help-28

[rapid rain]

how does cos(7pi/8)^2 become cos(14pi/4)^2???

[gritty rose]

maybe simplify by splitting the fraction into two ?

[polar plank]

Oh I see

I guess it's unsolvable then idk

[rapid rain]

it is solvable

what's the formula for cos(2x)?

[gritty rose]

oh you entered 0 and that's the right answer?

[polar plank]

0's the wrong answer

According to the program

[rapid rain]

the right answer is this

[gritty rose]

i see. i thought the red triangle meant the displayed answer was wrong

[rapid rain]

.

[polar plank]

cos(x+x) which is cos(x)cos(x)-sin(x)sin(x)?

[rapid rain]

yes so cos^2(x) - sin^2(x)

can you get rid of the sin^2(x)?

[polar plank]

I thought that's what I did tho no?

The cos^2(x)-sin^2(x) thing

[rapid rain]

well no the thing before that is wrong

cos(7pi/8)*cos(7pi/8) is definitely not cos(7pi/4 + 7pi/4)^2

anyways

cos(2x) = cos^2(x) - sin^2(x)

Can we write cos(2x) = (Something without sin^2(x))?

[polar plank]

Uhhh

Yeah I'm not sure how tbh

[rapid rain]

what is sin^2(x) + cos^2(x)?

[polar plank]

Ohhhhhhhh

Ok 1-cos^2 then

[rapid rain]

yes

[rapid rain]

so back to this?

[polar plank]

Tbh I memorized these formulas in isolation but could never connect them together in practice

[polar plank]

Taking a look rq

So cos(2x)=cos^2(x)-sin^x)
=cos^2(x)-(1-cos^2(x))

=2cos^2(x)-1

[rapid rain]

correct

which means that cos^2(x) = ?

[polar plank]

Wait but we never set this "2cos^2(x)-1" equal to anything though no?

[rapid rain]

we know that cos(2x) = 2cos^2(x) - 1

so cos^2(x) = ?

this is just rearranging

[polar plank]

Ohhh that one
Ok so (1+cos(2x)/2)

[rapid rain]

wrong place for the parentheses

[polar plank]

Forgot to move the 1 first yeah

Fixed now

[rapid rain]

uh the right parenthesis is still wrong

(1+cos(2x))/2

[polar plank]

Ohhhhhhhh wait yeah I see it now

[rapid rain]

ok

now we can finally apply what we did

so cos^2(7pi/8) = ?

[polar plank]

So cos^2(x) = (1+cos(2x))/2

Then cos^2(7pi/8) = (1+cos(2(7pi/8))/2 = (1+cos(7pi/4))/2
=(1+root2/2)/2
=(2+root2)/4

[rapid rain]

yep

[polar plank]

Ok so all I gotta do it seems is to see if I can apply sin^2+cos^2=1 whenver there's sin^2 or cos^2

[rapid rain]

it can help a lot to remember this first

[polar plank]

Yeahh

[rapid rain]

the formulas you need to remember by HEART are cos(x +/- y) and sin(x +/- y). All the other formulas can be found from them

But it's better if you know them all and understand how to find them

as you can see, we "wasted" quite some time finding cos^2(x) = (cos(2x)+1)/2

[polar plank]

Wait cos(x-y) can be analyzed as cos(x+(-y)) right?

[rapid rain]

yes

so really only two formulas to know

(and knowing that cos(-x) = cos(x) and sin(-x) = -sin(x) then)

[polar plank]

Also sin^2+cos^2=1 right?

[rapid rain]

well good formula to know as well, however :

sin(x)sin(x) + cos(x)cos(x) = cos(x-x) = cos(0) = 1

everything can be deduced from those 4 golden formulas

[polar plank]

Huh I see I seeee

[rapid rain]

so by order of priority :

• Memorize all formulas
• If you don't remember some of the formulas, try to deduce them from others

[polar plank]

Ik but the problem is that for tests, my memory for stuff that I can't attatch to other stuff I know or real life examples is very bad, and I make a lot of mistakes deriving formulas in algebra when I try to, especially during tests

I remember trying to use Anki to memorize formulas and nothing stuck

If I learn someting in other subjects like Linguistics for instance, I can connect info ik to prior knowledge of similar languages, or historical pattterns and culture

[rapid rain]

If you ask me, the best way to memorize the formulas is to prove them

[rapid rain]

only allow yourself those 4 starting formulas

and try to prove every other

(for example, why is sin(-x) = -sin(x))

If you do this, you will comprehend more WHY those formulas are true, and you will be more enclined to memorize them

[polar plank]

True
I've had mixed milage with proving formulas though
I remember like the pi/6 triange is the 1/2 (opp) root3/2 (adj) triangle bc of that proof with the equalateral triangle
But I also tried proving the quadratic formula multiple times and still can't remember it

I think it's like if there's more than one or two steps towards the proof then I can't remember it well

There's also a more than 50% change I make a small error doing algebraic operations too, even when I write out all the steps and look through them

[rapid rain]

I mean if you have a tendency to make calculation errors, slow down your writing and take more time checking every step

[polar plank]

Yeah I try to do that but I still end up missing stuff even after spending several minutes on one problem writing each step out and whatnot

Like my brain filters out minor details or errors like that in math

I can parse through formal logic in my class right now though so maybe its just numbers that obscure things for me

I can't really tell if say a problem's solution is "2root5x" and I get "3root4x" that I did something wrong

But tfl formal logic at the end it's either true or false, essentially two numbers at the core of everything

Might look into dyscalculla

Anyways it's getting late and I want to give this slot for other ppl to use

@rapid rain Thanks again for your help btw, I think I get the problem more now yee

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[dapper hazel]

Planter Box Project

You are building a rectangular planter box. The designer gave you the following instructions:
a) The top of the box should have sides parallel to 2x+3y=6. Since it is a rectangle, you know
that the other sides should be perpendicular to the given line
b) Two of the vertices are given as C (7,0) and E (3,7)
c) The rectangular box has a height = 3 feet.
d) Each side is made of concrete with thickness of 2 inches
e) All length measurements are in feet
f) The volume of a rectangle =lengthwidththickness

1. Find the equation of the lines that represent the sides of the top portion of the planter box
2. Find the missing vertices
3. Draw a sketch, by hand, of the top rectangle on a coordinate grid and another sketch of the box
4. Find the perimeter of the top rectangle. Round to the nearest hundredth.
5. Find the volume of the concrete in each side of the rectangle
6. If concrete costs $5.25 per 6 cubic feet, how much does the box cost?
7. It was mentioned in the instruction that the diagonal of the top rectangle makes an angle of
   2x+3 with the shorter side. Write an equation to represent the measure of the angle formed
   by the diagonal with the longer side.
8. If the angle formed by the longer side and the diagonal is 52 degrees, find x
9. Use Google Slides to represent your work and post it on your e-portfolio.

[dapper hazel]

someone pls help i've been stuck on this for the past hour

[gaunt zinc]

try posting individual questions

[dapper hazel]

my bad.

just need help with number 2

1. Find the equation of the lines that represent the sides of the top portion of the planter box
2. Find the missing vertices

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

[dapper hazel]

I'm stuck on finding the missing vertices because my teacher doesn't teach jack

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[lost raptor]

Would the first half also be effected by the negation? So would there exists turn into for all in a negation?

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[hushed arrow]

i am stuck on 4c. not sure where to begin for that. i can only think of a sequence that is bounded either above or below that fits this, but not one thats bounded on both ends

[fair oracle]

@hushed arrow

Hint: Look for an oscillating sequence

[hushed arrow]

like (-1)^n?

[fair oracle]

see if that works?

[hushed arrow]

thats where i get stuck. what would y be

i cant think of anything that would force it to also be bounded above

[fair oracle]

oh wait, I thought you were looking for a bounded divergent sequence

[hushed arrow]

itd be so easy if that were the case! - my professor after i confidently gave him the wrong answer

[fair oracle]

xn and yn can be any sequence but their difference has to be bounded and divergent?

[hushed arrow]

x_n can be any sequence, y_n must tend to infinity, but their difference produces a sequence that is bounded and divergent

[mighty ridge]

take x_n = n+(-1)^n
y_n = n
x_n - y_n=(-1)^n

[hushed arrow]

NAW...

How do you prove that sequence diverges?

I tried to prove it diverges once by looking at its subsequences

Is this sufficient:
x_{2n-1} converges to -1, and x_{2n} converges to 1. But this implies x_n is divergent because it contains both those subsequences, and by the uniqueness of limits x_n cannot converge to two different limits. Therefore it cant converge

[mighty ridge]

it is sufficient

[hushed arrow]

Are there any other ways

[mighty ridge]

an other way would be to go back to the def of limit to show that it can't have one

but your method is the easiest, there's no point in making things more difficult

[hushed arrow]

ic. i thought it wasnt, because it was marked wrong on another hw. im going to ask a question for that in another channel

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[winged spire]

how do you do this

[formal scarab]

you could rationalise the top

[winged spire]

huh

[wary jetty]

Essentially multiple the numerator and denominator by the opposite of the numerator so
(sqrt(22+x)-4) / x-6 ) times sqrt (22+x) + 4 / sqrt (22+x) + 4

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[terse laurel]

I have a question about writing "No student in your class has taken a course in logic programming" using logical connectives. I'm trying to understand why in the correct answer it's an implication instead of conjunction. This is my justification for why implication is correct and conjunction is not and I'd like confirmation.

My answer is $\exists x(P(x) \wedge Q(x))$ the correct answer is $\exists x(Q(x) \to P(x))$.

• $P(x)$ is $x$ has not taken logic programming.
• $Q(x)$ is $x$ is in your class.
• The domain is all people.

My answer $\exists x(P(x) \wedge Q(x))$ literally means "There is some $x$ that does not take logic programming and $x$ is not in your class."
The correct answer $\exists x(Q(x) \to P(x))$ means "if someone $x$ is in your class then $x$ has not taken logic programming".
Again the implication is implied.

This my justification and it basically amounts to "implication is implied".

I was hoping for a better explanation than just "implication is implied" because that's just so weak lol

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[wheat garden]

$s(t)=5t³-2t²+t-1$

[glossy valve]

Jash

[wheat garden]

Find when the speed is increasing

btw s(t) is position

[shell glen]

Differentiate wrt time to get velocity.

[wheat garden]

$\dv{s}{t}=\left(15t²-4t+1\right)\dv{x}{t}$

[glossy valve]

Jash

[wheat garden]

wait is there no dx/dt

[shell glen]

So you get v = 15 t^2 - 4t +1. Now, this is a parabola concave up. Its vertex is at t = 2/15, discriminant less than zero. Before that time, speed is decreasing and afterward it is increasing.

[wheat garden]

oh ok ty

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[light valve]

hi

[glacial pasture]

greetings

[light valve]

hello sir

can u help me with this question

[torn jolt]

what values will make the function undefined

[light valve]

I understand the it cannot be 9

[torn jolt]

yes

[light valve]

as fraction cannot be 0

[torn jolt]

so now, you only have to worry about $\sqrt{3-\abs{x-6}}$

[glossy valve]

help me

[light valve]

let me try solving

at the same time

[light valve]

u can continue

explainng

ill just do it on the side

@torn jolt

Does this make sense or no

[torn jolt]

yeah, now do the other part

[light valve]

which other part?

I did both the restrictions I thought

[torn jolt]

there are two parts to $\abs{x}$

[glossy valve]

help me

[light valve]

really?

can u show me

I dont wanna be confused

[light valve]

??

I am so confused

[light valve]

I learn better in practice

can u show me the answer

like the other step

I dont learn by doing some theories

[torn jolt]

$$3- (x-6) > 0 $$

[glossy valve]

help me

[torn jolt]

you already did

$3+(x-6) > 0$

[glossy valve]

help me

[torn jolt]

note any similarities

[light valve]

this is not what we had before

we had absolute values

[torn jolt]

bro

look at the image

[light valve]

I did look at the image

[torn jolt]

[light valve]

what are we talking abuot

Idk why he added that

this was my questoin

question

did I do it right, he said there was another part to it

thanks brother for helping me out

I appreciate it 🙏

oops

it didnt load sorry

what u wrote

thanks I will look at it

so the x and 6 is just flipped within the absolute value and u solve for that?

I kinda get it Ill try it brother

thanks soo much

u are the best

got it 🙂

Would that be the two possibilites?

Or where did I mess up

@stable spruce

noo thats not what I meant

is that the two possibilites for the inequality

I know how the domain works

oh I got -3

oh yeah ur right!

ok sounds good

thanks bro

how would I do this bro

@stable spruce

All good man thanks so much

@stable spruce did u get it

sorry bro dont mean to bother u

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[light valve]

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[torn jolt]

I'm not getting resultant of any of them 4

[torn jolt]

As the angle isn't specified I'm only supposed to use root of (a^2+b^2) right?

[onyx glen]

that would be assuming the forces are at a right angle.

here you want to think in terms of the triangle inequality instead

[torn jolt]

Oh

[torn jolt]

Can you elaborate ?

[onyx glen]

|u + v| ≤ |u| + |v|

but also |u + v| ≥ |u| - |v|

for any vectors u, v

[torn jolt]

This condition must be satisfied?

[onyx glen]

yes it must but that won't do much for you in this problem

[torn jolt]

Mhm

So what can i do

[onyx glen]

but also |u + v| ≥ |u| - |v|

[torn jolt]

Yes

[torn jolt]

What is this for thou?

[onyx glen]

you wanted me to elaborate on the triangle inequality

and i did

[torn jolt]

I'm sorry if i keep asking dumb questions 😭

[onyx glen]

by writing out both of its 'main' forms

[torn jolt]

Right so how will that help me find the pair

The triangle inequality

[onyx glen]

|u + v| ≥ |u| - |v|

check which pair of vectors cannot add up to one of length 4 based on this

[torn jolt]

Plug in the values of vectors?

[onyx glen]

lengths, not values

[torn jolt]

Only option can add right

Others the values are 6,8,10

[torn jolt]

Option one i meant

[onyx glen]

🙃

[torn jolt]

😭

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[torn jolt]

<@&286206848099549185> could anyone help, ty!

[torn jolt]

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[proper hawk]

what's the original question

[plain fox]

its wrong btw , its not x^2 thats being multiplied , its everything

also to find f(0) just let x = 0 , no need for multiply

[proper hawk]

you don't need to expand the bracket to find f(x)=0

[fast peak]

in fact you really dont want to expand

if you had it in expanded form, you would want to factor it

[proper hawk]

we have f(x) = (x^2+5)(x+3)(x+3)

we have three things multiplied together

so if any one equal 0 f(x) equals 0

you expanded the brakets wrong

[outer girder]

oh shit sorry!

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[abstract flax]

why did they make the discriminate = 0?

*discriminant

[light sonnet]

Because that's the general case of the discriminant

[abstract flax]

yeah but isnt there two points of intersection

[light sonnet]

That's why on the last line it says a > 0

[abstract flax]

im so sorry but could you elaborate

[light sonnet]

The discriminant has 3 cases D > 0, D = 0, or D < 0

If you wanted D > 0, meaning two real distinct roots, you can just solve it as D = 0, then change the sign back to >

[abstract flax]

so wouldnt the bottom line be (a > r^2/2) then?

[light sonnet]

Well actually, I read it wrong a > 0 is for something else, you just want to know where it intersects, so you don't need > 0, having it = 0 is sufficient

Have it = 0 means it has 2 intersections, it just repeats, that's the minimum

[abstract flax]

alright thank youu

[light sonnet]

Idk if that makes sense

[abstract flax]

yeah it does

thanks again

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[dark timber]

What am I doing wrong? I am trying to solve the equation x^2 + 2x = 0 by completing the square.

[dark timber]

How does it become x = 0 or x = 2?

[plain fox]

the real question is why subtract 2?

(x)^2 +2(1)(x) + (1)^2 - (1)^2 = 0

(x + 1)^2 - 1 = 0

@dark timber u there?

[dark timber]

But if I solve this one by subtracting 4 because it has 4x in it why can

[plain fox]

that is not how it works

[dark timber]

can't I do the same with the other one?

[plain fox]

cuz in that
x^2 -4x -5 = 0
x^2 -2(x)(2) +2^2 -2^2 -5 = 0

the value u use is half and square of the x co efficient

usually

[dark timber]

oh I think I get it, thanks for the answer

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[hollow pumice]

where is the sec^2 theta - tan^2 theta

[rocky vale]

they showed that it's equal to 1

[tacit swift]

what is the square root of 126?

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[torn jolt]

Yo, I need help with trig-sub

[torn jolt]

Where do I start when integrating the following?

[glossy valve]

🌐

[torn jolt]

<@&286206848099549185>

[solemn coral]

ooh that looks intresting

i assume a u sub is the first step

[torn jolt]

u = t^2 + 2?

[sinful quartz]

Put t^2 + 2 =u

[solemn coral]

👍

or use hyperbolic functions if u wanna be fancy

[torn jolt]

How does that help me though

I get du = 2tdt

Didn't learn hyperbolic trig

[solemn coral]

ah

ket me@work it out and dee

see

i think ur sub might be wrong

[torn jolt]

how abt u try to add and subtract 2 in the above situation

or no wait

how abt u try making a perfect square in denominator

then get the factors

n go for byparts?

not by parts

i meant partial fraction

[raven quail]

t^2+2=u^2 works i think

[solemn coral]

it does

[torn jolt]

but what will the benefit be i wonder

[solemn coral]

@torn jolt change hr u to u^2

[solemn coral]

partial fractions <<<

and this yields an easy polynomial to integrat

[torn jolt]

like if we substitute but before that better divide and multiply by 2

[raven quail]

the denominator will become u and cancel out with u in the numerator

[torn jolt]

then apply substitution

[raven quail]

you will jjust have (U^2-2)^2 du to integrate

no denominator

[torn jolt]

hmm thats also one thing

[torn jolt]

Didn't learn that either

So

u = t^2 + 2?

Or something else

[solemn coral]

that works but u*2 is easier

u^2*

[raven quail]

u^2 = t^2 +2

[solemn coral]

theres no real difference

its just cleaner w u^2

instead of having fractional powers to integrate

[torn jolt]

@solemn coral @raven quail

[solemn coral]

yh i think i got that too

[torn jolt]

Dope

Can we also go through this one please

@solemn coral

Are the 3 I'm having trouble with

[solemn coral]

u cant use hyperbolic trig?

try x = tan(u)

[solemn coral]

here do u = sint then cost will cancel off (common trick for integrals like this)

or not ry a trick but

finding a sub thats derivative is the numerator

always good

[solemn coral]

this one im honestly thinking

[torn jolt]

Got you

I got class right now but I’ll get to these in an hour or so and let you know how it goes

[fossil fjord]

@glossy valve

[solemn coral]

👍

he got that one

[solemn coral]

triple substitution seems too complicated relative to the other questions

also mot even sure if jts correct i rushed it

[raven quail]

you can also try ax =b sec u

[solemn coral]

oh try x = (b/a)secu

[solemn coral]

ye

probably the easier route

oh yeah cuz tanu cancells out

and then

yeah

probably reaches something

[raven quail]

yea

you will have to convert it in sin cos tho

then its easy from there

[solemn coral]

yeah

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[trim flint]

Yo

[trim flint]

Why 2 disappears in

2√x^3

[torn jolt]

what?

[trim flint]

It becomes valid like this: √x^3

[woven sand]

$2\sqrt{x^3}$ this?

[glossy valve]

M. Frost

[trim flint]

Yes

[tacit granite]

$2\sqrt{x^3} = 2\sqrt{x}\sqrt{x^2} = 2x\sqrt{x}$

[glossy valve]

TimK

[trim flint]

What does 2 do when it comes before √ ?

[woven sand]

That 2 will only go away if that term is divided by 2

Or you subtract a sqrt{x^3} from that term

[trim flint]

What does a number do when it comes before √ ?

Like this

6√9

[tacit granite]

multiply

[woven sand]

Multiplies sqrt{x^3} by 2

Or multiply by that number in general

[trim flint]

By the result of √9 ?

6 * 3?

[woven sand]

Yes

so $2\sqrt{x^3}$ is $2 \times$ whatever $\sqrt{x^3}$ equals

[trim flint]

By 2 or same number as the number before the √ ?

[glossy valve]

M. Frost

[woven sand]

The number in front of the square root is being multiplied to whatever the square root is

[trim flint]

And why 2 disappears?

[woven sand]

$2\sqrt{x^3} = 2\left(\sqrt{x^3}\right)$ if that helps

[glossy valve]

M. Frost

[woven sand]

I don’t understand, why do you say it disappears?

[trim flint]

What is √x^3 ?

[woven sand]

Did it disappear in the problem you’re working on?

[trim flint]

Im not in ur lvl in math so idk what to aay

Say

[woven sand]

$\sqrt{x^3}$ is simplified, unless you know what x is equal to

[glossy valve]

M. Frost

[trim flint]

√x = x^1/2

[woven sand]

Correct

[trim flint]

And if it's √x^3?

[woven sand]

You could write $\sqrt{x^3}$ as $x^{\frac{3}{2}}$

Both are generally considered simplified

Wait no that’s wrong

[glossy valve]

M. Frost

[woven sand]

Fixed

[trim flint]

Why tf 2 goes away?

2√x^3 ?

2 * x^3

[woven sand]

When does it go away?

[trim flint]

so

[woven sand]

$2\sqrt{x^3} = 2x^{\frac{3}{2}}$

[glossy valve]

M. Frost

[trim flint]

2√x^3 is x√x

And √x^3 is also x√x

[woven sand]

$2\sqrt{x^3}$ is $2x\sqrt{x}$ not $x\sqrt{x}$

[glossy valve]

M. Frost

[woven sand]

The 2 doesn’t go away

[trim flint]

Ok

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[tacit granite]

find such $x_1$ for which $12-5x_1=0$

then draw lines up with slope 5

[glossy valve]

TimK

[tacit granite]

here

@torn jolt

lol

that's the other way

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[reef dove]

Can someone help me understand the last part

[river owl]

basically

[reef dove]

Like how is the derivative just b

If there was ln before

Wait does d(ln y) / d(ln x) mean that i should treat lnx as a variable?

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[reef dove]

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[jagged agate]

can anyone explain why this is the answer

[kindred oriole]

a negetive quartic will have a maximum point

The range is all possible y values that could be given by the function. We can see the graph falls off to -infinity (hence that given). To find q you would have to differentiate the function to find the gradient function and put that equal to 0 as the gradient at turning point would be 0.

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@jagged agate Has your question been resolved?

[kindred oriole]

Then (as you know the shape will be like an upside w) the maximum y value with either be at the lowest x or at the greatest x and so you can just put them back int the original equation and find the maximum y value

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[compact tulip]

might be tired n cant really think straight rn but how do u get 27x+10 if u simplfy this

[compact tulip]

also (1 step back) if i rewrite 2sqrt(9x^2-5) / 9x^2 -5 i get 2/(9x^2-5)^2

cuz they also do that for the other part when they divide sqrt9x^2-5/9x^2-5 so im confused cuz isnt it the same thing

the answer is from a calculator online so it might be wrong but id highly doubt it cuz other websites say that that is the derivative so it must be right ig

<@&286206848099549185> can someone help plz

[compact tulip]

at least with this maybe 😭

yallll i thought this was a math server how can no one help me simplify a fraction man

[empty sinew]

I will help

Lemme write it down

[compact tulip]

THANK YOU

[empty sinew]

Tried my best

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[hasty vortex]

.reopen

Help

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[cedar monolith]

hello

[cedar monolith]

can someone help me prov this

[stiff musk]

this is in R^n?

[cedar monolith]

yes

[stiff musk]

maybe start by writing out the middle one

$\sqrt{x_1^2 + x_2^2 + \cdots + x_n^2}$

[glossy valve]

Bungo

[stiff musk]

can you see that this is >= |x_i| for each i?

[cedar monolith]

yes

[stiff musk]

and do you see why that implies $|x|_\infty \leq |x|_2$?

[glossy valve]

Bungo

[cedar monolith]

yes for the first inequality i get it

[stiff musk]

ok cool

so second one

let's fix a particular value of i

then $x_1^2 \leq x_i^2$, $x_2^2 \leq x_i^2$, ..., $x_n^2 \leq x_i^2$

wait sorry

that's not an arbitrary value of i

that's the i for which $x_i^2$ is the largest

[glossy valve]

Bungo

[cedar monolith]

ok

[glossy valve]

Bungo

[stiff musk]

now sum those inequalities and what do you get?

[cedar monolith]

i get $(x_1)^2 + (x_2)^2 + \ldots + (x_n)^2 \leq n(x_i)^2$

[glossy valve]

lilisworld

[stiff musk]

yes

now can you see how to get the desired inequality from this?

[cedar monolith]

yes thank you

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[clear mirage]

Im just beginning geometry. For x I got 8 square root of 5. And somehow for y I got 96 square root of 5. Please help

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[tidal hedge]

im confused on how they got 11 as the slope of the tangent line

[tidal hedge]

what other point am i supposed to use to find the slope??

[light sonnet]

Do you know derivatives?

[tidal hedge]

im learning about them now

[tidal hedge]

^

[light sonnet]

The derivative of that function relates to the slope of the line

So you take the derivative and plug in 2

[tidal hedge]

isnt the derivative the slope of the tangent line at a specific point

[light sonnet]

It gives you the where the point is

x = 2

[tidal hedge]

yea

i plugged that into x^3-x and got 6

so 2,6

[light sonnet]

.

Take the derivative of x^3 - x

Because the derivative relates to the slope of the tangent line

[tidal hedge]

i dont understand what you mean by take the derivative

[light sonnet]

I don't know what you don't understand, take the derivative means what it means, take the derivative of x^3 - x

Like the derivative of x^4 is 4x^3

[tidal hedge]

i havent learned that yet

[light sonnet]

I'm pretty sure you learned it, if you're given a question about the tangent line, it relates with the derivative

[tidal hedge]

is the derivative of x^3-x
3x^2-1x^0?

[light sonnet]

Yes

Now plug in x = 2

[tidal hedge]

so to take the derivative of something i just move the number in the exponent to the front and then lower the exponent by 1?

[light sonnet]

Yes, that's called power rule

[tidal hedge]

ah ok

i also have to plug in 2 into the original function in order to find the y value right?

[light sonnet]

Yes

But if you plug in 2 into the derivative, that's the slope

That's where 11 comes from

[tidal hedge]

ohh ok

ok ty

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[obsidian swift]

Where did I go wrong?

[quaint prawn]

were you born after 1993?

[light sonnet]

Here

You can't cancel that out because the denominator is (t^5 + 4)^3

The numerator is (t^5 + 4)^2

[obsidian swift]

Why if you’re multiplying?

Cuz if I expand it they would cancel out

[light sonnet]

How?

Expand how?

[obsidian swift]

((t^5 +4) (t^5 +4))/((t^5 +4)^3 (t^5 +4)^3)

To which can expand even further

Wait I realized what I did wrong

.close

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[fervent anchor]

If logical equivalent of p implies q is not p and q

[fervent anchor]

Would logical equivalent of p implies not q be not p and not q?

[spiral vigil]

well

technically yes

[spiral vigil]

but this is false

should be not p OR q

[fervent anchor]

Right mb

Mistyped

So let me retype

P implies q is not p or q

So

P implies not q is not p or not q

[spiral vigil]

yes

[fervent anchor]

Ok

Thank you

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[slender tundra]

I'm not sure what this is called, but I saw my teacher show something in class about lines and how we need to find a and b for example, we got like 2 points like (a,5) (9,b) and maybe we have more info than that but then we're asked to find a and b and I'm not sure how to explain it but yeah can anyone help? find something similar to what I'm talking about? I'd want to put that into practice. I'm currently learning about analytic geometry.

[slender tundra]

something like this

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@slender tundra Has your question been resolved?

[slender tundra]

like this too

[mighty ridge]

replace x by 4 in x²+y² = 25, 4 is the abscissa of A so the solutions of the resulting equation will be the possible values for the ordinate of A, which is b

[slender tundra]

I got b = 3

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[mighty ridge]

you forgot b = -3 :x

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[torn jolt]

is this spansih

u could try rational root theorem but thats prob still gonna take long

is there some factor by grouping

[west mango]

the translation to english is:
"Represent the polynomial ( f(x) = 3x^5 + x^4 + 15x^3 + 12x + 4 ) as the product of its linear factors.""

[glossy valve]

レナト (ping if reply)

[torn jolt]

i dont think this has rational root

[cyan kelp]

I think that wolfram alpha shows that these roots cant be written down in terms of radicals. So…

You got trolled

[torn jolt]

u can use the Tschirnhausen transformations to reduce the polynomial into x^5 + x + A lol

[cyan kelp]

Gotta do some galois theory to show its not solvable by radicals

[west mango]

what channel can I go to ask this to?

[torn jolt]

prob abstract algebra

[west mango]

<@&286206848099549185>

[brittle steeple]

idk what u want

[brittle steeple]

here's the roots

[west mango]

wdym that these cant be written down in terms of radicals?

[brittle steeple]

$3(x-r_1)(x-r_2)(x-r_3)(x-r_4)(x-r_5)$

[glossy valve]

thewizardofOU

[brittle steeple]

presumably not

[torn jolt]

lol

I agree with thewizardofOU

😍

[brittle steeple]

here if you want to check for yourself

https://math.stackexchange.com/a/355012

seems like a good resource

[west mango]

so there are no rational roots for this polynomial?

[brittle steeple]

nope

if there were they would have to be plus or minus 1, 2, 4, 1/3, 2/3, or 4/3

[torn jolt]

yes

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@west mango Has your question been resolved?

[west mango]

guys my professors sent me the question like this

what can I do to research so I can solve this?

above they told be it cant be factored, but I will try sending an email to see if they made a mistake, but I dont think so, this exercise was given to other 500 people

[torn jolt]

@zenith kernel

cogwheel of the mind

[cyan kelp]

Im making the assumption that if the roots were solvable by radicals, then wolfram alpha would be able to do it. I dont know enough (or any, really) galois theory to prove it cant be solved by radicals.

This means that you cant write down the roots in terms of +,-,*,/, or √ (or nth roots). So I’m not sure what your professor wants from you. Good luck

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@west mango Has your question been resolved?

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@west mango Has your question been resolved?

[west mango]

https://math.stackexchange.com/questions/4781062/representing-a-quintic-polynomial-as-the-product-of-its-linear-factors

I published the question in stack math

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[west mango]

.close

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[twin herald]

hi

[twin herald]

I keep getting very off solution

idk what I did wrong

my soln is 10 mins

the actual solution is 1 min

someone pro at stats pls help me out

?

[fast peak]

lets remind ourselves how scientific notation works

1E1 means 1*10^1

[twin herald]

ohhhh

silly mee

ty

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[royal halo]

I need help with the names

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[elfin lion]

Is it possible to get the inverse of f(x)?

[rain sundial]

In these type of questions, you needn't find the inverse

f^-1(x)=t
Now you need to find dt/dx
x=f(t)
1=f'(t)×dt/dx

[elfin lion]

ehm

So what function are you gonna calculate the derivative

[rain sundial]

f(t)=5t+2t^5

[elfin lion]

ok so f'(t) = 5+10t^4

then you say 1=5+10t^4*dt/dx

dt/dx=1/(5+10t^4)

[rain sundial]

Now see f(-1)=-7
-1=f^-1(-7)
f^-1(x)=t
Now when x =-7, t =-1

Substitute the value of t in dt/dx

[elfin lion]

1/15

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[torn jolt]

!help

[torn jolt]

Help me with this guys

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[torn jolt]

<@&286206848099549185>

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[torn jolt]

<@&286206848099549185>

[torn jolt]

The integrals here means that [] symbols here denotes greatest integer function

Yes that would be 1 right?

The |x| = 1/n where n belongs to natural number.

Could you pls elaborate more? How does this function f(x) = 0 came

So you made two cases: |x| > 1 and |x| <=1 , am i right?

Umm. It said n belongs to natural numbers

You are right but x is directly related to 1/n

Can you tellme this 1st part where you wrote that |x| <= 1

|X| takes form 1/n

[torn jolt]

No No it's fine. I understood the most of the part. Thank you so much for the solutions. Just 1 step i didn't understand that |x|<= 1 how it became 0. also at |x| = 1 wouldn't it become 1?

sorry sorry i meant the |x|<=1

ah I got it now. Thank you so much.

I understand this step now better

and for |x| <1 then 1/|x|>0 right?

WOWIE DUDE. HATS OFF TO YOUR THINKING. YOU REALLY CRACKED IT. I GOT THE CLARITY NOW.

only in case of irrational number the f(x) would be 1 right? otherwise it's 0

I really loved the style of your thinking. The bit by bit realization with the cases.

So the answers have 2 solutions 1 and 0 right?

This is a question from jee here. These type of greatest integer function questions and all other sorts of combinations are very prevalent here. I tried asking help but I didn't get any reply here. One dude tried but he said he will do tomorrow. Another dude called me rude for me saying "Provide the solution"

Ah i see now. But don't you think if z could be 17 like 1/(1/√ 17) will be √ 17?

since √ 17 is not a rational number here

FULLLLY UNDERSTOOD NOW. WOWIE.

Thank you so much dude. Helped a lot. This is really a good sum and I really liked your observations and case thinking skills.

This definitely helped a lot with the cases

Thank you so much 💝

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[night pulsar]

Is there a method for factoring cubics in the form ax^3 + bx^2 + d?
Or do u just have to be giga brain and see it

[formal scarab]

just guess bro

[drowsy wyvern]

u have to guess solution for the cubic first

[night pulsar]

U just have to guess?

Damn

[formal scarab]

you could use rational root theorem

but only if it applies

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[night pulsar]

Thanks

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[patent pelican]

Show that no entire function $f:\mathbb{C} \rightarrow \mathbb{C}$ can satisfy $f(\frac{1}{n})=e^{-n}$ for all $n\in \mathbb{N}$.

[glossy valve]

Casiel368

[patent pelican]

I would like to use the identity principle, but g(z)=f(z)e^(-1/z) is not defined at 0

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[patent pelican]

.reopen

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✅

[patent pelican]

.close

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[glad whale]

how this wrong plzzzz

I made f(x)=x^2

and g(x)=x/x+9

i felt like it made sense but is wrong sadly

[formal scarab]

wrong way round

[glad whale]

oh

so g(x) should be x^2

?

ohhhhhhhhhhhh

perfect ok

thnx

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[glad whale]

hi

[glad whale]

in this case

can i plug in 2 and -2

[viral jasper]

Yes. That would be a sufficient case.

1 and -1 would also work, fyi

[glad whale]

Ok nice

perfect Thnx

[rocky vale]

but they specified 0 <= x <= 7

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[dreamy eagle]

my prof hasn't covered this, could someone help me understand what to do?

[eternal juniper]

oo im doing that in class too

idk

is it like

the range of

x until 0

or something?

[dreamy eagle]

all i know is that there's different functions you need to plot on a graph

something of that sor

sort

[woeful path]

you basically plug in values for each scenario so i. is g(x) approaching 0 from the left

so -2 < x < 0 you plug in 0

for the graph you would sketch the piecewise function

everything <= -2 you would graph 1 - (x + 2)^2, -2 < x < 0 you would do | x + 1 | and so on

[dreamy eagle]

tyty

[dreamy eagle]

how does cosh in this instance work again?

[woeful path]

it would be a hyperbola but its just 1 cause its only at x=0

cosh(x) = (e^x + e^-x)/2 but cosh(0) is just 1

[dreamy eagle]

thanks

[dreamy eagle]

i figured it'd probably just be easier if i graphed it first right

[woeful path]

i mean theres nothing to graph except a point

x = 0 is just a point and if you plug in 0 its 2(1)-1

so just (0,1)

you essentially need to plot out all the important points (x = -2, x = 0) then play connect the dots when drawing the functions between them

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[red blade]

need help finding a counterexample

[red blade]

I know this thm doesn't make sense

.close

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[livid briar]

A phone manufacturing company needs 3000 screens per month at a fixed rate for its production,
and orders these from an external supplier. The screens are delivered in batches, and the fixed
delivery cost for each batch is e 375, independent of the number of screens ordered. The cost for
storing screens is e 1.60 per screen per month. Production can continue when no screens are on
stock, but it has been estimated that this comes at a cost of e 5.60 per screen per month.
(a) Determine the optimum order quantity, and the corresponding maximum shortage level (both
rounded to an integer).
(b) The lead time for ordering new screens is 1 month. Determine the effective lead time and
the stock level at the moment that a new order is placed

is there anybody who can solve something like this with the eoq formula

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[thorn crescent]

no idea how to solve it

anyone know how

[charred ivy]

implicit differentiation?

[thorn crescent]

what about this one

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[ashen falcon]

A state Senate has 230 Senators. On Wednesday several senators were absent due to the business trips. On Thursday at the number of Senators asked to illness was five more than the number of absent ones on Wednesday. On Friday three Senators who are ill and absent on Thursday returned. 188 senators were present on Friday. How many senators were absent on Wednesday?

My book says there was 50 senators absent on Wednesday but I can't figure out why. Can someone explain to me?

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[signal lake]

Hello, I need help understanding how to balance this equation
K4Fe(CN)6 + KMnO4 + H2SO4 -> KHSO4 + Fe2(SO4)3 + MnSO4 + HNO3 + CO2 + H2O

[signal lake]

I am starting with algebraic method and have done until assigning variables and making equations

but I don't know the next step now

[torn jolt]

I'm afraid we cannot help you with the chemistry itself (unless someone volunteers to do so) because this is a mathematics server. If you want help on solving the mathematical equations themselves, then you can post them and it would be right up this server's alley

[signal lake]

ok sorry can you recommend chemistry servers for me? cause I can't find any

[torn jolt]

There is one in #old-network, though I have no knowledge on how they operate and how active they are

https://discord.gg/eexdsFw

[signal lake]

ok thank youuu

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[severe basin]

How is the linear kernel a "valid" kernel?

[severe basin]

I know that a function K is a kernel function if it satisfies two conditions:
(i) The function K is symmetric and
(ii) The function K is positive semi-definite.

The dot product for two vectors in a space is of course symmetric.

But, it can be negative, so it violates the second condition and so it cannot be a valid kernel?

[fast peak]

the definition of positive semidefinite only uses one vector x

K(x,x)>=0

[severe basin]

Yeah, I know that

I am told that is this a valid kernel satisfying the properties I mentioned above, and x_1 and x_2 are different vectors

[fast peak]

a dot product of a vector with itself is always >=0

calculate it

its a sum of squares

(the magnitude of the vector squared)

[severe basin]

x_1 and x_2 are different vectors here

I do know that the dot product of a vector itself is is greater or equal to zero.

But it isn't the condition for two different vectors as it can be negative, and hence it cannot be kernel?

[fast peak]

the kernel can take two different vectors. but for the definition of positive semidefinite it is only relevant what happens when you plug the same vector in twice

[severe basin]

Do we just assume that?

[fast peak]

thats the definition of positive semi-definite

[severe basin]

.close

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[hot lark]

Why is there no r

[rough tundra]

no r, where?

[hot lark]

It says the sqrt^3 of -1 are:

And it shows

And u can see there isnt r

Just cos+isin

[rough tundra]

it's a unit circle with r=1, do you know what happens when we multiply by 1? :)

[hot lark]

How do j know r=1

This the formula

If its always one why put sqrt r

[covert wing]

Isnt it De Moivre's theorem again

[rough tundra]

well if it probably says, but it's a forgein language so I can't tell, but the image it appears so

[rough tundra]

[covert wing]

Hi Fancy (imma not vc t'day)

[rough tundra]

im in school rn

AP Psych

[hot lark]

Yes de moivre

[covert wing]

#serious-discussion

[hot lark]

Waitt

[rough tundra]

?

[covert wing]

||We cant do our own convo in a help channel.||

[rough tundra]

ik I was just making a comment lmao

[hot lark]

If r is always one

Why the formula has sqrt r

In it

[rough tundra]

we include r in the general case

but it appears here r=1

[hot lark]

How do u know without graph

[hot lark]

Also saqrt^3 -1 isnt complex

Im confused

[rough tundra]

wdym?

[hot lark]

This whole thing start with

Sqrt ^3 -1

[rough tundra]

where is that in the image?

[hot lark]

The text

"The three cubic sqrts of -1

[rough tundra]

you mean $z_0=\frac{1}{2}(1+\sqrt{3}i)$?

[glossy valve]

FancyBredFries

[rough tundra]

that is complex...

[hot lark]

Uhh

No

Idk why z0= that

Idk how they got there

$(-1)^(1/3)

[hot lark]

How did it get to this

Why would z0 be this

<@&286206848099549185>

[restive kelp]

cube root of -1 with your formula gives us these 3 numbers

[hot lark]

Yes idk how it gives tjem im missing something

Why is the angle = pi/3

Angle of -1 is pi

[restive kelp]

yes

[hot lark]

.

[restive kelp]

so in the formula its divided by 3

cuz u need the 3rd roots

[hot lark]

Right

Ok and

How does it get that result for z0

[restive kelp]

substitute in

[hot lark]

Wdym

[restive kelp]

you know the angle and the formula

[hot lark]

Yes

[restive kelp]

you put the angle instead of the teta

and evaluate it

like an equation

you have a variable x, and you just figured out x= pi

[hot lark]

Yeah but I dont understand the result

Where does 1/2 come from