jolt]

You can raise it to the power of 1/6

It is equivalent to taking the 6th root

[\sqrt[6]{x} \iff x^{\frac{1}{6}}]

[glossy valve]

♡LexQa♡

[sullen crater]

0.9142

[torn jolt]

It's an even powered root

It will have two solutions

So ±0.9142

[sullen crater]

R is 1 - 0.9142

[torn jolt]

,w (0.584)^{1/6}

[glossy valve]

Results provided by WolframAlpha

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Requested by ♡LexQa♡#5050

[torn jolt]

Okay

[torn jolt]

You have 1 - r = ± 0.9142

you have to account to both cases

[sullen crater]

I think I just need positive one.

This is part of some other equation

[torn jolt]

Okay w/e

[sullen crater]

@torn jolt can u check tho

[torn jolt]

Dunno I don't remember what the terminology for this stuff was

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[fickle dock]

could someone help me with find the values a and b

i got the derivative

[vast fossil]

If y = a/sqrt(bx + 1) passes through the point (1, 4), it means that you can plug in x = 1 and y = 4 into the equation and it'll still remain true

So 4 = a/sqrt(b + 1)

a = 4sqrt(b + 1)

And, since the gradient at that point is -3/2, you have f'(1) = -3/2

Giving you another equation in terms of a and b

[fickle dock]

yes

but i just cant solve to get to a and b

i ve tried multiple times

[vast fossil]

What did you get for y'?

[fickle dock]

-1/2ab(bx+1)^-3/2

[vast fossil]

Yeah, so $-\frac{1}{2}\frac{ab}{\sqrt{b + 1}^3} = -\frac{3}{2}$, but, since we've also shown that $a = 4\sqrt{b + 1}$, $\frac{4b\sqrt{b+1}}{\sqrt{b+1}^3} = 3$ and $\frac{4b}{b + 1} = 3$, solve for b

[glossy valve]

A Lonely Bean

[fickle dock]

ok let me try

[edgy musk]

I think u can set up 2 equations one with Ur original equation plugging in values of X and y

And second the derivitavw function = -3/2

[vast fossil]

That's what I did

[fickle dock]

omg

u re a genius hahaah

thanks bean

i have another question if u dont mind

[vast fossil]

As long as the channel is yours, you may post as many questions as you wish

[fickle dock]

thanks mate

i cant seem to work out 4b

[vast fossil]

Try integration by parts

Differentiate lnx and integrate 1/x^3

[fickle dock]

d/dx(lnx) =1/x

antiderivative of 1/x^3 = (x^-2)/-2

[vast fossil]

So integral of lnx/x^3 is -lnx/2x^2 - integral of 1/x * (-1/2x^2)

[fickle dock]

sorry i dont follow

"integral of 1/x * (-1/2x^2)" this part

[vast fossil]

You know integration by parts, right?

[fickle dock]

not quite

breaking down the term before integrating it?

still there?

[fickle dock]

?

[vast fossil]

Try learning integration by parts first though, part b can't be done without that

[fickle dock]

how do u integrate by part

[vast fossil]

There are many videos on yt explaining the technique

[fickle dock]

wait is it also known as integration by substitution

[vast fossil]

No

[full forum]

@fickle dock Has your question been resolved?

[fickle dock]

i have a question about integration by part

[vast fossil]

What is it?

[fickle dock]

i keepp seeing this equation

but they never explain the right hand side

like where its derived from

[vast fossil]

Recall the product rule

(uv)' = u'v + uv'

uv' = (vu)' - u'v

[vast fossil]

Integrate both sides with respect to x and you get this

[fickle dock]

ohh

[vast fossil]

Yeah, most of the integration techniques are derived from derivative rules

[fickle dock]

yea this wasnt covered in my syllabus

but apparently the questions requires it

but where does the dx at the denominator goes to

[fickle dock]

v' = dv/dx right

[vast fossil]

Yes

[fickle dock]

wait hold on

so wheres the dx then

in the image

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[fickle dock]

.reopen

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✅

[vast fossil]

/dx and dx "cancel out"

To say informally

[fickle dock]

right

however if u integrate dv/dx wouldnt u just get v

instead of dv

because integration undoes differentiation

[vast fossil]

No

It's u * dv/dx that's being integrated

And the antiderivative of u * dv/dx is not u * v

[fickle dock]

right

so how do u get integral of u*dv

[vast fossil]

Imagine doing a substitution

Or wait no

But dv is the same thing as dv/dx * dx

Alright I'll show the substituion

[fickle dock]

thanks

sorry for the trouble

[vast fossil]

Let t = v

Then dt = v' dx, right?

[fickle dock]

yea

[vast fossil]

So uv'dx becomes udt

And t is just a variable name, you can replace it with any letter

So it's udv

[fickle dock]

wait sorry i overlooked this part

dt/dx = v' ?

i dont follow how the denominator is dx

[vast fossil]

So dt = v'dx

We differentiate with respect to x

[fickle dock]

but theres no x only v

[vast fossil]

We're integrating with respect to x

Meaning there's dx

[fickle dock]

okay

so u replaced the t with v

[fickle dock]

but isnt it dv/dx*u

[vast fossil]

times dx

And v' * dx is dt as we've shown

[fickle dock]

okay sorry

its just confusing with all the variables

i get it

wait but from (uv)'

where did the apostrophe go for u

since the integration symbol is still present for u

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@torn jolt Has your question been resolved?

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@torn jolt Has your question been resolved?

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@torn jolt Has your question been resolved?

[wicked wyvern]

We can prove this using induction.

For the base case, let m = 1 and n = 1. In this case, the only possible value for x1 is 1, and !x1 = 1. Thus, 24;!x1,!.*,! = 1 * (1 + 1) = 2, which is equal to m(m + 1).. (m + n- 1).

Now, assume that the statement holds for some m and n, and consider the case where m = m + 1 and n = n. In this case, there are two possible ways to distribute the values of x1, x2, ..., xm+1 such that x1 + x2 + ... + xm+1 = n:

x1 = x1, x2 = x2, ..., xm = xm, xm+1 = 0
x1 = x1, x2 = x2, ..., xm = xm - 1, xm+1 = 1
In the first case, the value of !x1, !x2, ..., !xm, !xm+1 is equal to !x1 * !x2 * ... * !xm * !xm+1 = (m(m + 1).. (m + n- 1)) * 1 = m(m + 1).. (m + n- 1).

In the second case, the value of !x1, !x2, ..., !xm, !xm+1 is equal to !x1 * !x2 * ... * !xm * !xm+1 = !x1 * !x2 * ... * !xm * (m + n) = m(m + 1).. (m + n- 1) * (m + n) = (m + 1)(m + 2).. (m + n).

Thus, in either case, the value of !x1, !x2, ..., !xm, !xm+1 is equal to m(m + 1).. (m + n- 1) or (m + 1)(m + 2).. (m + n), which completes the induction step. Therefore, the statement holds for all values of m and n.

@torn jolt

[rapid laurel]

wait what?

u cant type that

in 1 min?

[wicked wyvern]

I was typing it before you asked me

[rapid laurel]

[wicked wyvern]

I’m just going down the list

[rapid laurel]

i love you ethan

[wicked wyvern]

I love to boki

[rapid laurel]

accept friend request

[wicked wyvern]

Why

[topaz valley]

[rapid laurel]

help with this

[torn jolt]

at least put a disclaimer before your answers if you are going to insist on using chat gpt

[rapid laurel]

whats chat gpt lol

[wicked wyvern]

It’s a bot

[topaz valley]

[torn jolt]

its an ai that gets most maths incorrect

[wicked wyvern]

[rapid laurel]

[topaz valley]

this is literally stars and bars

[rapid laurel]

snow just type out how to answer

[topaz valley]

why would you do it with induction

[rapid laurel]

[wicked wyvern]

Because why not

[topaz valley]

[rapid laurel]

,w chat gdp

[glossy valve]

Results provided by WolframAlpha

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

Requested by 電波的な彼女#7083

[topaz valley]

gdp

[wicked wyvern]

w bot

[rapid laurel]

gross domestic product

[wicked wyvern]

GDP stands for gross domestic product, which is the total value of goods and services produced within a country's borders in a given period of time, typically a year. It is used as a measure of the size and health of a country's economy.

[topaz valley]

[wicked wyvern]

precious ai doesn’t make spelling errors

[fleet cedar]

tf

[full forum]

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[finite bluff]

help with rearranging

[finite bluff]

can anyone see how general solution in pencil pic is derived

[brave blaze]

look for d'Alembert equation on the internet I think

[finite bluff]

just more whats my value of c in the last pic

as pic divides by c

[brave blaze]

c represents light speed if im not wrong

[finite bluff]

i can see where wy is from

[finite bluff]

no look at slide 1

its constant... a rearrangement

[brave blaze]

?

[finite bluff]

see this

top eq

[brave blaze]

$c^2 = \frac{E}{\rho}$

[glossy valve]

Ｈｅｒｅｌｓ

[finite bluff]

n i guess 1/c is

sqrt(rho/E)

[brave blaze]

$\frac{1}{c^2} = \frac{\rho}{E}$

[glossy valve]

Ｈｅｒｅｌｓ

[finite bluff]

THX

[full forum]

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[mild cobalt]

h

[mild cobalt]

hi

what is constant term of a binomial theorem

google doesnt explain that clearly

like for example

Find the constant term of
(20 + 3/x)^8

[devout valley]

The term that doesn't depend on x

[mild cobalt]

wdym

oh

wait

so a term that will have no x variable

so something for example like
10x^3 20x^2y 30xy^2 40y^3

the constant term would be 40y^3?

[devout valley]

Yeeaa this

[devout valley]

Well, only if y was a constant, probably y isn't the best choice for that...

[mild cobalt]

but which one is the x variable

what if its like (a+b)^n

which one would be x

[devout valley]

For this one you said, the constant term would, when you work it out, be 20^8

[mild cobalt]

what about for (a+b)^n

[devout valley]

Well, what are a and b?

[mild cobalt]

any variables

(4x+3y)^12 for example

[devout valley]

If both of them vary, then there's no constant terms you'll find from that

[mild cobalt]

i think i got it

[sinful canopy]

Ye

[mild cobalt]

its just a term that doesnt depend on the unknown basically

[devout valley]

Yeah, that

[mild cobalt]

ok

ty

wait

[sinful canopy]

Ok

[mild cobalt]

but how will i find it'

[sinful canopy]

Yeah

[mild cobalt]

in my book its asking

(4x + 1/x)^8
find the constant term

[devout valley]

Ah, for that, you'd want to find the term where the variables cancel out (I was thinking of an example like that tbh)

[mild cobalt]

i meant as in if there are any shortcuts to it or i have to do the whole expansion

[devout valley]

We know the binomial theorem is basically $(a + b)^{n} = \sum_{k=0}^{n} {^{n}C_{k}} a^{k} b^{n-k}$

[glossy valve]

chartbit

[sinful canopy]

Binomial theorwm

[mild cobalt]

so no shortcuts

have to expand

[devout valley]

Welll not really...

[mild cobalt]

well what would be a quicker way

[devout valley]

There is a shortcut, consider each of those terms

[sinful canopy]

$(4x)^k({1/x)}^8-k$

[devout valley]

We would like the 4x and the (1/x) to have the same power ideally, so that they cancel out in it

[sinful canopy]

Augh latex is hard

[mild cobalt]

oh

i see

so it would be 4th term

wait no

5th

lemme check rq

[devout valley]

Yea, good idea

[sinful canopy]

2r = 8

[mild cobalt]

5th term?

[sinful canopy]

=> r = 4

[mild cobalt]

but

[devout valley]

Errmmmm

Substituting everything into what we have, we ideally want $8 - k = k$, yea?

[glossy valve]

chartbit

[devout valley]

(Why?)

[sinful canopy]

As $\dfrac{x^r}{(4x)^{8-r} \Rightarrow r-8+r=0 \Leftrightarrow \boxed{r=4.}

[mild cobalt]

1st: 4x^8
2nd: 4x^7 (1/x)^1
3rd: 4x^6 (1/x)^2
4th: 4x^5 (1/x)^3
5th: 4x^4 (1/x)^4

[sinful canopy]

As $\dfrac{x^r}{(4x)^{8-r} \Rightarrow r-8+r=0 \Leftrightarrow \boxed{r=4.}$

[mild cobalt]

in 5th term they're both 4 so they'll cancel each other out when multiplied

[glossy valve]

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

[sinful canopy]

BRUH

[devout valley]

Ahhhh yeah I'm silly...

[sinful canopy]

As $\dfrac{x^r}{(4x)^{8-r}} \Rightarrow r-8+r=0 \Leftrightarrow \boxed{r=4.}$

[glossy valve]

Aqua

[devout valley]

I'm thinking like a programmer 😂

Counting from zero

[mild cobalt]

yea

that confuses me so much but im getting used to it

[devout valley]

It is the 5th term, but where $k=4$

[glossy valve]

chartbit

[sinful canopy]

This correct?

[mild cobalt]

no

because binomial starts from 0

essentially

[sinful canopy]

....

[mild cobalt]

1 = 0
2 = 1
3 = 2
4 = 3
5 = 4 etc

its confusing but it works

[sinful canopy]

Bro what

Ah yes

[mild cobalt]

1st term is 0

[sinful canopy]

Got it

[mild cobalt]

2nd term is 1

[sinful canopy]

Lmao

[mild cobalt]

oh

[sinful canopy]

Yeah

[devout valley]

I think "first/second term" etc is a horrible choice of wording here tbh 😂

[mild cobalt]

no other wordings sadly

[sinful canopy]

🇾e

[mild cobalt]

i have my math exam in 6 hours and i havent even started studying quadratic and linear functions

[devout valley]

(Personally I just refer to it by the powers of k 😂 )

[sinful canopy]

Oop

[mild cobalt]

bro aqua

can you speedrun me through inverse functions

i had a question like this

[sinful canopy]

Nop sry idk abt them

Can help u in quad

[mild cobalt]

idk what help i need in quad

i'm good enough at functions for my exam

[sinful canopy]

Just quadratic formula

🤡

[mild cobalt]

oh

tjhats simple

[sinful canopy]

Yeah

[mild cobalt]

_ _ _ _ _ _ _ _ _ _ _ _ /--------
f(x) = / 4x + 1
/

then you have to find inverse of that function

[sinful canopy]

Idk abt inverse functions bro

[mild cobalt]

yes bro

im just making it just incase someone knows

[sinful canopy]

$V^100+2V^50+1=0.$ Solve for$V \in \mathbb{R}$.

[glossy valve]

Aqua

[sinful canopy]

$V^{100}+2V^{50}+1=0.$ Solve for$V \in \mathbb{R}$.

[glossy valve]

Aqua

[sinful canopy]

@mild cobalt

[mild cobalt]

hi

idk what that is

[sinful canopy]

A slight difficult question in quad

[mild cobalt]

oh

quadratic formula

yea idk how to solve those

[sinful canopy]

100th power tho

[marsh surge]

you can take
t=V^50

[mild cobalt]

oh

lmao

that makes so much sense

[thorn crown]

or alternatively use the fact that (a+b)^2 = a^2 + b^2 + 2ab

[sinful canopy]

Thats the trick!!

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[fallen wyvern]

Can anyone help with a geometry question?

[full forum]

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[molten sundial]

im lost

[full forum]

@molten sundial Has your question been resolved?

[forest widget]

factorize both parts of the fraction
if it feels unfamiliar to you, try to get rid of negative exponents

[molten sundial]

would the numerator be (-2)/(x^2) - (1)/(x) + 1?

[forest widget]

yes

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[icy owl]

hi, heres what im stuck with. im trying to understand how to convert but im brain farting so hard rn

[twin lagoon]

Convert as in factoring?

[icy owl]

main language isnt english, so idk maybe

just an intuivite way to why x² -3x -10 = (x-5)(x+2)

[unreal quarry]

What's your main language

[icy owl]

arabic

[unreal quarry]

Yea, i think she/he is trying to convert it as in factoring

[twin lagoon]

ok

[next sail]

(x-5)(x+2) = x(x+2) - 5(x+2) = x^2 + 2x - 5x -10 = x^2 - 3x - 10

[twin lagoon]

For these kind of quadratics, an intuitive way I do is to look at the last number, -10
-10 has factors
1, 2, 5, 10 with one factor as a negative number and the other factor as a positive number

and then look at the first number, 1 (x^2 has a coefficient of 1 by default since there's nothing at front)
for 1, it only has 1 and itself (1) as a factor, which makes things easier.

so we can try multiplying the factors of the first and last number and adding the products one by one to see if we get -3 (the middle number)

1 * -10 + 1 * 1 = -9 no
1 * -2 + 1 * 5 = 3 also no
1 * -5 + 1 * 2 = -3 which is what we want```
so, we'll have ((1)x + (-5)) ((1)x + (2)) = (x-5) (x+2)

[icy owl]

k

thnx

[twin lagoon]

let me know if this helps

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[kindred mist]

Can someone prove this please ?

[fast peak]

try induction

[kindred mist]

okay imma try

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[torn jolt]

is this valid proof? do we have to consider the case where x = 0?

as the EVT requires the interval [a,b] to have that a < b

wait is the statement in the question and the statement i wrote down equivalent?

nvm it is not

.close

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[torn jolt]

whaat is the difference between putting the for all statement at the very and and at the very beginning of the statement?

[devout valley]

say .reopen please?

[devout valley]

(so you don't lose this channel)

[devout valley]

• for this, you know that f will attain a maximum and minimum value

[torn jolt]

.reopen

[full forum]

✅

[torn jolt]

isnt this simply just invoking the extermal value theorem and nothing else

[devout valley]

Hmmm, you could, though at least with my set of notes they use the "maximum theorem" and "minimum theorem" to prove the intermediate [extermal] value theorem

[topaz valley]

[torn jolt]

the theorem has been proven in the lecture notes so i think i can just use it

[devout valley]

Ah, can I see your version please?

How they state it

[topaz valley]

thats all you need to do

[devout valley]

Ah, yeah, they're basically saying what I am

[torn jolt]

yeah i was just unsure because this is the first hw question assigned being this simple

thx

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[mortal sleet]

If I want to write the solution for system of simultaneous eqations using the $\vec{p}+ker(M)$, how do I know how many vectors should be in span(u)? I have matrix ((0,2),(0,0)) and I dont know how many vectors will the span have.

[glossy valve]

marejak023

[mortal sleet]

Sorry, I have interpreted the question wrongly, I know that the span will have one vector, because $def(M)=columns-ker(M)$, which is in my case 2-1, so there will be one vector in span, $span(u)$, but I dont know how many parts does the vector has (u1,u2,...)

[glossy valve]

marejak023

[mortal sleet]

I think that the solution will be $span((\vec{0}))$, but not sure

[glossy valve]

marejak023

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[mortal sleet]

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[echo gale]

I’m not too sure what x≠3 means
Is it like x=2,1,0,ect ?

[atomic blade]

x ≠ 3 means "x cannot equal to 3"

In terms of domain

So $D: {x\in\bR | x ≠ 3}$
$$\text{}$$
But they shortened it to "x≠3"

Bruh

[echo gale]

Lol take your time

[glossy valve]

Umbraleviathan

[echo gale]

So how would I solve this? Do I replace ever x with a number that just isn’t 3?

[atomic blade]

Polynomial division

[echo gale]

Oh.. so do I divide the polynomials just to get my answer?

||(Btw warning, when it comes to math I can get confused easily so pls do know I’m not trying to annoy you)||

Guess so

[atomic blade]

Yeah

Sorry I was driving someone somewhere

[echo gale]

It’s okay, good job on staying on the road lol

[full forum]

@echo gale Has your question been resolved?

[echo gale]

I got another question actually

One minute..

[whole heron]

@atomic blade u still active ?

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@echo gale Has your question been resolved?

[atomic blade]

Nope I'm at a symphony rehearsal

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[restive leaf]

hi. can someone please explain how to do this problem. thanks

[boreal marlin]

Set up an equation, your unknown is the price increase and you want to maximize revenue (price times items sold)

[restive leaf]

ik the equation but i dont know how to get to it

[sinful canopy]

Nope

[restive leaf]

its y = (4000-100x)(30x+1x)

but idk how to get there

[boreal marlin]

(4000-100x) is the number of toys sold, it decreases by 100 by each dollar increased in price

[restive leaf]

alr

then what

[boreal marlin]

Other term should just be (30+x) 🤔

[restive leaf]

yea that works too

but idk what to do after finding the equation

[boreal marlin]

You derivate and see where the derivative equals 0

Or...

,w maximum of (4000-100x)(30+x)

[glossy valve]

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[restive leaf]

oh

idk how to derive and stuff

[boreal marlin]

You can also graph it and see

[restive leaf]

oh

yea

[boreal marlin]

,w graph(4000-100x)(30+x)

[glossy valve]

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[restive leaf]

oh

yea

i get it now

thanks sm

[boreal marlin]

[restive leaf]

.close

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[mortal egret]

Hello 👋

[sinful canopy]

Ok hello

[mortal egret]

Can you do anything more with x=2root2

[sinful canopy]

Square

x² = 8

[mortal egret]

Or is that it like you can’t equal it to zero or nothing?

[sinful canopy]

What

Do u mean

[mortal egret]

Oh mb I wasn’t specific, I got x=2root2 and was wondering if that was it or if I could somehow equal it to zero

[sinful canopy]

How can 2root2 be equal to 0???

[mortal egret]

I was asking if it can

[sinful canopy]

Wow

No it cant

[mortal egret]

Ight thanks

[sinful canopy]

Doubt resolved?

[mortal egret]

Sí

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[tawdry acorn]

all sorts of lost

[gritty rose]

https://tutorial.math.lamar.edu/classes/calciii/directionalderiv.aspx

[tawdry acorn]

@gritty rose is my unit vector not <20/sqrt20, -4/sqrt20>?

I GOT IT YESSSSSSSSSS

.CLOSE

😐

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[normal fiber]

help

pls

<@&286206848099549185>

[timber oriole]

!15m

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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.

[normal fiber]

what does

that mean

!15m

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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.

[normal fiber]

??

[timber oriole]

you are supposed to wait 15 minutes before using that ping

[normal fiber]

dude i need help

please

in 5 mins

i gotta shower

[timber oriole]

well I don't feel like helping because I clicked on this channel because of the ping. but it wasn't used properly

[normal fiber]

bro

[timber oriole]

shows you didn't read #❓how-to-get-help and don't respect it. maybe someone else will help

[normal fiber]

please

[normal fiber]

dude

i have to go

in 5 minutes

this is the last problem

and i dont know\

please

you are so petty

why

<@&286206848099549185>

pls

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[torn jolt]

Why does this:

[torn jolt]

srry here's clearer picture:

i only need help with the last bit though

why does that equal this:

pls somebody it's due tmmrw

[scenic wren]

where exactly is the problem?

[torn jolt]

sorry can you clarify?

[scenic wren]

im asking what you are struggling with

[torn jolt]

yeah sorry here

[torn jolt]

im having problems on understanding how its equal to this (the answer)

we didn't really study it in class

but our teacher still expects us to do it

[scenic wren]

so, theoretically we should come up with a function to get the area and then get the derivative to find the maximum points

but we can also just say that a square will maximize the area

knowing this, we have want all sides to be equal

we will only fence 2 sides though
let's call the sides x
we have two sides, which makes 2x
we have 32 meters fencing, which means 2x=32
therefore: x=32/2=16

to get the area, do x*x=16^2=256

[torn jolt]

got it tysm!

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[full forum]

Please don't occupy multiple help channels.

@lucid oasis Has your question been resolved?

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[sudden nova]

Is my answer correct?

[full forum]

@sudden nova Has your question been resolved?

[stiff musk]

the question is vague - do they mean a group under addition or a group under multiplication?

[sudden nova]

Yeah I think theres a mistake here

I just assumed it for my benefit that it's addition

under multiplication 1a = a1 it would be true tho

[stiff musk]

if m and n are two integers coprime to 30 then so is mn

so at least the set is closed under multiplication

what about inverses?

[sudden nova]

I guess Inverse also fails for addition a + (−a) = (−a) + a = 0

because we lack 0

[stiff musk]

addition fails in many ways, even if a is coprime to 30, then a+a = 2a isn't (it's divisible by 2, and so is 30)

multiplication seems like an immediate fail due to lack of inverses

assuming it's ordinary multiplication

[sudden nova]

how'd you write that proof in full?

[stiff musk]

i mean you can always define your own operation and make it a group, so again the question is vague

[stiff musk]

well for example, 7 is coprime to 30, but there's no integer m such that 7m = 1, so 7 has no multiplicative inverse

[sudden nova]

But: a · (a^−1) = (a^−1) · a = 1

[stiff musk]

but a^-1 is not an integer

i assume we are talking about integers here

[cosmic canopy]

we must be

"coprime" only refers to whole positive integers no?

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[torn jolt]

Is there an absolute max at x=-1?

[cosmic canopy]

are you aware desmos exists

[torn jolt]

yes

[cosmic canopy]

use that

don't use this to check your answers if you have access to answers

[fathom saddle]

Wolfram if you don't have quick access to desmos

[cosmic canopy]

^

[fathom saddle]

,w graph (2 - x)x^(2/3)

[glossy valve]

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[cosmic canopy]

if you have trouble understanding something then it is much better for us to help in that respect

[torn jolt]

do points have to change from a positive to negative to be considered an abs max?

[torn jolt]

,w graph (2-x)(x^(2/3))

[glossy valve]

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[torn jolt]

Oh lol

[cosmic canopy]

what does this mean

[fathom saddle]

,w maximum of (2 - x)x^(2/3)

[glossy valve]

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[fathom saddle]

Huh, no it's at x = 4/5

[torn jolt]

derivative*

[cosmic canopy]

yes it does

@torn jolt it has to

the derivative must change from pos to neg to be considered a local/global max

assuming the function is continuous

[fathom saddle]

I think you can find weird counter examples to that. Like y = 0

But yeah that's a good rule of thumb

[torn jolt]

i thought it just meant the highest value of y for the given interval

So the absolute max is on x=0.8 and not x=-1? Interval is [-1, 2]

[fathom saddle]

,w graph (2 - x)(x^2)^(1/3)

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[fathom saddle]

Okay neat, the order of operations matters there.

The absolute max, on the interval [-1, 2] is at x = -1.

There's notably a local max at x = 0.8. It is not the absolute max for that interval.

[torn jolt]

alright so absolute max just means the highest y value on the interval?

[forest widget]

yes, when you have a bounded interval remember to check boundary points

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[modest sail]

for the range, how can y be 1?

[forest widget]

[-3, -1], solution given is wrong

[modest sail]

for y to be 1, cos(pi*x) needs to be -3

which i don't think is possible

according to the unit circle

[forest widget]

ye it's just wrong

[modest sail]

oh ok

thanks for confirming that really helps

🙂

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[acoustic pebble]

(sinx+cosx)/(csc(x)+sec(x))

Cscx = 1/sinx and sec(x)=1/cos(x)

[craggy basin]

@patent gulch

[acoustic pebble]

Thwn

Yep

[torn jolt]

Hey guys how do I get smart I farded in my brain 🤯

[craggy basin]

#❓how-to-get-help

[acoustic pebble]

Eat math, drink math, do math all day

[torn jolt]

Ngl I’m struggling in chemistry class not math class LOL

[acoustic pebble]

Chem

Huh

[torn jolt]

discord.gg/chemistry

Does it work

[acoustic pebble]

I hate that subject

Nah

[craggy basin]

bruh

[acoustic pebble]

Mods

[craggy basin]

@torn jolt https://discord.gg/93rBJFPp

[sullen crater]

What

[torn jolt]

Kk

[sullen crater]

It's a network

Don't call mods for that

[acoustic pebble]

Ok

[craggy basin]

why tf calling mods

[acoustic pebble]

My bad

[craggy basin]

nvm

[sullen crater]

Links aren't really allowed, but this is part of network

[acoustic pebble]

Hmm OK

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Please don't occupy multiple help channels.

@thorn wolf Has your question been resolved?

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[autumn sierra]

THE NTH TERM OF A SEQUENCE IS 5N squared work out the value of the 17th term

[autumn sierra]

Is the answer 5 x 17 x 17

[thorny horizon]

do u mean $5n^2$ or $\left(5n\right)^2$ when u say 5 n squared

[glossy valve]

SilverSoldier

[autumn sierra]

The first one

No brackets

@thorny horizon

[thorny horizon]

yeah then yes

the answer is 5 * 17 * 17

[autumn sierra]

OK THANKS

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[weak plaza]

hey guys. today i started learning integers.

I came here in hopes of getting a piece of advice from you on how to learn it effectively and easily

Regards

[weak plaza]

maybe you can give me advice.

[shrewd hamlet]

Wdym learning integers?

[weak plaza]

maybe i mistake it for something else

for integrals

[shrewd hamlet]

O

[weak plaza]

like this for example

[shrewd hamlet]

Yep

Integrals

[weak plaza]

i started hearing about them today and am looking for a way to approach this

[carmine minnow]

practice integration techniques

[shrewd hamlet]

Biggest tip I can give is practice many types of problems

[shrewd hamlet]

Have u considered u sub

[weak plaza]

u sub ?

[shrewd hamlet]

U substitution

[weak plaza]

may i ask what source you use for this?

[shrewd hamlet]

Integration technique

[weak plaza]

I heard of it, but i Heard of many different things at once so im overwhelmed

[carmine minnow]

tbh I don't have a good source of such problems where you have to keep jumping between different methods (integration by parts/u sub...)

[weak plaza]

I am wondering how people study this the best

I can watch many different youtube videos which might all talk about fragments of the topic but it might not be that useful when I want a good overview on the topic

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[void frost]

,tex The salary of a professor is normally distributed. Suppose that 25% of the
professors have a salary of less than 60 000 euros and 25% of the professors have
a salary of more than 100 000 euros. What is the probability that a professor
has a salary of between 50 000 and 60 000 euros?

[glossy valve]

Magnus

[void frost]

,tex $\frac{100000-\mu}{\sigma}\approx0.6745 \newline \newline
1-\frac{60000-\mu}{\sigma}\approx0.6745$

[glossy valve]

Magnus

[void frost]

i have this system of two equations at the end because i tried to convert this normal distribution to a standard normal distribution in order to get the standard deviation as well as the mean

[clear lily]

well you can find the mean

[void frost]

yeah, but thing is i tested it all in wolfram alpha

[clear lily]

and then you can calculate the standard deviation

[void frost]

and reproduced P(x < 60 000)

and it isnt 0.25

so perhaps i failed with a step?

[clear lily]

its literally defined to be 0.25

so you did soemthing wrong

[void frost]

yeah thats what i mean

its defined in the question

[clear lily]

you need to find mu and sigma

mu you can find quite easily

[void frost]

i did find them but i dont know if theyre correct

hold on

,tex $\mu = \frac{7920000}{349}$ \newline \newline $\sigma = \frac{40000000}{349}$

[glossy valve]

Magnus

[void frost]

this is what i had

and i put them as parameters in wolfram alpha in a normal distribution, then checked if P(x < 60 000) would still be 0.25, and it wasn't

[clear lily]

how did you get mu?

[void frost]

i wont lie to you i did it in wolfram alpha as well

hold on, ill do it manually now

[clear lily]

mu is 80000

(60000 + 100000)/2

how could mu be 7920000/349

,calc 7920000/349

[glossy valve]

Result:

22693.40974212

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@void frost Has your question been resolved?

[void frost]

how is it 80000

<@&286206848099549185>

nevermind i got it

@clear lily

this should actually be the system of equations:

,tex $\frac{100000-\mu}{\sigma}\approx0.6745 \newline \newline
-\frac{60000-\mu}{\sigma}\approx0.6745$

[glossy valve]

Magnus

[void frost]

so that one i got was the mistake

now when i test the distribution for P(x < 60 000) just in case, it does result in 0.249997

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[warm perch]

it’s so simple yet every time i get it wrong??

[cloud moon]

what are 3 main rules that 2 triangles are congruent with one another

[warm perch]

SSS RHS SAS ASA

[cloud moon]

rhs doesn't apply here since we have no right angled triangles

[warm perch]

yh ok

so A is congruent as it’s SSS

B is impossible to tell

[cloud moon]

they both have 3 sides yes but they haven't defined the sides being the same

[warm perch]

C is not congruent

[cloud moon]

in A

you are given AAA

not SSS

[warm perch]

ohhhhh

man how i miss that

it’s all clicking thanks

[cloud moon]

also

there's another rule AAS

angle angle side that applies to B

so B is congruent

[warm perch]

lemme see if it’s correct

yh it is

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[umbral tendon]

hi! i need help

[light sonnet]

#❓how-to-get-help

You don't need an equation

The table gives enough info

If you had two equations, you would set them equal to each other, to determine where they intercept

The intersection is the solution to both equations, correct?

If the intercept is the solution, that means that point satisfies both equations

On the table, you want the point that satisfies both tables

Yes

What is the point on each table that is the same

The point that is the same is the intercept

Yes, but that's not the exact one. That's just the y intercept

Coincidentally it has the same y intercept

Unless that problem has a multiple solutions

You don't need that

[light sonnet]

.

There's multiple solutions on that table

[light sonnet]

.

Recall that I stated that for it to be a solution, it has the be the same point on both tables

You picked (0, 4). I'm pretty sure that one is not the answer, it's just a coincidence

Yes

[quick fox]

well is it possible that 9 = 0?

then that means this system of equations has no solutions

it means that for example, an infinite number of x-values will satisfy the equality like if you have 3x = 3x (as you can see, regardless of which values of x you choose, 3x will always equal 3x so there are infinitely many solutions to the system)

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[bronze magnet]

how do find the solution of the function when it is greater than 0

and then then less than or equal to

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@bronze magnet Has your question been resolved?

[quick fox]

its easiest to start by looking at where this function equals 0

at what x values is this function equal to 0?

[bronze magnet]

-6?

and 4

[quick fox]

yes

so know consider at what areas is the function greater than 0

aka where is the function above the x axis

(they should be inequalities)