help-38

[tardy blaze]

By am gm i found that abc >= 1/27

[plush skiff]

nice

since abc is +ve

[tardy blaze]

so take when a=b=c

[plush skiff]

yea\

1/3

[tardy blaze]

1/3+1/3/1/27 = 18

[plush skiff]

yes

is it the ans?

but

[tardy blaze]

idk its not multiple choice

[plush skiff]

i dont think it will be mininmum

it can be

but we are not sure so

[tardy blaze]

I think its the minimum

I take (0.1, 0.1, 0.8) the answer is 25

[plush skiff]

hmm but ..

it will better if we did it the right way

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[regal goblet]

How do I integrate 1/1-x^2?

[regal goblet]

I know that integrating f’(x)/f(x) gives you ln|f(x)| + C

[frosty marlin]

Do you know how to do partial fractions?

[hardy dove]

sin^{4040}x+cos^{4040}x

[knotty locust]

Don't interrupt other peoples channels

[hardy dove]

then where i can go?

[knotty locust]

!help

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[regal goblet]

We haven’t covered it in the course yet but it’s still a question given in the exercise

[frosty marlin]

I'm not sure what they intended then

Technically you still have access to the fact that $\frac{1}{1-x^2} = \frac{1}{2}\left(\frac{1}{1+x} + \frac{1}{1-x}\right)$

[regal goblet]

Hmm

Maybe I misinterpreted the original question hang on

I was doing a

[frosty marlin]

Ah, for a you do not need that

[regal goblet]

Ohh

[frosty marlin]

Do you know inverse trig integrals

Or derivatives rather

[regal goblet]

Yeah integrating that gives sine inverse

[frosty marlin]

Yeah

[regal goblet]

I just read the question as if it was a 3d solid 🤦‍♂️

Was I trying to solve b then? How would you solve that

Oh it’s around the y axis

I’ll try and do it myself

Yep I got it myself!

Thanks

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[somber kite]

i understand everything

except the teacher's note on the top

"Disregard angle theta for which sin(theta) = 0"

can someone clarify/explain that sentence for me?

[wraith hinge]

yes

you multiplied by sin theta so it means you have to disregard the values for which sin theta is zero

[somber kite]

oh i see

cuz then

since sin(theta) was on the denominator, it would be extraneous

right?

thats why we disregard/eliminate that answer

correct?

[wraith hinge]

indeed

[somber kite]

gotcha

much appreciated

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[delicate pagoda]

Ax is a given 3×3 matrix.
x is a given vector in R^3.

"Using Gauss-Elimination (with column pivoting), find x"?

First of all if x is a vector then Ax can't be 3x3, second, x is given so why am I looking for x?

Is this a typo in the assignment or am I missing something?

[hallow cliff]

Yea x if is a 3x1 vector then Ax will have only one column

[delicate pagoda]

so the task makes no sense?

[hallow cliff]

Can't be 3x3

Yeah it doesn't make much sense

[delicate pagoda]

so Ax in R^3×3 and x in R^3 can not be interpreted in any sensible way?

[hallow cliff]

Not to my knowledge, no

Ax can't be 3x3 with x having just 1 column

[delicate pagoda]

I think they meant something like Ax=b and wanted to give A and b

[hallow cliff]

Yeah

Thats what I was thinking too

A is 3x3 and given. b is 3x1 and given and they probably want you to find x via gaussian elimination

Thats a pretty common exercise

[delicate pagoda]

yeah but they didn't.

anyways, thanks for confirming

[hallow cliff]

👍

[delicate pagoda]

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[marsh forum]

Could I have a hint?

[marsh forum]

I started by subbing $u=sin(x)$

[solid kiln]

Why am. I here

[marsh forum]

so we have $2u^3+2u^2(1-u^2)+4u-4=0$

[solid kiln]

Why am. I here

[marsh forum]

is there any quick way to solve this?

[orchid wagon]

its a quartic, and a painful one at that

i would rather expanding the trig themselves

[lusty delta]

good idea

[light karma]

sin2x as 2sincos

then cos^2x as (1-2in^2x)

[marsh forum]

I did

[light karma]

the sin^3x gonna get canceled

[marsh forum]

that's how I got $2u^2(1-u^2)$

[solid kiln]

Why am. I here

[lusty delta]

ye

then you can consider expanding that

although one of your terms is wrong

it's 2u(1 - u^2)

[marsh forum]

hmm, so we have $2u^3+2u^2-2u^4+4u-4=0$$

[solid kiln]

Why am. I here
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[lusty delta]

,

[marsh forum]

ah, got it

Thanks!

[lusty delta]

yeah i think that was the main thing then

[light karma]

yes

[lusty delta]

after that, you can probably complete the problem

[marsh forum]

Thanks!

so 6u=4?

[light karma]

yeah

[marsh forum]

hmm, so there will be two solutions in teh first cycle

that's 0 to 2π

and one more in 2pi, 5π/2

[light karma]

yup

so n = 5

done

[marsh forum]

thanks!

[light karma]

:)

[orchid wagon]

thats weird

i tried expanding sin^3x

and they cancel out

[light karma]

.

[lusty delta]

ye they made a mistake originally

[lusty delta]

you can see in this img what happened

[orchid wagon]

oh yeah i see

in that case then yeah theres your answer

[marsh forum]

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[marsh forum]

$9\int_0^9\sqrt{\frac{10x}{x+1}}dx=9\left(\int_0^{\frac{1}{9}}0dx+\int_{\frac{1}{9}}^{\frac{2}{3}}1+\int_{\frac{2}{3}}^93\right)$

[marsh forum]

oops, made a mistake

just a mo

$9\int_0^9\left[\sqrt{\frac{10x}{x+1}}\right]dx=9\left(\int_0^{\frac{1}{9}}0dx+\int_{\frac{1}{9}}^{\frac{2}{3}}1+\int_{\frac{2}{3}}^92\right)$

where [x] is the floor function

is there any way to generalise the integral upto any natural number n

wolfram doesn't return any output

,w integrate floor(10x/(x+1)) from 0 to n where n is a natural number

[solid kiln]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by physicsrocks

Why am. I here

[boreal zodiac]

,w Integrate[Floor(10x/(x+1)), {x, 1, n}]

[solid kiln]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by jeffgroves

[boreal zodiac]

That makes it understand the query, but not solve it

[marsh forum]

ah,OK

[boreal zodiac]

10 Floor (-1 + n + Log[2] - Log[1 + n]) Mathematica comes up with that but I'm not sure how you'd get there otherwise

[marsh forum]

that's nasty

Thanks though

[boreal zodiac]

At some point, doesn't that value just become 9 and stay 9 forever?

[marsh forum]

9 as in, floor(f(x))=81?

that would mean that the function has an asymptote, wouldn't it?

[boreal zodiac]

As in floor(10x/(x+1)) has a limit of 9 since it's the floor function

Well, since you're taking floor, a very flat asymptote yes

[marsh forum]

wait, what, as x approachs infinity, it approachs 3, doesn't it?

[boreal zodiac]

It's very close to 10x/x which is 10, but the x+1 means its always less than 10

so the floor is 9

[marsh forum]

ah, thanks!

ok, that makes it a lot prettier. Thanks!

Can I close the channel now?

[boreal zodiac]

Sure, if you want

[marsh forum]

.close

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[waxen spear]

why are we allowed to do this?

[quasi wasp]

are you wondering how they equal to each other?

[waxen spear]

yes

i think i just got it

[quasi wasp]

they've combined the terms in $1-\frac{\sqrt{3}}{1+\sqrt{3}}$

[solid kiln]

Talent Unlimited

[quasi wasp]

you can write as 1/1

and then take the lcm of the denominators, and simplify accordingly...

[waxen spear]

so in our case its $1 = \frac{1+\sqrt{3}}{1+\sqrt{3}}$

dammit one second

[solid kiln]

キマイラ

[waxen spear]

like this?

[quasi wasp]

exactly

[waxen spear]

ohhhh thats very smart okay i get it

thank you

have a great one

[quasi wasp]

which results in $\frac{1+\sqrt{3}-\sqrt{3}}{1+\sqrt{3}}$

[solid kiln]

Talent Unlimited

[waxen spear]

yea i see

so its $1 + \sqrt{3}$ finally right?

[solid kiln]

キマイラ

[quasi wasp]

hmm no, why do you say so

[waxen spear]

when we continue with our original problem

simplified

[quasi wasp]

this would become $\frac{1}{1+\sqrt{3}}$

[solid kiln]

Talent Unlimited

[waxen spear]

but we have the one one top of all of it

double fraction

[quasi wasp]

oh yeah, yes

it would become the inverse

[waxen spear]

yeah yeah thats what i was thinking too

[quasi wasp]

you were right 👍

[waxen spear]

thank you haha

and thank you for your time

[quasi wasp]

i forgot we were simplifying the denominator haha 😂

[quasi wasp]

np!

[waxen spear]

have a good one

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[supple bluff]

How many seven-digit numbers are there such that the digits are distinct integers taken from {1,2,...,9} and such that the digits 5 and 6 do not appear consecutively in either order?

[supple bluff]

<@&286206848099549185>

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[trim thicket]

try total cases - cases where 5,6 occur together

[supple bluff]

How do you count cases where 5,6 occur together?

I got 2x8=16

[trim thicket]

whhat is X 8?

[supple bluff]

$2\cdot8=16$

[trim thicket]

there are 6 possible places in which 5,6 can occur together

in a 7 digit no.

so i should be 6 X 2(coz 5 and 6 caninterchange) X no. of ways of arranging the rest of the no.s

[supple bluff]

ohh

$2\cdot 6 \cdot \frac{7!}{2!}$

[solid kiln]

schrödinger

[trim thicket]

yes

[supple bluff]

the set of 7-digit numbers where 5 and 6 appear but not consecutively. How do you count the set?

[trim thicket]

u just found the cases where 5 and 6 occur together, now subtract this from the total no of 7 digt no.s which can be formed

[supple bluff]

I already done this but there is a simpler solution which involves counting this set

[trim thicket]

also isnt this different from thhe original question

[supple bluff]

No it is not

[trim thicket]

the origiinal question doesnt require 5and 6 to appear

[supple bluff]

If you split the set into S1, S2, S3, S4 depending on whether 5 or 6 is in the 7 digit number

Then count each of this set

nvm

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[ionic hull]

I need help with question letter b

I have gotten the answer for a which is, how high above the ground is the top of the chimney is 20.2m. (please do check my answer also)

I'm now at B I need help, I was wondering if my diagram is correct and whether I should put 50m also since it says "from the same point"

[orchid wagon]

send your diagram

[ionic hull]

Here

[orchid wagon]

irrelevant but for simplicity its better if you express everything as 2d

[ionic hull]

Alright

[orchid wagon]

is 50m the cathetus or the hypotenuse?

[ionic hull]

The adjacent

[orchid wagon]

how did you arrive to the answer of part a?

[ionic hull]

Here

[orchid wagon]

seems to check out

now construct a 20deg angle from the 22deg angle

the point where it intersects should be the roof

[ionic hull]

Is this wrong though?

[orchid wagon]

well, kinda

,rotate

[orchid wagon]

this part is not the chimney, its both the house and the chimney

[ionic hull]

Oh I see

However the answer is correct?

[orchid wagon]

yes

[ionic hull]

Got it

Wrong?

[orchid wagon]

correct

,rotate

[orchid wagon]

for sake of convenience i shall name these points accordingly

part B requires you to calculate AD

and part C requires you to calculate DC

which shouldnt be too hard

[ionic hull]

Just minus right for part C?

[orchid wagon]

yes

[ionic hull]

Alright thank you so much! You were a great help

[orchid wagon]

anytime

[ionic hull]

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[covert lodge]

Hi I need help with this problem

[covert lodge]

Eight friends have to occupy eight single rooms reserved for them in the hotel where they have arrived to spend their holidays. How many ways can they arrange the rooms? When they arrive at the hotel, however, they find that four double rooms have been reserved for them. In how many ways can they form pairs?
How many ways can they occupy the four rooms?

I managed to solve the first question, but I can’t find a way to solve the 2nd one…

I tired C(8,2)+C(6,2)+C(4,2)+C(2,2) but the result is not correct

[wraith hinge]

the room thing is irrelevant i think

you just need the number of possible pairs

so you dont have to

distribute the pairs

to each room

[covert lodge]

I see I see, maybe it’s useful for the third question though

[wraith hinge]

so just divide by 4!

[wraith hinge]

whats the third question

oh wait nvm

[covert lodge]

Oh Okok

[wraith hinge]

there is a third question

[covert lodge]

Sorry what should I divide by 4?

[wraith hinge]

this would be the answer for the third question

[wraith hinge]

the C(8,2) + ..

[wraith hinge]

4! btw

[covert lodge]

Wait…

[covert lodge]

This is, and I hope I calculated it correctly, =50

No wait

Should I multiply or add the combinations

[wraith hinge]

multiply

mb i didnt notice that

[covert lodge]

It’s ok !👍

So…. I got 2520 possible combinations

[woven nova]

👍

[covert lodge]

For the pairs

Gotta divide that by 4! Right?

[wraith hinge]

yes

[covert lodge]

= 105

Well seems to be the right answer

Thanks mate

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[woven nova]

@covert lodge

are you sure the result is correct?

i don't think you have to divide by 4!

We choose two people for the first room
for the first person: 8 possibilities
for the second person: 7 possibilities
and so on
we get 8!=40320

To remove the double countings, we divide by (2!)^4

Another method would be:
In the first room we choose 2 from 8
in the second we choose 2 from 6
and so on
the possibilities of this are binom(8,2), binom(6,2),...
so in total we get:
binom(8,2) * binom(6,2) * binom(4,2) * binom(2,2) = 2520

[covert lodge]

.reopen

[trim jolt]

✅

[covert lodge]

I used the second method and it worked for me

[woven nova]

but why divide by 4! ?

[covert lodge]

That was my main comcern

Concern

I was about to ask

4! Are the permutations of the 4 rooms

But idk honestly

[wraith hinge]

you dont have to consider distributing the pairs to each room

its just making pairs

so the order of the pairs doesnt matter

if you were to distribute them it would be (8C2 * 6C2 * 4C2 * 2C2) * 1/4! * 4!

which is 8C2 * 6C2 * 4C2 * 2C2

[covert lodge]

So diving by 4! Basically divides the pairs into the 4 rooms

[wraith hinge]

no

dividing 4! gives you the total amount of different pairs possible without considering the order of them

for example (a,b) , (c,d) and (c,d), (a,b) is the same thing

youre going to distribute them later

[covert lodge]

But why is that? Isn’t the combination itself made for elements without an order?

Sorry for my level of English 😅

[wraith hinge]

youre multiplying the combinations though

so its a different thing

[covert lodge]

That’s true but how does it work then?

I never thought about it

[woven nova]

i made a little simulation to check it, and it also gave 2520 (not a proof, but very very certain)

the process:
create an array of the 8 people
shuffle them around
treat 2 people in a room as an unordered set, so that (a,b)=(b,a)
then add every new unique order of people to the solutions
do this very often
print the amount of solutions

[wraith hinge]

so if you dont multiply 1/4! (a,b),(c,d),(e,f),(g,h) and every possible order of these pairs becomes disntinct

which you dont want in this question

consider a pair as one person

youre not calculating the number of possible arrangements of 4 people

[covert lodge]

Wait so

They are repeating

And each time with a different order

That can be found by 4!

[wraith hinge]

yes

[covert lodge]

Thank you so much🙏

Should I close this?

[wraith hinge]

probably

[covert lodge]

.close

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[stiff locust]

how would I solve this

What I found out was to use only the left side of the absolute value

[digital bolt]

yeah so

[stiff locust]

Ok

[digital bolt]

you can just consider x from like

-6 to -4

or -10 to 0 or something

like, when x is around -5

|x| is always around 5

when x is negative, |x| = -x

so you can just replace |x| with -x

[stiff locust]

Ok so

5 - - x / 5 + x

5 + x / 5 + x no?

[bold jay]

use more parentheses pls but yea

[stiff locust]

wouldn't it be 0/0

[bold jay]

if you try to evaluate (5 + x)/(5 + x) at -5 yes

but that's not what you should do

other than at -5, (5 + x)/(5 + x) is just 1

when you look at a limit as x goes to -5 you're only concerned with what's happening near -5, not at -5

[stiff locust]

right right ty

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[keen void]

Determine if possible all pairs of integers (x, y) such that $x > y > 0$ and $x^2 - y^2 = 1573$
(Hint: Use the conjugate rule, factor the upper term, set up a few systems of equations and solve them in parallel.)

[keen void]

[solid kiln]

Merineth

[keen void]

I'm not even sure where in linear algebra this is located

[zinc ginkgo]

this problem is from a linear algebra class?

,w prime factorization 1573

[solid kiln]

Results provided by WolframAlpha

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Requested by rie.mann

[zinc ginkgo]

yea okay

factorize x^2 - y^2 then use ^

[keen void]

$(x+y)(x-y) = 1573$

[solid kiln]

Merineth

[keen void]

I think i need to study or read up on this

By any chance, do you know which area within linear algebra this is from?

[zinc ginkgo]

i don't see any reason anyone would use linear algebra to do this problem

maybe brute force solve it first, or wait for another helper, or ask in #linear-algebra

[keen void]

I'll try asking there! Need a break either way for now

tysm tho

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[copper kiln]

hi guys could someone help me? i been trying to solve this combined operations and after searching i dont know what to do with the numbers now, cause i dont got any sign to show me what i must do now

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[copper kiln]

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[grand vale]

I'm trying to understand the P vs NP problem. Is it saying that any problem which can be verified in polynomial time can be solved in the same order of polynomial, or that it merely can be solved by any polynomial time. Been looking alot, but I can't quite make sense of the formal defintion(to say the least), and the informal ones are somewhat unclear as to what it means

[grand vale]

it appears this is the wrong section to ask this in, so

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[warm dune]

i need help i understand linear approximation i just dont understant the first sentance

(dN/dt) = 0.07N(t)

ik this is the derivitive or somthing i just dont really understand it

[hallow spruce]

have you been exposed to differential equations before?

[warm dune]

i dont think so

[hallow spruce]

alright then we'll somewhat ignore it for a second

first off, set up your linear approximation

[warm dune]

thats the part im struggling with

ik its gona be the slope of the tangent line to n(t) at 4 and then plug in 4.1 into x

i just dont know how to get there from (dN/dt) = 0.07N(t)

[hallow spruce]

would it help if you rewrote this as N'(t) = 0.07N(t)?

[warm dune]

yes it would

thank you

would that mean its slope is 0.07*4

100

sorry

[hallow spruce]

it's neither 0.07*4 nor 100

[warm dune]

like 0.07*100

[hallow spruce]

better

[warm dune]

and y is 100

100 = 0.07*100(4) +b

y=7x+72?

and then plug in 4.1

100.7

[hallow spruce]

i'll stop you when you do something bad

[warm dune]

so then L(x) = 7x+72

and L(4.1)=100.7

would that be the answer then

cuz its asking for L(4.1)

[hallow spruce]

i haven't stopped you yet have I?

[warm dune]

ok so we are all good

thank you

you hellped alot with the re phrasing

[hallow spruce]

[warm dune]

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[drifting rose]

could someone explain to me how do you do something like this, I have never done vectors in the 3rd dimension before

[drifting rose]

<@&286206848099549185>

[left oriole]

any thoughts on how you would do it in 2 dimensions?

say it was D = [3,1] and E = [5,2]

[drifting rose]

would you add them together?

[left oriole]

nope, you want the vector that is the offset from D to E

so it's actually a subtraction

[drifting rose]

oh

so it would be the same with this?

[left oriole]

yep

works the same in any dimension

[drifting rose]

wait subtraction?

[left oriole]

yea

[drifting rose]

I cannot visualise that in my head

could you give me a diagram of it? 😅

[left oriole]

here's a random picture i found, does this help at all?

haha they managed to screw it up

OB should read (b1, b2, b3) not (a1, a2, a3)

lemme find a better one

[drifting rose]

yes i understand

hmm, thats weird though

the answer would be [-2, -1, 1] right?

apparently thats wrong?

[left oriole]

well this is the next question

difference

does it mean D - E or E - D

you're going from D to E

[drifting rose]

yes

[left oriole]

so the vector is E - D

[drifting rose]

so D - E

[left oriole]

because:

[drifting rose]

oh

[left oriole]

D + (E - D) = E

you want the vector that takes you from D to E

D + vector = E

solve for vector:

vector = E - D

[drifting rose]

ahh

so it would be 2, 1, -1?

[left oriole]

yep

[drifting rose]

thats weird to think abt

[left oriole]

it can be a bit confusing at first

you'll get used to it though

[drifting rose]

the vector itself is E - D

[left oriole]

yea

[drifting rose]

but we want D to E

[left oriole]

yes

D plus (some offset) = E

(some offset) = E - D

just remember it that way

[drifting rose]

i'm trying to imagine it as a 2d vector but I think thats not a good idea

[left oriole]

it's easier to draw in 2d

[drifting rose]

bc i know you can find the resultant vector by adding them together right?

[left oriole]

and you don't really lose anything important by looking in 2d

[drifting rose]

like tail to head

[left oriole]

in that picture above, B is the vector from A to C

you can think of A and C as points, or equivalently as vectors from the origin to those points

doesn't really make much difference

[drifting rose]

oh I think I know why I'm so confused

its because the letter represent the vector itself rather than 2 points like AB

[left oriole]

yea people tend to be kinda loose between those two concepts

you can think of a point say (1,2) as either just a point, or as the vector from (0,0) to (1,2)

in the latter case you do the difference (1,2) - (0,0) which is just (1,2) again

which is why it doesn't matter which way you think of it

[drifting rose]

ah

I think I got it now

just to quickly ask one more question

[left oriole]

sure

[drifting rose]

this one would be addition then right?

[left oriole]

well v is the vector from F to G, so you know (by what we said above):
v = G - F

so solve for G

you get G = F + v

so yep

addition

[drifting rose]

nice

ok thank you for the help

[left oriole]

sure, gl

[drifting rose]

👍

ty

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[grand sable]

i dont understand c

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[fresh gazelle]

Anyone knows how to approach this?

[fresh gazelle]

I’m thinking N(0) = 500, dN/dt = N

But it doesn’t seem to form a diff equation

[subtle prairie]

yes

it should be rather $\frac{dN}{dt} \propto N$

[solid kiln]

Dubs

[subtle prairie]

$\implies\frac{dN}{dt}= kN$

[solid kiln]

Dubs

[fresh gazelle]

What’s k?

[subtle prairie]

proportionality constant

[fresh gazelle]

How do I find the value for that?

[subtle prairie]

i mean, you don’t find the value of k, you need to solve the diff equation

[fresh gazelle]

Wiuld it be just like this?

Also, when I’m dealing with constants, am I putting e^C as well since it’s arbitrary?

[subtle prairie]

There is small thing you missed

in the second last step you took the exponential both sides right?

[fresh gazelle]

Wra says it’s this but i don’t know how

[fresh gazelle]

Yup

[subtle prairie]

$N= e^{kt+C}$

[solid kiln]

Dubs

[subtle prairie]

You took the exponential of the entire right side expression which includes C

the idea here is arbitary constants here are constant multiples not additive constants

[subtle prairie]

do you see how this step came?

[fresh gazelle]

Yeah, I understand somehow

But how does it equate to ce^kt?

[subtle prairie]

$N= e^{kt} e^{c}$

[solid kiln]

Dubs

[subtle prairie]

notice c is just a constant so e^c is also a constant, eg: e^4

Set $e^{c}= c_{1} \implies c_{1}e^{kt}$

[solid kiln]

Dubs

[fresh gazelle]

Wait, i didn’t know e^x+z = (e^x)(e^z)

Is that a rule?

[subtle prairie]

$a^{m+n}= a^m a^n$

[solid kiln]

Dubs

[fresh gazelle]

Ohh okay fair enough, that makes sense now

[subtle prairie]

for any real number base a

not just for e

[fresh gazelle]

Oh yeah, that makes sense

[subtle prairie]

e is actually just another number like 3 or 5

[fresh gazelle]

So for question b, it would just be plugging in values to formula?

[subtle prairie]

It has a value 2.72…

[fresh gazelle]

C = 500 right? How would I find k?

[subtle prairie]

500 is your intial condition

[subtle prairie]

ie x(0)=500

yep, so c=500

you can use part b to solve for k

[fresh gazelle]

Is this how I would find k?

[subtle prairie]

yep

[fresh gazelle]

Thanku so much!!

[subtle prairie]

hopefully you can now find the bacteria after 10 hours

[fresh gazelle]

That should be easy now once I’ve got the formula

Thanks!!

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[grand sable]

stuck on c and d

help me

ping

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@grand sable Has your question been resolved?

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[patent gale]

Hello Everybody! How do I go about solving this equation? Thank you in advance!

[light karma]

can you find the maximum value of the function

read the question like this, at what value of x(units) will I get the maximum value of function R(x) (maximum revenue)

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@patent gale Has your question been resolved?

[patent gale]

6250

that means that the x cord is the amount of units correct?

<@&286206848099549185> Just want to make sure that the answer is $6250 at 125 units

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[daring dragon]

How would I know to use +sqrt x-3 or -sqrtx/3?

[orchid wagon]

you dont

plus minus means the answer is both +sqrt(x-3) and -sqrt(x-3)

basically its a 2 in 1 problem

[daring dragon]

Ah.

[daring dragon]

So the answer I have is fine?

[orchid wagon]

yes

[daring dragon]

Alright.

Thanks

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[jovial anchor]

plz help trigo annoying

[faint quiver]

sure

[trim thicket]

ik

[jovial anchor]

Wtf do I do, trying to find c

U can't use sin, cuz it'll just give you a
can't use cos, because u don't have c
can't use tan cuz u it gives you a
pitagoras sentence doesn't apply (a^2 + b^2 = c^2)
so wtf do I do 😭

[wraith hinge]

Ahh

[vernal warren]

use sin to find a
use pythagoras

[wraith hinge]

just find a

[jovial anchor]

that's what I tried

but how?

[wraith hinge]

I think tan is better

tanA= BC/AC

[jovial anchor]

pythogaras doesn't apply since I only have 1 variable which is b

[wraith hinge]

a=20,000 isnt it

[jovial anchor]

that's what I figured

but I don't think that's true

[vernal warren]

sin gives c
sin(theta) = b/c

[jovial anchor]

theta? what's that

[trim thicket]

a+d=20000

[wraith hinge]

oh yeah

I though th ewhole side is a

now look in smaller triangle

get d

tan45=e/d

[jovial anchor]

same thing lmao

[wraith hinge]

you will get d

and a as well

you can get c+f

from pyhtagoras

and f from the smaller triangle ( can use cos45 or sin45 any u wish since you know both d and e)

when you know f, get c

@jovial anchor get it?

[jovial anchor]

wait wait..

so we found a and b

what now? we gotta find d

[wraith hinge]

$(a+d)^2+b^2=c^2$

[solid kiln]

EinPest

[wraith hinge]

actually a+d=20,000

Use the smaller triangle to get d

[jovial anchor]

alright, one sec

[wraith hinge]

use tan

for finding d

[vernal warren]

cant u use sin here?

sin = perpendicular / hypothenuse
= b/c

[wraith hinge]

yeah

sin=b/c+f

[jovial anchor]

sin?

[wraith hinge]

@vernal warren

[wraith hinge]

u proceed with tan

because tan45=1, easy calculations

[jovial anchor]

wha-

I'm so confused

we gotta find d

[wraith hinge]

Okay so listen

do we knwo that $a+d=20,000$

[solid kiln]

EinPest

[vernal warren]

oh yeah i didnt see f , my bad

[wraith hinge]

now look in the smaller triangle

[jovial anchor]

uh.. no

a = 20,000

we don't know how much b equals to

[wraith hinge]

$tan45=$\frac{e}{d}

[wraith hinge]

are you blind?

b=20,000

its given!

[jovial anchor]

yeah, I got that

[wraith hinge]

and a isnot equal to 20,000

[jovial anchor]

oh...

[wraith hinge]

its a+d=20,000

[jovial anchor]

I'm stupid nvm

[magic karma]

Use the 45 45 90 identity

[jovial anchor]

I thought this said a + b 💀

[wraith hinge]

damn

Okay

now finding d

look at smaller triangle

[magic karma]

d+a=d

[wraith hinge]

$tan45=$e/d

[solid kiln]

EinPest

[jovial anchor]

but we don't have e

[wraith hinge]

$d=$e

[jovial anchor]

and we don't have d

[solid kiln]

EinPest

[jovial anchor]

we only have tan45

[magic karma]

This is true because its a 45 45 90 triangle.

[wraith hinge]

e=45 look again

[wraith hinge]

yeah right

its isosceles, you can approcah it that way

[jovial anchor]

isosceles?

[wraith hinge]

@jovial anchor look at the question first

[jovial anchor]

I am looking at it

[wraith hinge]

you are provided with e and b

[wraith hinge]

scarp that

[jovial anchor]

I'm provided with e

[jovial anchor]

we don't know how much d is worth

[magic karma]

c = sqrt2*b

[wraith hinge]

yup, thats why lets dig into the smaller triangle

[jovial anchor]

ok

[wraith hinge]

this diagram can help if you don't understand tan

now give a relation between e and d

[jovial anchor]

here is smaller triangle

what now, How do we find d?

[wraith hinge]

yes look at the 45 degree angle

Do you know sides opposite to same angles are equal?

[jovial anchor]

sides of opposite to same angles are equal

that's a complicated sentence I do not understand

[wraith hinge]

Okay do you know what tan45= to in this triangle?

[jovial anchor]

equals to e/d

i think

[wraith hinge]

yeah!

right!

[jovial anchor]

so tan45=45/d

I can do that

[wraith hinge]

yeah and tan45=1!

so you have 1=45/d

can't you find d now?

[jovial anchor]

we transfer gaps

so d = 45

[wraith hinge]

100% correct

[jovial anchor]

Uh?

[wraith hinge]

now do u remember that $a+d=$20,000

[solid kiln]

EinPest

[wraith hinge]

didn't we calculate that earlier

can't you find a

[jovial anchor]

ok, but what if this is the triangle now

[wraith hinge]

yes we can still solve

[jovial anchor]

mk

[wraith hinge]

instead of tan45 we take tan55

[jovial anchor]

lemme try

[wraith hinge]

tan55=1.42

[jovial anchor]

so tan55 = 45/d

right?

[wraith hinge]

yeah

but lets not go there

lets stick to our original question

[jovial anchor]

got 64.26

[jovial anchor]

this is the original. A friend gave me a challange and changed it

[wraith hinge]

Oh

[jovial anchor]

so d=64.26?

[wraith hinge]

$d=$45/1.42

[solid kiln]

EinPest

[wraith hinge]

so $d=$31.6

[solid kiln]

EinPest

[jovial anchor]

eh?

[wraith hinge]

I think you used wrong value for tan55

tan55=1.42

[jovial anchor]

I did this: 45*tan55=d

[wraith hinge]

$tan55=$45/d
$tan55 * d=$45
$d=$45/tan55

[solid kiln]

EinPest

[wraith hinge]

no!

[jovial anchor]

uh..

[wraith hinge]

multiply both sides with d

and divide by tan55

[jovial anchor]

but we don't know d

ehhhh

[wraith hinge]

yeah no wories

you can still divide by d

the unknown d will cancel out on the RHS

and you will get a d on LHS

[jovial anchor]

wait a sec

here's the small triangle

Still don't understand how we find d from here

[wraith hinge]

by using tan55

tan55=1.42

so $e/d=$1.42

[solid kiln]

EinPest

[jovial anchor]

but tan gets you a

that makes no sense

it literally says here
tan alpha = a/b

[wraith hinge]

Im taking abt the smaller triangle!

[jovial anchor]

yes ik

[wraith hinge]

look at this triangle

[jovial anchor]

oh.....

d is also equal to a

just in the smaller triangle perspective

[wraith hinge]

YUP!

[jovial anchor]

oh ok, that's simpler

[wraith hinge]

exactly

now can u get d?

[jovial anchor]

yeah gimme a sec

got 64.26

is that correct?

[wraith hinge]

no!

How cant u solve this!

man work on linear equations first

[jovial anchor]

do u need to calculate tan55 before dividing?

[wraith hinge]

yeah

and it is 1.42

[jovial anchor]

oh, ok

now I got 28,336.1

this is the problem basically

in the end, I found that c= 34,657

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[dapper prairie]

Find the function that satisfies and knows f(1)=-3

[dapper prairie]

<@&286206848099549185>

[covert echo]

what do you need help with?

[dapper prairie]

I need to find a function that satisfies the above conditions

[kindred pier]

Who gave this to you and why are you trying to solve it?

[dapper prairie]

This is my exercise

[kindred pier]

Could you translate?

[dapper prairie]

This is the equation that the function needs to satisfy

[kindred pier]

Oh I see

[wraith hinge]

This is a linear ordinary differential equation

Separate Y' and -y on one side put everything else on the other, find and multiply both sides by the integrating factor

[dapper prairie]

because it has e^... so I don't know how to handle it

[wraith hinge]

Wait...

[dapper prairie]

Can you make it clear for me?

[wraith hinge]

Now that I saw that the translation changed the equation

[dapper prairie]

yes

so I had to send it back

[blissful bison]

read and continue:

[dapper prairie]

Next, use the stellar linear differential equation

[blissful bison]

what do you mean precisely?

the transformed diff euqation is :linear ordinary non-homogenous equations, its theory is very nicely discussed

[blissful bison]

yes

[dapper prairie]

Next we use this, right?

[blissful bison]

correct

u ' +p(x)u = q(x)

[dapper prairie]

Thank you, this is not taught in our Grade 11 program

[blissful bison]

i agree, i teach it to students of polytechnique

[dapper prairie]

so I'm having trouble handling it

[blissful bison]

on third semester

yes i understand

i can eventually give you a formula fo rthat

[blissful bison]

for equation of the form:

[dapper prairie]

this u(x)

I'm not sure if I solved it correctly

[blissful bison]

correct:

now initial condtion: y ( 1 ) = -3 <=> u ( 1 ) = exp( - 3)

[dapper prairie]

C=0

[blissful bison]

yes

[dapper prairie]

ohhhh

ýe

yes

=))) thank you very much

[blissful bison]

yvw)

[dapper prairie]

I have one more exercise, if you are free, can you help me?

[trim jolt]

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[lilac ridge]

hi again, how do i continue this exercise?
the question is "solve"

[trim thicket]

since the powers are equal

u can multiply both the fractions inside paranthesis together

and raise the whole thng to power 2n-1

[lilac ridge]

and the result is (-1)^2n-1 ?

[wraith hinge]

you can simplify this further

[lilac ridge]

how

[wraith hinge]

wait

no you fucked up

[lilac ridge]

?

[wraith hinge]

its not (-1)^(2n-1)

[lilac ridge]

then what?

[trim thicket]

yea

which is -1

[lilac ridge]

(-1)^2n-1=-1?

[trim thicket]

yea

[wraith hinge]

its not mentioned that n is specifically an integer so you cant say that i think

[trim thicket]

oh ok

ye

[wraith hinge]

(-1)^(1/2) is undefined, for example

[trim thicket]

i

lol

yea

so ig just lleave it aas (-1)^2n-1

[lilac ridge]

this is in the book

[wraith hinge]

i guess they want u to assume its an integer so like

just go with -1

[lilac ridge]

okay

thanks a lot @wraith hinge @trim thicket

.close

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[keen tusk]

Hey i got a problem with this

Equation

My subs teacher sended it to me

Becouse i wasnt at school

But its new topic

And i dont really get it

[vernal warren]

what do u not get?

[wraith hinge]

look up "solving a system of linear equations with two variables" this will be the best way you can learn in

there are a lot of resources online to guide you

[keen tusk]

Like why its happening why did the y dissepear

[keen tusk]

Oh okay thanks ill try it out

[vernal warren]

u will get it once u learn it

[keen tusk]

💀

[vernal warren]

these are known as simultaneous equations , and there are many ways to solve 1

[keen tusk]

Yeah but i dont understand it

[vernal warren]

here they use the elimination method where they eliminate 1 variable and get the value for the other one

[keen tusk]

The teachwr said there are like three uh ways to solve it and first is with +

[vernal warren]

the easiest method (in my opinion) is to substitute value of 1 variable from 1 equation in to the 2nd equation

[keen tusk]

Whaaaat

[vernal warren]

like here , from first equation
2x = -9+ 5y
x = (-9 + 5y)/2
use in equation 2
3(-9+5y)/2 + 2y = -4
and then solve for y

[keen tusk]

Oooh

Okay

Thanks

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[wraith hinge]

How do I move forward I am not getting it

Help

Tried something like this for the P part but got something weird and not matching with any of the options in column

[trim thicket]

fiitjee module?'

[wraith hinge]

why

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@wraith hinge Has your question been resolved?

[wraith hinge]

<@&286206848099549185>

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@wraith hinge Has your question been resolved?

[honest comet]

Zrisi a

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[solar tinsel]

I j need help

[solar tinsel]

It’s an ellipse and the questions asks for standard form

The question is

X^2+4y^2+14x+72y+273=0

[boreal zodiac]

Can you factor that?

[solar tinsel]

I keep messing up and don’t know where to end

[solar tinsel]

The answer is (x+7)^2/100 + (y+9)^2/25 = 1

[boreal zodiac]

Your steps seem correctish, but let's go through them. What's the first thing you do?

[solar tinsel]

Subtract 273 from both sides

[boreal zodiac]

OK, sure

[solar tinsel]

X^2+14x +4y^2 + 72 y = -273

Wait I might have forgot to make it subtract lol one sec

[boreal zodiac]

Your paper doesn't have the negative

[solar tinsel]

Yea just realized

Although it would only add up to -143