help-38

[dense zealot]

Will do that

Question 25^^🤮

Kinda gross

[vagrant marsh]

whats q25

[gloomy basalt]

25-"Let a, b, c be nonzero real numbers such that (ab+bc+ca)³ = abc(a+b+c)³. Prove that a, b, c are terms of a geometric sequence."

[vagrant marsh]

thanks

[trim jolt]

@dense zealot Has your question been resolved?

[dense breach]

Wtf jeez

I thought the main trick would be b²-ac or such

that's awful

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[rugged latch]

Not sure how to get the sum of squared error

how do i get the transpose of 5/3 if thats what its asking

.close

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[uneven parcel]

how do i start this

[wraith hinge]

um

[wraith hinge]

What part are you confused about

so here are my answers and I am confused about C

The teacher substituted 0

Its to find the height of the building, but I dont know why she subbed 0

She subbed in 0 for t

going maniacal as to why she did that

um 🥺

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[pine ingot]

<@&286206848099549185> are these good?

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[wraith hinge]

TGTM

Also

!15

!15mins

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[pine ingot]

<@&286206848099549185>

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@pine ingot Has your question been resolved?

[wraith hinge]

It hasnt no one answered...

Omfg that was a bot 💀

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[hallow token]

(Square root 3/2)*(1/2)+1

woulnd't it be

Square root 3

---

4

And +1

[dense breach]

ye

[hallow token]

How would it be that?

[dense breach]

1 = 4/4

[hallow token]

I am bamboozled

[dense breach]

it's the same as your answer

[hallow token]

OH

[feral vessel]

yes

[hallow token]

I'm not thinking straight, mb

[dense breach]

no worries

[hallow token]

Heya

The bottom would just be 2

Since

The multiplication would cancel both the tans out to be a 1

and add 1

so 2

and at the top

I honestly have no idea what I do at the top

[feral vessel]

do you know what tan 60 degree is

[hallow token]

Mhm

Square root 3/1

[feral vessel]

what about tan 30 degree

[hallow token]

1/3square root

[feral vessel]

there

plug it in

[hallow token]

How would I subtract them?

[feral vessel]

you can leave it as is after doing some simplification

[hallow token]

Uh

What simplifications?

[warm kernel]

make both fractions have the same denominator and then just subtract and rationalize

[feral vessel]

rn you have:

[solid kiln]

3_n

[hallow token]

Ya

How would I do that?

How would I get the same denominator

[feral vessel]

$\sqrt{3}=\frac{\sqrt{3}}{1}$

[solid kiln]

3_n

[feral vessel]

multiply top and bottom by a number

[hallow token]

Still, confused

Sorry

[feral vessel]

hmmmm

quick example

[solid kiln]

3_n

[hallow token]

Honestly don't know

[feral vessel]

very nani, what about this:

$\frac{3}{4}-\frac{1}{4}$

[solid kiln]

3_n

[hallow token]

just

2/4

[feral vessel]

yeah

[hallow token]

Would that one up there just be

2/ square root 3

[feral vessel]

yeah

[hallow token]

Bruh

[feral vessel]

ahahh

so now

back to the question you're working on

[hallow token]

so how would I get the two up here

to have the same denominator?

[feral vessel]

you know you can multiply the same number on numerator and denominator right?

something like $\frac{1}{2}=\frac{1\times 2}{2\times 2}=\frac{2}{4}$

[solid kiln]

3_n

[hallow token]

yea

[feral vessel]

the denominator is 1 right now

how do we get it to sqrt 3

[hallow token]

Multiply it by sqrt 3?

[feral vessel]

yes

you got it

[hallow token]

so

sqrt 3 - (sqrt 3/sqrt9)

?

[feral vessel]

very nani

[hallow token]

huh

...

Uh

[feral vessel]

so uhm let's tidy things up for a bit

[solid kiln]

3_n

[hallow token]

I'd have to

Multiple by sides by sqrt 3?

or a

[solid kiln]

3_n

[hallow token]

I'd just square it

making it like a

3-1/3

getting ride of the sqrt?

[feral vessel]

this operation is not valid ahah

remember what did you get

[solid kiln]

3_n

[hallow token]

Hm?

[solid kiln]

3_n

[feral vessel]

right?

[hallow token]

Why would I multiple that side?

[feral vessel]

which side

[hallow token]

wouldn't we multiple the right?

Ohh

So i'd be

[feral vessel]

we are trying to get the left and right to have the same denominator

so we can subtract

[hallow token]

oh

So now it does?

Since

Both have

Sqrt 3 as the denominator

[feral vessel]

yessssss

[hallow token]

We'd do that to both sides wouldn't we?

[feral vessel]

$\frac{\sqrt{3}\times\sqrt{3}}{\sqrt{3}}-\frac{1}{\sqrt{3}}$

[solid kiln]

3_n

[hallow token]

We would have to multiple both sides wouldn't we?

[feral vessel]

for left I mean sqrt{3}, for right I mean 1/sqrt{3}, btw

uhmmm note that this is not an equation

for soemthing = something yes

[hallow token]

I'm sorry man, i'm still not getting it

[feral vessel]

hmmmm let me try another approach

Let's recognize the difference between equation and number

[hallow token]

sqrt 9/3 sqrt

[feral vessel]

close

[solid kiln]

3_n

[hallow token]

Ah I c

wait

Do i c

[feral vessel]

do u see

or let's make it simplier

[hallow token]

Bro 😭 how would I subtract 1 from 9 sqrt!

how!!'

[feral vessel]

what is sqrt 9

[hallow token]

3

bro

[feral vessel]

there

[hallow token]

Oh myu

[feral vessel]

how do you subtract 1 from 3

[hallow token]

2/3sqrt

Is the answer

[feral vessel]

nop nopnopnpnonp

hold on

[hallow token]

Alr

[feral vessel]

remember the original expression you have is

[solid kiln]

3_n

[feral vessel]

now you just found out $\sqrt{3}-\frac{1}{\sqrt{3}}$ is the same as $\frac{2}{\sqrt{3}}$

[solid kiln]

3_n

[feral vessel]

so you get $\frac{\left{(}\frac{2}{\sqrt{3}}\right{)}}{2}$

[hallow token]

Oh yeaaaaaaaa

What d

then i'd

[solid kiln]

3_n
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

3_n

[feral vessel]

cancel 2 and voila

[hallow token]

So the answer is just

2/sqrt3

[feral vessel]

nani

[hallow token]

1

1/sqrt3

[feral vessel]

there

voila

[hallow token]

uhm but

Not very sure how we got that

If we multiple

Did we multiple the whole thing by

We only multiple the sqrt 3 by sqrt 3

Right?

[hallow token]

if multipled it, don't we HAVE to multiple both sides?

[feral vessel]

there are no "both sides" since this is NOT an equation

[hallow token]

Hm

[feral vessel]

you get the whole ugly looking stuff by plugging in the tan60s and tan30s

[hallow token]

Okay, I kinda understand how you did this

But for another equation like this

I'm not sure i'd be able to solve this

Thanks tho

[feral vessel]

np let me try to throw you some exercise in dms ahahha

[hallow token]

Thanks! I appreciate the help

i got review materials for tomorrows test, understood everything except forrrrrrrrrrrrrr Special angles 😒

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[lime lagoon]

If Randy's wrangling a deal, then provided that questions won't be raised, somebody is going to get rich.

How do I convert this to sentential logic using the provided Atomic Symbols

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[viral shore]

ok

R/ \ ~Q

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[sharp arrow]

hello

[sharp arrow]

need some mechanics wizardry help

spring constant is k btw

[lament jewel]

u shld

try a physics disc

💕

[sharp arrow]

maybe i shud

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[lament jewel]

LOL

yes

🥣

[sharp arrow]

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[split aspen]

[Probability]
There is this exercise that goes:
"The chances of guessing the outcome of a match is 50%(this team will win or lose).
A spam bot gives random guesses for 4 week straight to an n number of people, and at the end of the day it manages to correctly guess for 100 people

How many people did it have to contact to convince 100 people that his prediction algorithm was the real deal?"

Can anybody push me to the right resources to do this exercise on my own? What knowledge should I look for? I'm kind of a newbie so even basic suggestions are welcomed😌

[trim lichen]

what is the probability of correctly guessing on a fifty-fifty gamble 4 times in a row?

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@split aspen Has your question been resolved?

[split aspen]

Ehm let's see.
1/2 + 1/4 + 1/8 + 1/16?

[wraith hinge]

"The chances of guessing the outcome of a match is 50%"

maybe draw a tree diagram for this

[split aspen]

Ok👍

[wraith hinge]

like this

[split aspen]

Oh

Then its gonna be 0.5^4?

[wraith hinge]

yes you have to multiply 0.5 x 0.5 x 0.5 x 0.5

or just 0.5^4

,calc (1/2)^4*100

[solid kiln]

Result:

6.25

[wraith hinge]

6.25%

[split aspen]

I thought that each time the likelihood would split, that's why I come up with my previous solution, and then I added the probabilities up

[split aspen]

This multiplication is associated to the probability that both events occur?

All 4 of them*

Are they independent?

I'm getting confused here

[wraith hinge]

The chance for guessing right is always 50%

2x right = 0.5 x 0.5 = 25%
3x right = 0.5 x 0.5 x 0.5 = 12.5%
4x right = 0.5 x 0.5 x 0.5 = 6.25%

[split aspen]

Ok thanks a lot, I learned something new today 🙂

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[runic reef]

Question:
In triangle XYZ;
XY = 15cm
YZ = 13.5cm
Angle YXZ = 57 degrees
Work out the size of angle XYZ (Two possible combinations)

I'm able to get the first solution with the sine rule but I'm not sure how to get the second one

[trim comet]

cosine rule

And the sum of the angles in a triangle is 180°

[runic reef]

Ah alright thank you

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[warped wraith]

so i am trying to find the center of mass of this centroid given these functions, now I know the formula and steps but I am confused which would be the top and bottom function

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[warped wraith]

.close

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[cyan zinc]

how does one derive stirlings approximation?

[edgy cedar]

You can look up on YouTube or something

https://youtu.be/-k7s_nXGuO0

For example

https://youtu.be/rHVlS9i80x8

Or this one

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Please don't occupy multiple help channels.

[quiet spruce]

Yes it is for any grade

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[quick timber]

what’s the difference between 1 and 4 as well as 2 and 3?

[night zodiac]

It says horizontal compression/expansion in 1 and 2 and vertical compression/expansion in 3 and 4

[quick timber]

would the graphs not look the same though

oh oh wait

i see

how do i vertically compress something?

or expand

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[stable drift]

So how do you make a velocity time graph

[young swift]

the velocity is the integral of acceleration right?

so Make the graph of the integral

@stable drift

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[stable drift]

shoot mb

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[stable drift]

whats the integral

[young swift]

the area under the curve

[stable drift]

ohhh yes

but how would i make a graph out of that

[young swift]

at 1, the value would be 3, and 2 the value would be 6, etc

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[queen basalt]

need help

[queen basalt]

for 8d

it says its 20x + 30 but how?

i got 15x + 30

[quaint gazelle]

you forgot the first x

[queen basalt]

ah i see

so you have to add that too

lemme do the equation again factoring that

i only distributed 5

[quaint gazelle]

just expand the first parenthesis 3(x+2)

then simplify

then expand the [ ]

[queen basalt]

@quaint gazelle im getting 25x + 30 still

[quaint gazelle]

show me

how

[queen basalt]

is there a whiteboard

i cant take a pic rn im on pc

[quaint gazelle]

write the seps with your keyboard

5[x+3(x+2)]=......

[queen basalt]

ok ok

@quaint gazelle

bruh i rushed

i distributed the 3 to get 6 x and 3x

not x

[quaint gazelle]

yeah so why is the first x distributed?

[queen basalt]

good question

[quaint gazelle]

x isnt multiplied by the expression in brackets

only 3

[queen basalt]

@quaint gazelle so this is how u solve it

[quaint gazelle]

yeah

[queen basalt]

thank you man.

have a great morning/night

.close

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[drifting crow]

This question asks me to let $(X, d)$ be a metric space and fix $x,y\in X$, show that if $d(x,y)<\epsilon$ for all $\epsilon>0$ then $x=y$

[solid kiln]

kawaii_pear

[drifting crow]

I assumed by contradiction that x != y and I want to choose an epsilon such that d(x,y)<? contradicts that x != y

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@drifting crow Has your question been resolved?

[drifting crow]

<@&286206848099549185>

I have thought of a solution

So

I showed the contrapositive

and assumed that x != y and let epsilon = d(x,y)/2

since then d(x,y)>0 then 2d(x,y)-d(x,y)>=0 so d(x,y)>=d(x,y)/2=epsilon

which is the negation of d(x,y)<epsilon

thus the original statement holds

[quaint gazelle]

good

[drifting crow]

is that right?

[quaint gazelle]

yeah its right

[drifting crow]

okay thank you

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[sage mural]

how do I factor 2x^2-50=x^2-1

[sage mural]

also the fixed problem ( all terms on one side = to 0 is x^2-49= 0 right

[quaint gazelle]

a^2-b^2

[sage mural]

?

[quaint gazelle]

a^2-b^2=(a+b)(a-b)

[sage mural]

Sorry I don’t understand when you just put math terms without elaborating

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[wraith hinge]

.close

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[sand pendant]

a bit confused of finding general solutions to linear diophantine equations 🤔

[sand pendant]

in the book they have the example 45x + 21y = 72 and supposedly the answer is (x, y) = (24 - 7n, -48 + 15n) but using an online calculator, the sign for the n terms are always reversed

e.g x = 24 + 7n and y = -48 - 15n

whats up with that?

[dense breach]

that's because n can be any interfer

integer

so

if 5 produces a certain solution in the first equation

Then -5 would produce the same solution in the other

[sand pendant]

but why would the sign be different just from pulling out x and y from (x, y)?

[dense breach]

what u mean?

[sand pendant]

(x, y) = (24 - 7n, -48 + 15n) <--- notice the `-` and the `+`
x = 24 + 7n <-- sign change, 
y = -48 - 15n <-- sign change

[dense breach]

they probably use a slightly different method to solve it

but the solution is equivalent

like

Do you know set notation?

[sand pendant]

yeah

[dense breach]

Like if I said {3n+1 | -5 ≤ n ≤ 5}

[sand pendant]

yes

[dense breach]

could you tell me what that set is

[sand pendant]

{-14, -11, ...}

[dense breach]

{-14,-11,-8,-5,-2,1,4,7,10,13,16}

right

now {-3n+1 | -5 ≤ n ≤ 5}

see I put a negative on the n term this time

[sand pendant]

oh i see

so whats the typical general solution people tend to use then?

like by convention

[dense breach]

there isn't one really

Theyre both fine

[sand pendant]

alrighty

[dense breach]

{3n+1 | n is an integer} or {-3n+1 | n is an integer}

same set

[sand pendant]

yeah

just caught me off guard

thank you for the help

.close

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[mint peak]

how to prove that $ln(x) sin^2(x) \in O(log_x(2^x))$

[vast zephyr]

my names michal asw ell

damn

[solid kiln]

Michal

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[quasi walrus]

how can i get draw the sum of the 3 vectors

[zinc ginkgo]

do you know how to draw the sum of 2 vectors?

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[acoustic bay]

can someone explain why you do this for part b

[acoustic bay]

is the max arg the bit i highlighted in blue?

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[acoustic sierra]

I need help on 10

Here is my work

Please tell where I have made a mistake

[slender shard]

(x+2)^2 = x^2 +4x + 4

[acoustic sierra]

Im finding the derivative of f(x)

Idk how that would help

[slender shard]

You won't calculate the correct derivative if you don't calculate the correct derivative.

[acoustic sierra]

Nvm

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[dawn heart]

How do i complete thte square of g(x) = -0.5x^2 -2x + 3

[dawn heart]

a. Complete the square to determine the vertex
b. Plot, then reflex y int
c. Sketch the function and label the 3 points

[long basin]

To find the vertex?

Alright give me a sec

[dawn heart]

👍

[split chasm]

start by factoring -0.5 out of the first two terms

(or three depending on personal preference)

[dawn heart]

The worksheet my teacher gave said to 1) group the 2 terms, 2) divide the x co-efficent by half and square it then add it to the trinominal and do the opposite

but when i tried i kept doing it wrong when i graphed it

[split chasm]

show work

[split chasm]

ah, those were the steps for the basic stuff where you have a monic

where the coefficient of leading term is 1 which isn't the care here

start by factoring -0.5 out of the first two terms

this might help

$\advcts$

[solid kiln]

ℝamonov

[long basin]

$$\begin{align*}
\f(x) &= ax^2 + bx + c \
&= a\left(x^2 + \frac{b}{a}x\right)+ c\
&= a\left(x^2 + \frac{b}{a}x + \frac{b^2}{4a^2}\right) + c - \frac{b^2}{4a} \
&= a\left(x-\frac{b}{2a}\right)^2 + c - \frac{b^2}{4a}
\end{align*}$$

SEND

FUCKING

WIFI🗿

Bruh everything just piled on

[solid kiln]

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

[long basin]

I love wifi moments

[dawn heart]

im so confused

[austere sierra]

https://youtu.be/C206SNAXDGE

here you go!

maybe this vid can help

[long basin]

Plug in

[dawn heart]

what about h(x) = 4x^2 -12x

do i just factor it out?

to (x-3)^2

so the y int would be 0, correct?

@split chasm

<@&286206848099549185>

[split chasm]

no

[dawn heart]

dang

my teacher really gave us this

[split chasm]

y int would be 0
but you don't just factor to (x-3)^2

4x^2 -12x isn't the same as (x-3)^2

[dawn heart]

okay

so how would i do this then

[split chasm]

were you trying to complete the square for this as well?

[dawn heart]

yes

[split chasm]

first factor out the 4

[dawn heart]

4(x^2 - 3x)

[split chasm]

not quite

[dawn heart]

oops

3x

[split chasm]

and then complete the square for the
x^2 - 3x within the parentheses

$\cts$

[solid kiln]

ℝamonov

[dawn heart]

-3/2 = -1.5

so that would then be i think: x^2 -3x - 1.5

or actually

(b/2)^2 = (-3/2) = 9/4 = 2.25

@split chasm yes? good?

hello?

[split chasm]

(b/2)^2 = (-3/2) = 9/4 = 2.25
missing ^2 on the (-3/2)

now write the full thing out

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[restive shard]

could someone explain to me why the range can not be -8 or 0?

[split chasm]

-4 and 4 aren't in the domain

[nova spire]

for every x in the domain of f, f(x) = x-4 is in the range of f
Yet -4 and 4 are not in the domain, so -4-4 and 4-4 arent in the range

[wooden thorn]

because h(x) being the denominator can't be 0

h(x) = x^2 - 16 = (x+4)(x-4)

it can be 0 only when x=-4 or x=4

[nova spire]

h(x) is the opposite

1/[(x+4)(x-4)]

[nova spire]

From this you have that -8 and 0 are not in the range. They would be if -4 and 4 were in the domain (bc in that case we would have f(-4) =-8 and f(4)=0)

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[restive shard]

wdym?

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[wraith hinge]

a

[wraith hinge]

guys

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[open zinc]

If they must have six characters - - - - - -

and can be made up of 3 letters followed by 3 numbers or 6 letters or 6 numbers

[open zinc]

very simple question

icounting principle question

i got 327491776

[wraith hinge]

What must have six characters? Passwords?
26 letters and 10 numbers?

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[open zinc]

its a license plate

if a license plate has six characters...

[open zinc]

@wraith hinge

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[past sapphire]

What is question trying to say bro (q15)

[vagrant marsh]

1.001^4=(1+0.001)^4

[past sapphire]

Can you explain how that works and why

[past sapphire]

!

[vagrant marsh]

you split the number to make it easier to deal with, kind of like foil

[past sapphire]

Oh

That’s simple

Thank u

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[wraith hinge]

I personally do not know this sort of “subject” but there is for sure people here that do

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[left plover]

hey guys, I got a little problem.
I have a multidimensional distribution and I'm trying to do numerical integration but the problem is that it gets very very inaccurate for moments when it's many standard deviations away. What's an algorithm that can solve this problem?

[left plover]

f() is the probability density

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[left plover]

<@&286206848099549185>

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[obsidian vault]

Hey is anyone willing to solve four 2d motion - horizontal velocity questions? It’s an old assignment that I don’t have time to do rn

[grand ridge]

do better m8

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[acoustic bay]

how do i do A?

[dark quest]

Check whether or not AB is perpendicular to BC. If yes then you are done. 🙂

[acoustic bay]

ohh ok lemme try

[acoustic bay]

but how does that mean if it is a diameter if they are perpendicular

[acoustic bay]

OH YEAH that circle theorem rule

ty

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[opaque vapor]

How do I do this problem?

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[wraith hinge]

<@&268886789983436800>

oh wrong ping

<@&286206848099549185>

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[wraith hinge]

I struggle making functions

[supple copper]

Did you fill the table

[wraith hinge]

No

I am clueless when it comes to the most basic algebra questions

When t=0 let its quantity be Q

After t=1 it will be .....Q/2

After t=2 ......Q/4

And so on ?

[wraith hinge]

How would I solve for Q?

That would be the amount of medication

[supple copper]

Ok when it say the initial quantity is 20mg

What does that mean

[wraith hinge]

It means the Quantity is 20
So that means if t increases by 1 it would increase exponentially?

[supple copper]

So there’s more of the drug?

This is half life not double life

[wraith hinge]

[supple copper]

The half-life of something means after x time half of the substance decays to something else

[wraith hinge]

So it would be declining exponentially

[supple copper]

Yep

[wraith hinge]

oh

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[wanton dust]

Why the h is in dominator

[wanton dust]

Instead of being independent

[trim lichen]

because it's f(x+h) not f(x) + h

[surreal flume]

f(x+h) means u replace all the x u find in in f(x) with x+h

[wanton dust]

Thanks

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[wraith dagger]

Why is this simplification wrong

[marble wharf]

,rotate

[wraith hinge]

Factorize?

[marble wharf]

so the first line is $5^x\cdot 5^3 - 5^x \cdot 5$ ?

[solid kiln]

Denascite

[wraith hinge]

I mean write factors of 3000 and compare

[marble wharf]

and the second $5^x\cdot (5^3-1.5)$ ?

[solid kiln]

Denascite

[wraith dagger]

no

thats not it

i ll send u the question

[marble wharf]

well what you wrote down looks like it

[marble wharf]

maybe $5^x \cdot (5^3-1\cdot 5)$ ?

[solid kiln]

Denascite

[wraith dagger]

The 7th

a point means * here

[marble wharf]

if you mean this then it is correct

[wraith dagger]

yeah its

this isthe q

[marble wharf]

yes I saw that. your simplification is correct

[marble wharf]

,rotate

[wraith dagger]

But its incorrect

[marble wharf]

who says that

[wraith dagger]

In the correct factorization there is no -1

[marble wharf]

well I don't know why you put it there

[wraith dagger]

The correct form is( 5³×5)

[marble wharf]

but $1\cdot 5=5$ so you can just ignore it

[solid kiln]

Denascite

[marble wharf]

$5^x \cdot (5^3-1\cdot 5) = 5^x\cdot (5^3-5)$

[solid kiln]

Denascite

[wraith dagger]

Oh ffs i messed up the Pemdas rule

Sorry man

Ty

i look like an idiot now

/close

[marble wharf]

dont worry, you don't

.close

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[wraith dagger]

.reopen

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✅

[wraith dagger]

dude i dont get this equation

the 8th

[atomic herald]

Notice something look the same

[wraith dagger]

yeah 3x

oh i can put it on same deno

[atomic herald]

Yes

[wraith dagger]

so 3xsaquare

[atomic herald]

Can you erase the denominator on the left?

[wraith dagger]

ofc not

[atomic herald]

Not x²

2³×2³ is not 2⁹

[wraith dagger]

ofc not its 2to power 6

[atomic herald]

Yes now fix yours

[wraith dagger]

oh 3to power 2x

[atomic herald]

Yes correct

Now can you make the denominator dissapear?

[wraith dagger]

we can but only dumb would do that, i ll do 8*3to power x as a good mathematician

[atomic herald]

Yes do that

[wraith dagger]

but i have a question why did we switch denominator

[atomic herald]

Because you multiply both side by the denominator

[wraith dagger]

is the equation not doable with out multiplying the both side

[atomic herald]

Probably it can but harder

[wraith dagger]

oh ok so whats next

[atomic herald]

Can you solve it from there?

Show the equation if you cant

[wraith dagger]

i smell a 2nd degree equation

[atomic herald]

Yes correct

[wraith dagger]

so y=3to power x

[atomic herald]

And you must aware of something

[wraith dagger]

?

[atomic herald]

Yes you can substitute with that

[wraith dagger]

what was your idea

was it the same as mine?

[atomic herald]

Yes, use subtitution

But dont forget you are solving for x not y

[wraith dagger]

yeah i ll replace once i get the y value

to the x

[atomic herald]

Yes correct and dont forget exponent cant get to negative

[wraith dagger]

yes sir thats logic

but someting wrong here

[atomic herald]

Whats wrong?

[atomic herald]

Its wrong

[wraith dagger]

tell me the line i ll find it

[atomic herald]

you're correct until line 3

[wraith dagger]

senoir is this correct?

[atomic herald]

No, do you want a hint?

[wraith dagger]

yes sirr

oghh

ohh

[atomic herald]

The 8 is bound to y

[wraith dagger]

nah i found it first

[atomic herald]

Yeah now fix it

[wraith dagger]

so from here delta and ezz

[atomic herald]

Yep

[wraith dagger]

i found y 9 and -1

-1 does not exist

cause exponetial function is amways above the 0 axis

of y axis

and ifs 3power x = 9

x=2

[atomic herald]

Yep correct, good job

[wraith dagger]

ty senior

adigos

[atomic herald]

Np

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[wraith dagger]

@atomic heraldcaptain sorry for the mention im having hard time with this

[wraith dagger]

The 13th

And i tried like this

[atomic herald]

You're getting there

Look at the rule of logarithm

There is a form like that

[wraith dagger]

i ll check it

sorry senior i cant find the rule

[atomic herald]

We can go back to line 5

Can you make
2² = 4
In logarithm form?

[wraith dagger]

its log base 2 of 4=2

[atomic herald]

Yep use the form for line 5

[wraith dagger]

log was introduced to me a few days ago so i m still learning it

[atomic herald]

Yeah its quite annoying at first

[atomic herald]

Yep correct

[wraith dagger]

oh wait is that the answer?

[atomic herald]

Yes you got the x

[wraith dagger]

got the x value without any efforts

there is like more than 5 demostration and we just started the chapter idk how will i survive

[atomic herald]

You'll do find, lots of tutorial on youtube

[wraith dagger]

yeah i ll try to understand with yt or else i will come find u😂

[atomic herald]

I'll help if im free

[wraith dagger]

alr ty i ve to practice word problems now

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[simple thicket]

Help

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@simple thicket Has your question been resolved?

[simple thicket]

<@&286206848099549185>

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@simple thicket Has your question been resolved?

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@simple thicket Has your question been resolved?

[sonic vector]

@simple thicket But what do you need help with? You didn't solve any of those? Did you try?

[simple thicket]

Yes I tried

[sacred jackal]

then show us ur work

[wraith hinge]

Hes playing League of legends!

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[burnt cloud]

reserved

[burnt cloud]

I am just doing some introductory logic question. I am a bit confused on if this statement can be considered biconditional. Can anyone help me understand?

I feel like it is because I could re-write it as Today is the longest day of the year IF AND ONLY IF the summer solstice occurs today. However, I am not actually sure if this meets the constraint of what a biconditional statement is.

in order for a statement to biconditional MUST IT include a logical statement and its converse?

Also what would this statement's contrapositive be?

[atomic herald]

There is a another form of biconditional using converse

[burnt cloud]

I'm not sure excactly how to abstract this into logical notation as I haven't actually learned the notation yet.

Is it true that this would be a biconditional statement using the original questions logic.

[atomic herald]

You havent learn something like P-->Q

[burnt cloud]

No sir

I think it's in the next lesson to be honest

These questions the teacher said to ignore for now

but I wanted to try to solve them

[atomic herald]

What does it take for the statement to be biconditional?

You can use logic here its okay

[burnt cloud]

one condition is true if and only if the other condition is also true?

[atomic herald]

Yes

[burnt cloud]

then it is biconditional

Ok so biconditional just means both constraints must be true in order for the statment to evaluate true

it's like the logical operator and then

in a programming statement?

[atomic herald]

And if one statemnet false the other will be false too

[burnt cloud]

i.e. Condition = 1 AND condition =1, statement = 1 but if either condition were 0 the statement would evaluate 0

[atomic herald]

I would say it looks like the negation of XOR

No3

If both false then its true

Its wrong if one is true the other is False

[burnt cloud]

right

so both must be true basically?

[atomic herald]

Both can be false too

[burnt cloud]

or both can be false

ok

[atomic herald]

Yes

[burnt cloud]

so

(condition) AND (condition), 1 AND 1 = 1, 0 AND 0 = 1, but 1 AND 0 = 0 or 0 AND 1 = 0 if that makes sense. Like in boolean logic.

[atomic herald]

Yes

Just use True and False like python

[burnt cloud]

ok

Do you know what bi-conditional would be?

or

excuse me lol

I mean contrapositive

of the statement

[atomic herald]

Contrapositive has same value with conditional

It usually use to prove something

[burnt cloud]

so in my above example

if I was going to write the contrapositive statement

[atomic herald]

Contrapositive is like inversing the statemnet then converse it

[burnt cloud]

really? uhm

so

[atomic herald]

??

[burnt cloud]

If the summer solstice does not occur today, then today is the longest day of the year?

compared with the original statement:

[atomic herald]

is not

[burnt cloud]

is not yeah

[atomic herald]

Yeah

[burnt cloud]

interesting

logic is very fascinating

I will have to investigate these things in much more depth

[atomic herald]

Logic is just a tool

Its like a basic thing to prove something

[burnt cloud]

Like a methodology sort of

it implies the rigor of mathematics though

[atomic herald]

I think this channel has a book recommendations about mathematical prove, its a good book

Only 400+ pages, not too much for a math book

[burnt cloud]

in #books-old?

[atomic herald]

Yes

[burnt cloud]

Do you know a good resource to study introductory logic?

This book you are referencing then?

[atomic herald]

Wait

• INTRODUCTORY BOOKS

A Programmer’s Introduction to Mathematics (Jeremy Kun)
Aimed at programmers
Explains e.g. linguistic conventions and jargon in a very accessible way; well suited to self-study

Mathematical Proofs: A Transition to Advanced Mathematics (4th Edition) (Chartrand, Polimeni, Zhang)
No prerequisites
https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0134746759
Very clearly written, neither too slow nor too fast. Modern notation and low levels of handwaving. Contains worked examples and outlines of proofs, full solutions to many exercises. Later chapters serve as introduction to various topics.

The Art and Craft of Problem Solving (Paul Zeitz)
Assumes some basic calculus and comparable fundamentals. Anyone with an open mind should be able to profit from it.
The book is really well written, and focuses a lot on the process of solving a problem in addition to actual problem solving. It has a lot of problems after theory. It focuses on the basics of problem solving, and have chapters on problem solving strategies, cross-over tactics, combinatorics, number theory, geometry and some analysis and linear algebra.

How to Prove It (Daniel Velleman)
No prerequisites
A great introduction to proof oriented mathematics (higher/pure mathematics), for people who have never done that kind of thing before.

Mathematical Proofs : A transition to advance mathematics

This book is good, at least for high school level

[burnt cloud]

Yes, that is my current level of understanding

Thank you very much for your help

[atomic herald]

Np

[burnt cloud]

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[turbid crane]

I thought the answer inside of the integral was (x^2+2 - 1)^2 - (2-1)^2

[turbid crane]

but my teacher had wrriten it like that ^

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[turbid crane]

washer method btw

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[ionic sleet]

no clue where to start, just might need some help starting out and then i should be alright

[rugged latch]

Write tan in terms of sin and cos

@ionic sleet

[ionic sleet]

What exactly do u mean by that sorry

[rugged latch]

How do u get tan from sin and cos

Look top right

[ionic sleet]

Ohhhhh

I see i see so just write tan as sin over cos and solve starting there

[rugged latch]

Ye

[ionic sleet]

ty ty

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[slim flicker]

hi can i please get help on this q

[slim flicker]

the answer is sqrt(2)

[muted maple]

so what is the acceleration vector

[slim flicker]

the second derivatitve?

[trim lichen]

yes, so are you having trouble taking the second derivative of any of these three coordinate functions?

finding $\ddot{x}(0)$, $\ddot{y}(0)$ and $\ddot{z}(0)$ should not be very hard imo

[solid kiln]

Ann

[slim flicker]

uhh ill try that rn

im just confused on how to approach this q

[trim lichen]

there is no approach, there is do

this question is not the kind that demands creativity in the slightest

[slim flicker]

my apologies

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@wraith hinge Has your question been resolved?

[inland orbit]

Do you understand how the vector equation of a line works?

$\vec{x} = t\vec{v} + \vec{p}$

[solid kiln]

tatpoj

[inland orbit]

Where p is a point on the line, and v is a direction vector

So, have you tried anything yet?

Yeah well, there's more than one right answer

But just take the first choice

See how the p is (0,1), right?

So if you plug in t=0, then you get x=(0,1)

Do you agree?

Is (0,1) on the line y=2x+1?

Now, pick a second value for t.

What if you plug in t=1, then what point do you get?

Is that point also on the line y=2x+1?

There's only one possible line between two points

So if you match two points, then that's an equation for the line

Nope, not if you check at least two points

So the vector with the blank is the direction vector

Can you come up with a direction vector that's parallel to that line? Even if it doesn't match the -1?