help-28

[true peak]

so i did get root 30 minus 2

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[glossy valve]

cosove

[grave elm]

well we wont solve it for u

we can guide you through it

but if you know how to do it, then you will probably get it done faster by just doing it yourself

we dont solve laziness

[steel solar]

For x, try to us the nested root technique (e.g. setting an expression inside the root equal to x)

[grave elm]

for z, try writing out first few terms

🔭

[rough tundra]

and for y expand the determinant along the first column

[grave elm]

both x and z are integers, so its not that difficult fortunately

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@wicked sigil Has your question been resolved?

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[keen vector]

you can check ur answer on a graphing calculator

[frigid estuary]

Is this not a tech free question?

[keen vector]

i don't know

but you are here so someone can check your work right?

what's your question?

[frigid estuary]

How to do this question

[foggy vapor]

So what is the slope of the line 2y + 6x = 15

[frigid estuary]

-3?

[foggy vapor]

Yes

So

[frigid estuary]

Ok so i gotta derive

[foggy vapor]

It functions as the slope of the tangent line at the point (0, 7.5) of the graph

[foggy vapor]

So the derivative of the graph is 3ax^2 + 2bx + c as you correctly wrote

And you know that at x = 0 the slope of the tangent line of the graph is -3

Are you able to connect those ideas together

[frigid estuary]

Um

[foggy vapor]

Nah its x = 0 still

[frigid estuary]

Wtf ;_;

[foggy vapor]

Not 15/2

[frigid estuary]

I dont understand

[foggy vapor]

at the point x = 0, you have y' = -3

[frigid estuary]

Yes

Ok

I see

[foggy vapor]

What you wrote says at the point x = 15/2, you have y'= -3

Which isn't what's happening

[foggy vapor]

Ye

So you have d and c now

Just a and b left

[frigid estuary]

So..

[foggy vapor]

Look at the second part of the question where it says yhere is a stationary point at B(3, - 6)

First of all

[frigid estuary]

Ok

[foggy vapor]

A stationary point at B(3, - 6) means the graph exists at point x = 3 and you have y = -6

Write that out

[frigid estuary]

What have i done wrong, it says b = -5/2

[foggy vapor]

This is so hard to read/follow

[frigid estuary]

Soz

@foggy vapor is this better

[foggy vapor]

Yes let me see

Darn I don't quite see what's wrong on either

[frigid estuary]

😞

[foggy vapor]

,w rref [[27, 6, 3], [27, 9, -9/2]]

[glossy valve]

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[foggy vapor]

OK it is -5/2

[frigid estuary]

Wth

[foggy vapor]

So you fucked up your algebra somewhere in there

Let me see

[frigid estuary]

Damn it

[foggy vapor]

Urgh we are both just so dumb

15/6 = 5/2 lmao

Your answer is right

[frigid estuary]

Ph

Oh

😿

Doing math at 1:40am is not for the weak

Ok i got it all now thanks

[foggy vapor]

Np

Gl

[frigid estuary]

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[acoustic flint]

The cross section of the right prism is a right angled triangle. find the value of cos <AFB.

[full forum]

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

[acoustic flint]

2

[hushed stone]

well ig we know all the angles

so lets first write them down

[acoustic flint]

huh

angles?

[hushed stone]

we know all the sides

and we have a right angle

so we can do inverse of any trigonometric function

for example

sin30 is 1/2

so if ration of perpendicular and hypo is 1/2

we know angle is 30

[acoustic flint]

AC=10cm

[hushed stone]

yep

ab/bc is 3/4

tan 37 is 3/4

so angle acb is 37

you can use the calculator and check

[acoustic flint]

CF=24 then AD=24

AC=DF=10

but i cant prove that adc is right angle

so i cant do pythagoras

[hushed stone]

first off

we know angle acb is 37

[acoustic flint]

okay

[hushed stone]

so we know almost all the angles of the intial fig

then maybe we can do something

tbh i not getting anything

[acoustic flint]

what i think is like this

i cant prove bcd and adf is right angle

[hushed stone]

if abde is a rectangle then adf is 143 degree

[acoustic flint]

no we need to stop at the angle there

because like cos <AFB we dont know what afb is

we cant know what <ABF is

[hushed stone]

ima do a method which may be labeled as cheating

since they asking cos then one angle has to be 90

[acoustic flint]

ok

[hushed stone]

only angle which look like 90 is fab

since we have that 90

oh wait nvm

[acoustic flint]

but we cant prove that its 90 even if it looks like

[hushed stone]

that wont work

tbh just ask your teacher

i not getting anything

[tight quest]

why can't you just find BF?

[shut prairie]

That's what I was thinking

You don't need the degrees dude

[tight quest]

Lol

[shut prairie]

Just go by the edges idk what they're called in english

Wait are you sure you got the edges correct?

I feel like the question wants a 7 24 25 or I might be just delusional

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[glad heart]

Okay how do I graph this

I know +4 means to shift up 4

I guess 1 is default?

log5(x) makes it 5 on the x axis ?

[unique wagon]

it seems to me that it is already plotted correctly?

log_5(1)+4 = 4 and log_5(5)+4 = 5

hence those two values

[glad heart]

Yeah I asked for help but don't fully understand it

[stone meteor]

sure plug in 5

as x

what should your y value be

log base 5 of 5 = 1

[glad heart]

so 1 here wuold be the x and =4 would be the y ?

[unique wagon]

u can try a few test values as i did, we pick the easy ones

log_n (1) = 0

[stone meteor]

yes

[unique wagon]

then the other easy value is
log_n (n) = n

[glad heart]

Okay then log_n(5)=1??

[unique wagon]

only if n=5

u may have seen
ln(e) = 1

convert back to exponential, itll be easier

5^x = 5

which is the same as
log_5 (5) = x

[glad heart]

Okkay I think I understand

In this example I got it wrong

this example is the right answer

it came out as 5,-4

not sure about the -4

[unique wagon]

log is an increasing function

why would u make it decreasing

[glad heart]

I guess the -5 I see where I messed up on that

Getting this one wrong too

[unique wagon]

what was the original graph they provided?

[glad heart]

I'm not sure what you mean? You're looking at it

[unique wagon]

ah the mistake is that the second coordinate should be

(7,6)

[glad heart]

Okay how do I get those numbers?

log 7 would give me 7?

[unique wagon]

log_7(7) is?

[glad heart]

1?

[unique wagon]

yes

1+5 is?

[glad heart]

1+5=6

[unique wagon]

yes

[glad heart]

Okay I see

Okay I get it now awesome

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[lyric oxide]

stuck on what to do for B.

for question A i got y=0.44x+22 just need help with b

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[devout nova]

sub in x=221

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[topaz shard]

yo

oh woops

[inland fern]

hellooo

can you help me with this integral

[inland fern]

how do i even start

[midnight acorn]

Uhhh try rewriting cot and tan? And splitting the integral along the +?

[inland fern]

wait a sec

[verbal jolt]

maybe you could try getting rid of the cos4x first

[midnight acorn]

Yea

[inland fern]

but how

[midnight acorn]

Identities?

[devout nova]

try simplifying the expression first

[inland fern]

cos 2x ones ?

[inland fern]

bu converting it to sin and cos ?

[devout nova]

use the formula cos²a = ½(1 + cos 2a)

[devout nova]

yes

[devout nova]

cos 2a = cos²a - sin²a

sin 2a = 2 sin a cos a

[inland fern]

on it

2+2cos^2(2x) \ cot(x)-tan(x)

now what

[inland fern]

?

<@&286206848099549185>

[gritty rose]

try writing the denominator in terms of sin and cos

[inland fern]

tried , doesnt help

[gritty rose]

it should

keep manipulating until you don't get fractions / fractions

[inland fern]

ok

thankyouuu soo much @gritty rose @devout nova

[gritty rose]

[inland fern]

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[glad marten]

What did I do wrong

[glad marten]

And also the next one

[gritty rose]

,rotate

[gritty rose]

in b, you can't always square both sides and keep equality if one side is negative and the other side is positive

[glad marten]

How else would you solve it

[gritty rose]

you just say square root is always positive or zero so there are no solutions

[normal tree]

a little bit irrelevant, but you also wrote that 16 + 5 = 19 😭

[gritty rose]

,w plot sqrt(x-5) + 4

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[glad marten]

Oh whoops…

[glad marten]

But there is no negative for a

[gritty rose]

what is a

[glad marten]

Like now I know b is no solution

[glad marten]

2a the question

[gritty rose]

where is that

[gritty rose]

,rotate

[gritty rose]

mistake here

[glad marten]

Ohh

So did 3.5?

[gritty rose]

plug it in and check

[glad marten]

How would I do b? Like how do I find the gf if I only have the gf for every 3 spots

I thought I would find the cube root but it gives me a number over 1

[summer flax]

is A 8/27

it is exponential decay so you have to make a equation with respect to time

as it decreases over time

[glad marten]

But I cant make the equation if I don’t find the gf

[summer flax]

lowkey hard to explain without just answering it maybe wait for someone else

the best i can offer is look at what you have mg at t=0 and mg at t=1.5 you can do smth with those frr

[glad marten]

For 5 c on the answer key it says for the exponent it must be 2h and not just h why do we have to multiply the hours?

Like I know it’s because it is every haft an hour. But it is not like we are increasing by 1 for the normal rate the normal rate is increasing by haft hours so why would we multiply it by two

[summer flax]

its exactly why cause it is 2x an hour or 2h

[glad marten]

Sorry I don’t UNDESTAJD

Because now it I want to input 4 for four hours after the medicine now we are measuring for 8 hours after

But our gf is for every haft hour so why are we making an equation for every hour

How do we know what is the normal amount on other equations

[summer flax]

because it says make an equation in terms of h, number of hours

to make half hours into terms of h, just do 2h

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[halcyon moth]

is what i did here wrong?

[umbral dome]

it's not the most direct approach but it seems correct

[halcyon moth]

whats a better way of solving it?

[umbral dome]

a more direct approach would be to set the two parametric equations equal to each other, then that gives you a linear system of equations to solve for t, m, n

either way works though

[analog sand]

The second way is better but imma check your way too

Oh nm its been checked

Nice

[halcyon moth]

Ty so my way works too?

[halcyon moth]

but like you bav e 3 variables tho

how do you solve

[umbral dome]

using gaussian elimination

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[halcyon moth]

whats that

can someone help me check again

this is 5a

idk why they got LS does not equal RS???

i plugged it to equation 1 btw

and since LS = RS then theyre coincidental rigiht

oh wait nvm was i supposed to check for x y and z equations

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[cold anvil]

Can someone tell me why i cany get the right answer

[cold anvil]

I thought my solution was rational enough

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[fierce spruce]

quadratic equation

[serene hazel]

!da2a

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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

@fierce spruce Has your question been resolved?

[brittle parcel]

you've convinced me. I'll vote for you

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[calm spoke]

j

[calm spoke]

could someone explain why k(k-1)=6 wouldnt work here

[rough tundra]

zero product property

the only reason that we can factorize and break it down is because the two factor multiply to 0

(a\cdot b=0\implies a=0\text{ or }b=0)

[glossy valve]

PajamaMamaLlama

[calm spoke]

ohhhh

thank you

.close

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[surreal path]

Hey guys so i was doing cubic root long division but i just cant get it
Calc and Ai kept saying its 24 but i somehow just cant get to the conclusion of 24

[surreal path]

[unreal wren]

It would be easier to find roots just using guess and check tbh

Like you can see that the last digit is 4, so what number could be cubed such that it's cube has 4 as it's one digit?

It can't be 1,2,3,5,6,7,8, nor 9. It can only be 4, then check that 14^3 is too small, then obviously it would be 24 because 34^3 is way too large

If you really want to use long division then search up a tutorial on yt or continue asking for help here

[surreal path]

I did
Thats in the picture i showed

But then again i want it to be 100% instead of guessing

<@&286206848099549185>

[unreal wren]

Hold up I'mma do research

[unreal wren]

5824 comes from 91 times 64 right?

But where did you get 91

[surreal path]

I didnt

And i dont know

[unreal wren]

Oof

So you just entered random number there or what?

[surreal path]

What do you mean?

[unreal wren]

Where did you get 5824 from?

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[surreal path]

8 subtracting 13??

[unreal wren]

Oh yes sorry

[surreal path]

Welp

[rocky rapids]

!xy

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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.

[surreal path]

?

[analog sand]

Read what the bot said

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[analog sand]

What no

Put the original q

[surreal path]

question?
in the picture THERE IS the original question

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[surreal path]

[fervent dove]

@surreal path they want you to send the actual question you are attempting, not just your attempted solution

its sometimes hard to help by just seeing your attempt and a description of the question

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@surreal path Has your question been resolved?

[normal tree]

isn't the question pretty straightforward? calculate the cube root of 13824 by hand

that's pretty clear, and I don't think you need the original question

[analog sand]

Ok so the number is 13824. Let's start with 8 as our divisor:
We get 8* 1728 = 13824.
Then we can divide 1728 by 8, which gives us 216.
Lets divide that again, so we get 27.

So so far we have

8*8*8*27

Which is 2^9 * 3^3

[analog sand]

Now we can see that when we take the cuberoot of this number

We get 2^3 * 3

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[analog sand]

Which is 8*3

Which is 24

Sorry for not answering earlier, i got a little confused seeing the work

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[undone inlet]

Yes

[onyx glen]

$z = vx - c \ln(x)$

[glossy valve]

Ann

[onyx glen]

this?

[undone inlet]

Yes

[onyx glen]

you're cooked.

!xy

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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.

[undone inlet]

Well I was solving some physics and it came up

[onyx glen]

ok show the original physics problem then ig

[agile lake]

hi

[undone inlet]

So there was puck sliding around a wall with N=(v^2/R)*m and friction coef of a wall is known

Then I would solve for v(t) through integration

[urban jacinth]

Interesting

Show your work

[undone inlet]

Then I would absolutely love to get x(t) as well so I couldnt come up with better idea than to integrate 2nd time and get this

[onyx glen]

hi. this channel is currently occupied by someone else's question

!redir

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This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[onyx glen]

!occupied

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[undone inlet]

Oh nvm I messed up the integration part

Still curious how could one express smth like this tho

[onyx glen]

you can't

unless you're willing to fuck with the Lambert W function or whatever ig

[undone inlet]

Oh alright

Thanks for trying to help either way

.close

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[lime hull]

how do i work this out?

all i know is that the length ratio between the triangles ABE and ACD is 2:5

and that to get the area you need to square something

im stuck on what to do calculations wise

[boreal slate]

lets say that AB and BC are the bases of the triangles and they each have corresponding heights

what is the ratio of the base of the big triangle to the small triangle?

and same with the heights

[lime hull]

3:2?

[boreal slate]

not quite

oh wait my bad

i meant to say AB and AC

[lime hull]

oh right

5:2

?

[boreal slate]

yes

[minor veldt]

is that precal

wait oops wronv channel

[boreal slate]

so on the big triangle, if we have the base of the bigger triangle is (5/2)b and the height is (5/2)h in comparison to the smaller triangle, how do the areas compare?

[lime hull]

i am not sure

where did the b and h come from

is that just showing base and height

[boreal slate]

area of the smaller triangle is bh/2

area of the bigger triangle would be changed based on the scaling factor of 5/2, so the base and height would be scaled by 5/2

[lime hull]

could you try to explain that using calculations with the 8cm^2

[boreal slate]

so we know that bh/2 = 8cm^2 for the small triangle

now we need to find the area of the bigger triangle

we know the base is (5/2)b

and the height is (5/2)h

so the area of the bigger triangle is (5/2)^2*(bh/2)

do you understand where that came from?

[lime hull]

is the b in this the base of the smaller triangle?

[boreal slate]

yes

sorry if i did not make that clear

[lime hull]

no worries

okay give me a moment to try understand

[lime hull]

i think so

we get the area of the smaller triangle, 8cm^2, then multiply it by the scale factor 5/2 squared
and its 5/2 squared instead of just 5/2 because its an area ratio so we square the length ratio

is that right

to get 50cm^2

final answer

[boreal slate]

yup!

a more general rule is that if you have a scaling factor, lengths multiply by the scaling factor, areas multiply by the square of the scaling factor, and volumes multiply by the cube of the scaling factor

[lime hull]

ahhh thanks

thank you so much for the help

[boreal slate]

youre welcome

[lime hull]

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[lime ether]

nice

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[primal pelican]

I'm lost

[sour prawn]

I think most people would be. You haven't provided the problem you're supposed to solve.

What are you trying to do?

[primal pelican]

mb

[sour prawn]

Gotcha.

So you got the diagram.

[primal pelican]

yes

[sour prawn]

I might suggest changing y to 2y.

It'll make your calculations a little easier.

[primal pelican]

why

[sour prawn]

You can call that side of the field whatever you want, and since you'll be dividing it in half, you'll have an easier time with each half being exactly y feet long.

Keeps you from dealing with unnecessary fractions.

Otherwise, you have your area formula good.

Your perimeter formula also looks good, but if you change the sides to 2y, you'll need to adjust that accordingly.

So what do you think is the next step?

[primal pelican]

so i can keep A and P as i have?

[sour prawn]

Sure! If we keep it simple, and we just use what you have written.

Since you're looking to minimize the cost of the fence, what is your next step?

[primal pelican]

dirivative

[sour prawn]

Of which equation?

[primal pelican]

-3x^2/2

[sour prawn]

Sorry, which of the two: perimeter or area?

[primal pelican]

area

[sour prawn]

Are you trying to minimize the area?

[primal pelican]

perimeter

[sour prawn]

Right.

That's the one that would give you the critical points related to the amount of fence you need.

So what's the derivative of the perimeter equation?

[primal pelican]

.

wait

-6x/2

-3x

[sour prawn]

Which variable are you differentiating with respect to?

x or y?

[primal pelican]

y

[sour prawn]

Whichever you choose, you would need to do implicit differentiation on the other term, then.

The other possibility is that you convert everything to a single variable.

That is probably easier.

[primal pelican]

i can do both

[sour prawn]

You can do both what?

[primal pelican]

implicit differentiation, convert everything to a single variable.

[sour prawn]

I recommend the second one.

So how would you go about converting to a single variable?

[primal pelican]

the -3x?

[sour prawn]

I think you're getting caught up in some of the math you already did on the page.

Right now, we have two equations:

$$1.5=x \cdot y$$ and $$3x+2y=P$$

[glossy valve]

bloogercloge

[primal pelican]

im confused what your trying to say

[sour prawn]

And you want to differentiate the second equation.

[primal pelican]

oh we going back to the begining

[sour prawn]

Yes.

[primal pelican]

oh

[sour prawn]

Cause some of your stuff is wrong.

So if you want to change the second equation into one of a single variable, what could you do?

[primal pelican]

set the perimeter one =y

[sour prawn]

Sure!

[primal pelican]

then multiply by x

[sour prawn]

Wait.

[primal pelican]

from a=xy

oh

[sour prawn]

I don't think this is super helpful at this point.

[primal pelican]

ok

[sour prawn]

You want to find some interplay between the two equations.

How can you use the first equation? It's there for a reason. You have two equations and two unknown values.

[primal pelican]

substitution

[sour prawn]

Right!

So how does that work?

[primal pelican]

seto one = to a variable then in the other equation put what the variable =

[sour prawn]

Right, so what does that give you? Say you want to replace y in the second equation.

[primal pelican]

so set it to y

?

[sour prawn]

Right, this is where you would work it out on the paper or type out some equation in here.

What do you get when you re-order the first equation in terms of y?

y = ?

[primal pelican]

-3x/2

[sour prawn]

How do you get that?

[primal pelican]

wym

[sour prawn]

How did you reach that answer?

[primal pelican]

3x+2y
2y=-3x
y=-3x/2

[sour prawn]

You've added an equal symbol in between the first and second lines.

What is the first expression equal to?

3x+2y=?

[primal pelican]

perimeter

[sour prawn]

Okay, so why does P disappear in the second and third lines?

[primal pelican]

oh

[sour prawn]

Right.

Is there an equation that you have numbers for?

[primal pelican]

thought it was just like a placeholder to know what it is

xy=1.5m

[sour prawn]

It is, but you can't get rid of placeholders! (Otherwise, they're not really holding a place very well.)

[sour prawn]

Right!

So manipulate this one to get x or y by itself. I recommend y.

[primal pelican]

3x+2y=p
2y=p-3x
y=(p-3x)/2

[sour prawn]

You're manipulating the wrong equation.

We can't really do much with that one until we know either x, y, or P.

Manipulate xy=1.5

[primal pelican]

y=1.5/x

[sour prawn]

Great.

Now you can substitute.

But substitute into the original equation:

P=3x+2y.

[primal pelican]

i might be stupid

[sour prawn]

Don't sub into your complicated one.

[sour prawn]

Nope!

This stuff is challenging until you've done it a few times!

[primal pelican]

i forgot about the 1.5

[sour prawn]

Math is all about learning to see what you're not getting.

[sour prawn]

Most people do. But, unless your teacher/professor is unusually mean, any information you're given is probably useful in some way.

So, after substitution, what is the equation?

P = ?

[primal pelican]

3x+3/x

dirive?

[sour prawn]

Yes! Now you can take the derivative!

P' = ?

[primal pelican]

3-3/x^2

[sour prawn]

Yes!

What are the critical points?

[primal pelican]

find 0

[sour prawn]

$$3-\frac{3}{x^2}=0$$

[glossy valve]

bloogercloge

[primal pelican]

-1,1

[sour prawn]

Okay, great.

So, you can do something with that.

Can x ever be negative?

[primal pelican]

yes

[sour prawn]

Are you sure? What does x represent?

[primal pelican]

wait are we talking bout the same thing

[sour prawn]

Yes.

[primal pelican]

.

[sour prawn]

You have two critical points, but not all of them may be meaningful.

In your original problem, what is x?

[primal pelican]

area and perimeter cant be -

[sour prawn]

Right. You couldn't build a fence with negative length.

[primal pelican]

unless its talking bout direction?

[sour prawn]

Is it?

[primal pelican]

no

[sour prawn]

Right.

So now you need to check that 1 is a minimum of your function and not a maximum.

(Given that you only have one answer, it's probably a minimum. But it's always important to check.)

[primal pelican]

a table?

[sour prawn]

Sure! However you learned how to do it.

I always did mine on a little number line.

0 --------- 1 ----------- infinity

In between 0 and 1, is your derivative positive or negative?

[primal pelican]

second dirivitive test?

[sour prawn]

I don't think you need to do that.

[primal pelican]

oh

[sour prawn]

You can, but it's probably easier just to calculate the value of the derivative at 1/2 or something.

[primal pelican]

it goes positive

[sour prawn]

Oh!

That looks great.

We both forgot a critical point, though.

[primal pelican]

0

[sour prawn]

Right. So if you toss 0 in, what does that change?

[primal pelican]

VA

DNE

[sour prawn]

Right. Does it change any of the calculations at all?

[primal pelican]

no

[sour prawn]

Right.

So between 0 and 1, your derivative is negative. The perimeter is decreasing.

Then after 1 and moving upwards towards 1.5, the perimeter is increasing.

That sounds like a minimum to me.

[primal pelican]

i should graph it

[sour prawn]

You can.

Your little number line chart basically does that for you.

[primal pelican]

Ik how tho

[sour prawn]

Sure.

It's just not necessary.

[primal pelican]

ik

[sour prawn]

If you were to do that on an exam, it would be wasted time.

But feel free to graph it if it would help your thought process now.

[primal pelican]

unless it asks for it

[sour prawn]

Right.

[primal pelican]

how do i show its a min

[sour prawn]

My teacher, back in the day, would have accepted the little number line chart.

[primal pelican]

back in the day?

[sour prawn]

I took calculus probably 10 years ago.

You could also write something like:

$$P'(x)<0, 0<x<1$$
$$P'(x)> 0, x>1$$

[glossy valve]

bloogercloge

[sour prawn]

But that's pretty formal.

For most high school or undergrad calc classes.

Do you understand how this shows you're at a minimum value? Even without the second derivative test?

[primal pelican]

never seen it like this

ill stick to the line thing

[sour prawn]

Yeah, I would. That should be enough.

You can just make a note near the line that 1 is a minimum value.

So your teacher can track your thought process.

So now that you have a minimum at x=1, how do you finish the problem?

[primal pelican]

is just where - changes to +

[sour prawn]

Yes!

[primal pelican]

is the min

then max is opposite

[sour prawn]

And changes from + to - are maximums.

Right!

[primal pelican]

k

[sour prawn]

Because the derivative is the slope of your graph. It'll be 0 at the peaks and the valleys, but until it actually hits that point, the function is increasing or decreasing.

And that corresponds to the + and - values of the first derivative.

[primal pelican]

ye

[sour prawn]

So wrap it all up for me.

[primal pelican]

im shooting blanks

[sour prawn]

What is the ultimate goal of the problem? That should always be your starting place when you run out of ideas.

[primal pelican]

minimize

[sour prawn]

Minimize what?

[primal pelican]

cost

well amount of fence

[sour prawn]

And the cost is essentially the same as the length, right.

[primal pelican]

ye

[sour prawn]

So you have the x value for the length of the fence.

[primal pelican]

do i

[sour prawn]

What's the x-value that minimized the function?

[primal pelican]

1?

[sour prawn]

Right.

You had three critical points: -1, 0, and 1.

Two of those make no sense for building fences.

And 1 is a minimum, based on the line you drew.

[primal pelican]

dont want to be indebt fences

lol

[sour prawn]

So can you build the fence now?

Or are you still missing information?

[primal pelican]

y

[sour prawn]

Okay, so how can we solve for y?

[primal pelican]

sub

[sour prawn]

Given x=1.

[primal pelican]

y=1.5

[sour prawn]

Great.

[primal pelican]

this cant be right

[sour prawn]

Well, there's an issue with the units.

[primal pelican]

yes

[sour prawn]

But you have the numbers right.

[primal pelican]

the ratio is right

[sour prawn]

When you derived the function, you got $3-\frac{3}{x^2}$

[glossy valve]

bloogercloge

[sour prawn]

It really needed to be $3-\frac{3,000,000}{x^2}$.

[glossy valve]

bloogercloge

[sour prawn]

Because the area is 1.5 million sq ft.

[primal pelican]

so i just gotta split the 0s?

[sour prawn]

Basically. When does x^2=1,000,000?

[primal pelican]

y=1500
x=1000

[sour prawn]

Right.

Sorry for not catching that sooner.

But that's where you can stop.

If the question asked you specifically for the perimeter, you'd want to calculate that.

But your teacher just asked, "How can he do that?"

And you've given the different lengths of fencing.

[primal pelican]

so just the lengths

[sour prawn]

I think that's enough.

If you have time on an exam, I might calculate the perimeter just to be safe.

But if you're crunched for time, no need to do more than they asked.

[primal pelican]

ye

wanna walk me through another?

[sour prawn]

Unfortunately, I have to head to bed.

But somebody else might be able to!

[primal pelican]

ok thanks for your help

[sour prawn]

And if you just take it step-by-step, you've got the common-sense intuition you need.

You caught the issue with the units, so your brain is recognizing when you've made an error somewhere.

[primal pelican]

i just get confused

then i feel overwhelmed

[sour prawn]

With most people, they just let their work get disorderly. If you keep your work organized on the page and go step-by-step, without jumping, then you can go back and check things or cross out work and start back at an earlier step.

It helps prevent confusion.

If you've written 50 things at different points all over the page, then it's hard to keep track of what you've done.

[primal pelican]

like idk whats next or remember what to do

its just like this for word problems pretty mych

[sour prawn]

Always a common problem! Just remember the goal of the problem, and then try to figure out whether you've used all of the information you've been given.

But I think Pai may be trying to take over.

🫡

[latent drum]

Sorry to interupt, but @primal pelican did you manage to finish the fencing problem?
I dont normally leave in the middle of helping* but i was cooking dinner 😅

[primal pelican]

well earlier i couldnt remember how to do simple algebra with synthetic division or finding x=0 of trig

[latent drum]

Oh not tsking over. Just wanted to know how it went

[primal pelican]

i found out my math wasnt mathing

i accidentially put in 700 in the calculator instead of 750

@latent drum i had y=65 but was supposed to be 75

[latent drum]

We can work on it together in a bit then. Whats the problem youre currently getting help with now?

[primal pelican]

think its done now

[latent drum]

Oh its the same onem

[primal pelican]

old

[primal pelican]

new

@latent drum

[latent drum]

Got it got it
Let me catch up with what you've already worked out then

[primal pelican]

they were similar

we had one that gave us perimeter

the new one gave us area

this new one should be done

the answer is correct according to the backof the book

[latent drum]

Oh nice then

[latent drum]

Good start
Love that you drew a diagram. Keep going

[primal pelican]

the base should be a perfect square right?

[latent drum]

Thats right, because they stated the base is a square
What about the sides of the box?

[latent drum]

Try the 2nd volume equation again
Are you sure you mean 2xy?

[primal pelican]

X squared

[latent drum]

Yes, x²
We want to keep the proper notation bc 2x =/= x²

[primal pelican]

i just messed up

[latent drum]

No worries
Go ahead and correct it
Is there anything else you can writr out before sharing and update of your work?

[primal pelican]

area =2x+4xy

[latent drum]

You did it again 😅

[primal pelican]

wut

[latent drum]

It isnt 2x

[primal pelican]

forgot to change it

x^2+4xy=A=1200

[latent drum]

Good
Whats the next thing you can do?

[primal pelican]

make it substitutable

for y

[latent drum]

Perfect
What do you get once youre finished with that?

[primal pelican]

numbers

[latent drum]

Lol thats why i saiid once you finish

[primal pelican]

then put it in volume then dirive

[latent drum]

Perfect
Remember to simplify so you can just use chain rule instead of product rule

[primal pelican]

Why di I need chain

Quotient?

[latent drum]

Thatd why i said to simplify
Less algebra to deal with if you simplify before deriving

[primal pelican]

how

[latent drum]

Show me first what you get after substituting y in your volume formula

[primal pelican]

300x-x^3/4

[latent drum]

How did you get 3/4 for the exponent?

[primal pelican]

300x-(x^3)/4

v=

[latent drum]

Ohhh okay

Good good

Do you see what i mean now about simplifying though? 😅

[primal pelican]

findwhere its 0

[latent drum]

Thats right
Remember to only use the value that makes sense for the problem

[primal pelican]

sqrt400/3?

thats very wrong

20

[latent drum]

I assume you figured out the mistake?
Thats good!
Go ahead and find y then the volume

[primal pelican]

put 100 instead of 300

[latent drum]

At least you found it. Thats good you can self correct

[primal pelican]

didnt seem right

its a max

thats good

[latent drum]

Right
But you still have to finish the problem
Did you get y and the volume yet?

[primal pelican]

do i plug that intop the area euation

[latent drum]

Yeah. But skip down to where you already solved for y so you dont have to solve for it again

[primal pelican]

y=10

[latent drum]

Awesome
And now the volume?

[primal pelican]

4000

[latent drum]

Awesome
So the max volume you can have with the given material is 4000cm³

[primal pelican]

yes

is that it

[latent drum]

Thats it 👍

[primal pelican]

ty

[latent drum]

Any time ⭐️

[primal pelican]

ill be back tommorow with more of these fyi

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[urban nebula]

My idea was to have n divide the number 2023^k - 1 and claim that since 2023^m-1 divides 2023^k-1 if m|k and take n as a factor of 2023^m -1

[hoary ember]

which part are you on?

[urban nebula]

I am on the second one

[uncut skiff]

If you have any two solutions then their product is also a solution

So you can construct infinitely many solutions

[urban nebula]

Oh

3 and 9 are solutions

[uncut skiff]

You'll have to prove this tho

[urban nebula]

That looks much easier to prove

[hoary ember]

i was thinking if m is a solution, then 2023^m-1 is also a solution

[urban nebula]

Yes but

That is even

. solved

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[hoary ember]

you got it?

[urban nebula]

I am trying the method he told

I shouldn't have used .solved though

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[heavy scarab]

We know that in 1D a cubic function has 3 roots. Can we say anything similar about say, a function 2xy^2 which has degree 3 in 2D?

[onyx glen]

not really cause the zero-set of any such function is a curve and not a finite set of points anymore.

!xy though

[full forum]

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.

[heavy scarab]

Ahhh I see, yes. Thanks!

What do you mean by the way with !xy?

[fast peak]

https://en.wikipedia.org/wiki/XY_problem

[onyx glen]

http://xyproblem.info/

it's because we suspect that this question came from some bigger problem

and we would rather address that than answer a somewhat out-of-left-field query

[heavy scarab]

I see i see, so we are talking about implicit surfaces in class, and the context here is that given some data points, we are using moving least squares (MLS) to approximate the underlying function (of which the zero level set is the surface, or curve in 2D)

In doing this, we can use polynomials as our basis functions. And we can try out different things like linear basis {1, x, y} or quadratic basis {1, x, y, xy, x^2, etc.}. I think the point that was trying to be made here is that using a quadratic basis or some higher order polynomials will lead to new zero level sets somewhere in R^2, i.e. using a quadratic polynomial will lead to two new zero crossings instead of a single one, so we tend to just use a linear basis. But I still can't view this intuitively, i suppose

[onyx glen]

hm...

not sure i understand that

[heavy scarab]

Yes, this is a more graphics adjacent issue than mathematics I think, hence the reformulated question hahah. But I will ask them this some other time, for now thanks a lot!

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[lament compass]

For a telescoping series, how do you know how many partial sum terms to write out before you can notice a pattern / how can you see the pattern?

[lament compass]

For example this question

[grave elm]

we usually do partial fraction decomposition

[lament compass]

you have to write out till the 4th before you can see the pattern

but like on a test how would you know itd be the 4th before you like give up

[lament compass]

hi and yeah I get that part atleast

[void nova]

For this reason I don't like writing them out fully, I prefer to use summation notation (with Σ) and change of variable

[lament compass]

can you show what you mean please?

like from what I understood you do this

and you go from the first terms to last terms to find Sn as like an equation that you can do lim n--> infinity of easily to prove if there is a value of S so you can say whether the original series converges or diverges

[void nova]

Sure

[lament compass]

wow i see I understnad that i think

but can you do that with like all telescopign series?

or like I guess what im trying to say is it feels like rather than following the steps or whatever I was taught you kinda just manipulate it like its algebra and solve it but will you always be able to do something like create the variable to separate sum_n=4 ^ 3 1/n and stuff like that because I feel like on a test it would be hard to see that vision

[analog sand]

Yes

[analog sand]

It's a bit harder than writing the entire series out but definitely less time consuming.

And less a waste of space as well.

[lament compass]

do you think its worth learning method 1 or 2 because I understand how both work but like realistically on the tests when the harder problems show up, the tricky ones that you dont see in class yk will I be able to easily see hwo to manipulate the sums like that?

[lament compass]

yeah

[analog sand]

With practice, yes you can.

[lament compass]

but im ujst trying to do whateve rmethod is safer even if it takes a little extra time

[analog sand]

So method 2.

But only if you have enough time to practice before the test.

[lament compass]

hmm ok Ill have to grind hella today then 😭

[analog sand]

Otherwise just expand for now and learn it later.

[lament compass]

lmao test tomorrow

wait does this work with other series too then?

[analog sand]

Yes

[lament compass]

@analog sand wait do you know then so when you do the fraction decomp and u see 1/n - 1/? then you just try to manipulate the second term to be 1/n + ? since you know something will have to cancel out?

and if the first term was like 1/(n+1) or something you do the same where you just try to get that term again so you cancel it out?

or is there another strategy

[analog sand]

Yes that's how it works

[analog sand]

Yeah

[lament compass]

ok that makes sense for now... Ill try practicing this before I ask anything else lol

ty @analog sand and @void nova

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[glacial marsh]

is this right?

[hot herald]

yes

[foggy vapor]

Sure is

[gloomy sail]

yes

[glacial marsh]

i’m confused if i count the ‘-‘ in front of the 3 when timing

oh really!

thank you guys

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[glacial marsh]

is this right ?.😭

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[runic galleon]

yes

[runic galleon]

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[rustic briar]

what would the Degree of this polynomial be? I answered 4, however my teacher graded it as incorrect.

[serene hazel]

!show

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[lime ether]

where is 4 coming from

[rustic briar]

idk

[nimble crane]

the question here really is: this is a polynomial in what variables?

if it's a polynomial in both m and n, I would agree with you that it's degree is 4, because of the m^2n^2 term

if it's only a polynomial in n or m though, then it'd be 3

[rustic briar]

I guess that's what they meant since they said 4 was wrong.

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[vocal sonnet]

I got v_y as x^2 / (x-y)^2

since
a = xy
a' = x
b = x-y
b' = -1

then
(x)(x-y) - (-1)(xy) = x^2 - xy + xy = x^2
and
b^2 = (x-y)^2

so

$v_y = \frac{x^2}{(x-y)^2}$

[glossy valve]

smeagol

[vocal sonnet]

then for the second time

[onyx glen]

,w d/dy (xy/(x-y))

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[onyx glen]

ok your v_y is correct

[vocal sonnet]

a = x^2
a' = 0
b = (x-y)^2
b' = 2(x-y) * -1

so

[indigo pier]

is it crazy my brother is doing this at 12

[magic obsidian]

no

[indigo pier]

oop wrong channel

[magic obsidian]

where'd you get -1 from

[vocal sonnet]

-y

[magic obsidian]

y is a constant

[vocal sonnet]

no

it's partial with respect to y

[magic obsidian]

you're solving v_yx right?

[indigo pier]

isn’t algebra supposed to be taken and 8th or 9th grade

[vocal sonnet]

I put it in the wrong box

[onyx glen]

you're doing (v_y)_x yes?

[vocal sonnet]

[magic obsidian]

are you doing v_yx or v_yy

[vocal sonnet]

I was doing v_yy

but I put it in the v_yx box

[magic obsidian]

,w d/dy (d/dy (xy/(x-y)))

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Requested by hailinqs

[magic obsidian]

this expr is correct for v_yy yes

[vocal sonnet]

ok

i'm annoyed a bit

I did the problem like 4 times

but now I got it

thank you

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[haughty ember]

Question 9

[haughty ember]

Lmk if u want me to translate it

Aparentou the answer is 8

Apparently*

[steel solar]

Sure

Actually wait, nah

[haughty ember]

I’ll do it anyways

[steel solar]

Ok, YES, locked in, I need a translation

[haughty ember]

lol

[steel solar]

I'm probably missing something

<@&268886789983436800> Yooo, fam! Free money! Definetely not a scam!

[haughty ember]

The 40 students in a class sit in n rows of desks, each with (n + 3) desks.
If no desk is left empty, how many students are there in each row?

[analog sand]

This guy fr.

[haughty ember]

lol

Oh hey 👋

[analog sand]

Hallo

[haughty ember]

😓

Lowkey living here rn

[steel solar]

Ok, so, I was missing something

[haughty ember]

What did I get wrong

[steel solar]

The answer IS 8, because n is not your answer

[haughty ember]

Ohhhhhh

5+3

[steel solar]

Notice what the question is asking

[haughty ember]