help-19

[mortal hinge]

4-3 class work at the top

[mystic saffron]

perhaps write $sin(\frac{11pi}{6}$ as $sin(\frac{12pi}{6}-\frac{pi}{6}$

man

[clever fjord]

Prime Minister

[mortal hinge]

why ?

this is my work btw

[mystic saffron]

write $sin(\frac{11\pi}{6})$ as $sin(\frac{12\pi}{6}-\frac{\pi}{6})$

[clever fjord]

Prime Minister

[mystic saffron]

LETS GOOOOOOOOOOOOOO

okay now

[toxic monolith]

sine is positive only in the first and second quadrants

[mystic saffron]

12pi/6 becomes 2pi and it goes bazoonk because its a full circle and we dont count full circles because youre essentially back where you came from

so you remain with $sin(-\frac{\pi}{6})$

[clever fjord]

Prime Minister

[mortal hinge]

oh 😭

[mystic saffron]

which to say is the same as $-sin(\frac{\pi}{6})$

[clever fjord]

Prime Minister

[mystic saffron]

ye

basically its -1/2

[mortal hinge]

right right

[mystic saffron]

sorry yapped too hard

[mortal hinge]

ok wait let me try the second one

then u can keep yapping

if i get it wrong

okay wait i'm trying to draw it but like

where do i make the right triangle

[mystic saffron]

why draw

you learn them numbers by heart

[mortal hinge]

ugh

its easier to draw than memorize them

okay what numbers

[mystic saffron]

its cos60 degrees

htink of π as 180, then you just do simple division and youre gucci

[mortal hinge]

oh im dumb

i got it

[mystic saffron]

except like the first one where its a little quirky

[mortal hinge]

then for the last one

tan(180)

[mortal hinge]

wait what do you mean do division

[mystic saffron]

π/3 = 180/3 = 60

π/6 = 180/6 = 30

[mystic saffron]

yee tan 180 that is a solid zero

[mortal hinge]

okokk

ty

.close

[odd edge]

Channel closed

Closed by @mortal hinge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vital wadi]

i simply dont get the sentence

[vital wadi]

and the thing in general

[past solar]

it says sum of the first n terms is equal to the quadratic expression

[vital wadi]

yeah

may you help

[past solar]

try finding sum of first terms

[vital wadi]

8 and 2 ?

[tepid acorn]

use the formula for sum of first n terms

and equate that value, to 8n^2 - 2n

[vital wadi]

huh ?

i dont get it

[tepid acorn]

also consider when n = 1 to find first value

[past solar]

no

[tepid acorn]

whats formula for sum of first n terms in arithmetic progression

[vital wadi]

answer pwease :3

[tepid acorn]

if u don't know it, then this problem might be too advanced for u

[vital wadi]

this math software is poopoo

[past solar]

!noans

[odd edge]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[vital wadi]

it gives either too easy or too hard

awh :(

[tepid acorn]

yea u have to have an understanding of arithemtic sequences for this

[past solar]

try finding sum of first terms

[vital wadi]

my brain is not at its fullest since its 1 am where i am

[past solar]

3 am here

[tepid acorn]

a) hint: if you take n = 1, then what happens?

[past solar]

it works fine

[tepid acorn]

b) use the formula, S_n = n/2 * (2a + (n-1)d)

and plug in what a is equal to (because a is the initial value), which you get from part a)

[vital wadi]

yeah

so 1/2

[tepid acorn]

you have a simple quadratic in d

[tepid acorn]

if u don't have a good understanding of arithmetic sequence, as well as algebra then this problem is probably out of ur reach and its not gonna be helpful to u

[vital wadi]

its not that i dont understand algebra its easy but the problem is that a english isnt my first language and b my brain is not at its smartest since i was in winter holidays

[tepid acorn]

ok, an arithmetic sequence is a sequence like 3, 5, 7, 9, ...

[vital wadi]

yeah

[tepid acorn]

where the difference between each term is a cosntant (typically d)

[vital wadi]

mhm

[tepid acorn]

the formula for the sum of the first n terms of an arithmetic sequence

can be derived as following:

[vital wadi]

oooooh

[tepid acorn]

sum = # of terms multiplied by avg. value of term

let # of terms be n, common difference be d, and first term be a

the # of terms is just n

and the avg. value of term is equal to (first term + last term) / 2 because it is an arithmetic sequence

first term is a, last term is a + (n-1) d

[vital wadi]

.close i will do it tomorrow with a bright head

[tepid acorn]

so the avg. value of term is (2a + (n-1)d) / 2

[odd edge]

Channel closed

Closed by @vital wadi

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[old whale]

Can someone help check my work

I tried to find a “better integral”

For the gamma function

Someone tell me how much I messed up

[odd edge]

@old whale Has your question been resolved?

[old whale]

<@&286206848099549185>

[odd edge]

@old whale Has your question been resolved?

[old whale]

<@&286206848099549185>

[old whale]

<@&286206848099549185>

What did I mess up

Did I mess up because I am probably did

[odd edge]

@old whale Has your question been resolved?

[tall veldt]

what are you even trying to do?

[old whale]

<@&286206848099549185>

[mystic saffron]

refer to what @tall veldt said

[tired girder]

this kinda hurting my brain

[stiff kettle]

gamma function?

[odd edge]

@old whale Has your question been resolved?

[old whale]

<@&286206848099549185>

I wanted to find another way to “generalize” the gamma function. I’m not sure if it is correct though.

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[tame delta]

why is this not possible

[crisp wadi]

Open another channel, you just closed this one by deleting the first message

[tame delta]

.close

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pseudo vigil]

I was unsure as to how to do A here, so I checked the mark scheme. After checking it, i'm still unsure as to how to factorise from
3(log3p)^2 -8log3p + 4 = 0 into the next line, could someone explain?

[pseudo vigil]

i don't get where the -8 coefficient to the log went

[nimble blaze]

have you factorised quadratic equations before?

would you be able to factorise the similar expression:
$$3x^2 - 8x + 4$$

[clever fjord]

ℝαμΩℕωⅤ

[pseudo vigil]

yes i have,

[pseudo vigil]

(3x-2)(x-2)

i just confused with the 3 coefficient out the bracket and then it goes inside, and where the -8 coefficient to the log went

[nimble blaze]

same idea applies here

just instead of $x$ you have $\log_3p$

[clever fjord]

ℝαμΩℕωⅤ

[nimble blaze]

$3\underbrace{(\log_3p)^2}{x^2} - 8\underbrace{\log_3p}{x} + 4$

[clever fjord]

ℝαμΩℕωⅤ

[pseudo vigil]

ohhh

i understand nw

thanks @nimble blaze

.close

[odd edge]

Channel closed

Closed by @pseudo vigil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[frigid canopy]

if {$x$} denotes the fractional part function, find {$\frac{3^2n}{8}$} , where n is a ntural number

[frigid canopy]

*fractional part of 3^n/8

I did get 1/8 by trial and error

but how would I get a result more rigourosly

[shy smelt]

You would look at 3^n mod 8

[lavish kite]

well if n = 1 then 3^n/8 is 3/8 and the fractional part of 3/8 is not 1/8 so uh

[frigid canopy]

I meant 3/8 my bad

[lavish kite]

well if n = 2 then 3^n/8 is 9/8 and the fractional part of 9/8 is not 3/8 so uh

[shy smelt]

It depends on whether n is even or odd

[clever fjord]

Why am. I here

[lavish kite]

yeah

[frigid canopy]

2n

not n

my bad

sorry

[shy smelt]

ooh, then it's 9^n, right?

[lavish kite]

(3^(2n) is written 3^{2n} in latex)

[shy smelt]

$\left{\frac{3^{2n}}{8}\right}$

[frigid canopy]

is there any way without modular arithmatic? modular arithmatic isn't in my syllabus

[clever fjord]

Jelle

[frigid canopy]

yes, this is my question. TYSm

[lavish kite]

i guess induction on n?

[shy smelt]

I mean, modular arithmetic is essentialy looking at remainders

so you can prove something about the remainder after division by 8?

[frigid canopy]

hmm, thanks!

.close

[odd edge]

Channel closed

Closed by @frigid canopy

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[twilit flax]

Hey guys, I wanna ask for help:D
basically, my question is
f(x) = ax^2 + bx + c
f(x) = x^2 + 2x + 5
I did is
y - 5 = x^2 + 2x + _
then
[(1/2) (b)]^2
[(1/2) (2)]^2
[(2/2)]^2
(1)^2
then
y - 5= x^2 + 2x + 1
and i did
y - 5 = (x+1)^2
then i tranposed 5
and got f(x)= (x+1)^2 - 5
and my a,h,k are 1,1,-5

[twilit flax]

(its confusing but i can make it on paint)

[iron grotto]

please do

[twilit flax]

aight

something like this

:)

[iron grotto]

whats the question

[twilit flax]

like that

[iron grotto]

uh

[twilit flax]

yea idk

[iron grotto]

all is see is equations

what's this

[twilit flax]

hold up

its my assignment, but i dont get it , but i'll show the picture of the question

[iron grotto]

yeah

[twilit flax]

yea

[iron grotto]

ohhh

[twilit flax]

i dont get it either

im also not sure what method to use

[iron grotto]

i understand

method of completing square

[iron grotto]

do you know this?

[twilit flax]

yea

[iron grotto]

yup

just that

[twilit flax]

i did (x + 1)^2

then subtract the -5

to make it (x + 1) -5

i meant

+5

[iron grotto]

• 4 *

(x+1)^2 + 4

[twilit flax]

why 4?

oh

oh yea

what we did in right side, we do in left side

i forgot about that

[twilit flax]

so the a h and k are 1,1,4

?

I also have another question, cause i'm confused about it and i cant complete the square

[odd edge]

@twilit flax Has your question been resolved?

[iron grotto]

the coefficient of x^2 should be 1

[twilit flax]

what?

yea

i know

but i have another question

cause i cant solve this and i dont know how to do it

[iron grotto]

can you show that

[twilit flax]

basically the question is

f(x) = 2x^2 + 5x + 4

i got to the part where i got in
y - 4 = 2x^2 + 5x

I don't know how i'm gonna factor out 4

[iron grotto]

divide by 2

both the sides

then complete the square

[twilit flax]

how

5/2?

that doesn't look like it cant be factored tho

[twilit flax]

oh?

my answer would be just 5/2x?

jeez

[iron grotto]

oh wait

[twilit flax]

i dont get anything

[iron grotto]

he didnt ask to complete the square

[iron grotto]

yes

[iron grotto]

forget that

[twilit flax]

its until to complete the square

i was thinking to get like

2(x^2 + 5/2x) + 2

or smth

[iron grotto]

you were trying to complete the square right?

[twilit flax]

yup

for a,h, and k

[iron grotto]

its done like this

[twilit flax]

what is that

[iron grotto]

this term is (x+5/4) ^ 2

[twilit flax]

but why 4?

[iron grotto]

um its a method

you said you knew completing the square

?

[twilit flax]

yea

but (x + 5/4)^2 looks different

[iron grotto]

i did the same thing

[iron grotto]

wait

i forgot

[twilit flax]

i was thinking if a was 2

cause its in outside or smth like that

[twilit flax]

like uh

[iron grotto]

its correct now

i forgot we had taken 2 common

lol

[twilit flax]

wait can u type this

wouldnt be the 4, 2?

oh wait

[iron grotto]

2(x^2 + [5/2]x + (5/4)^2 ) + 4 - 2(5/4)^2

[twilit flax]

damn

steps?

i was thinking uh since equation was 2, wouldnt be 2 added to left side or no?

[iron grotto]

i first made the coefficient of x^2 to be 1

and not 2

https://cdn.discordapp.com/attachments/903463355619110912/1192467961034854500/image.png?ex=65a92f54&is=6596ba54&hm=00e7e15241e112a0a4db05ca81138146203364da9e95fdb6a29153f25edfcb36&

this step

[odd edge]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[twilit flax]

but how do you get the 5/4 as the final answer

[iron grotto]

yeah im telling you

[twilit flax]

with other stuff like that

[iron grotto]

now we add and subtract the ** half of the square of the coefficient**

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[twilit flax]

oh yea

[twilit flax]

i dont know how that works

[iron grotto]

yeah

understood?

[twilit flax]

how do you do tihs?

they never taught us that, or i just forgot it

[iron grotto]

um its the way i remember

i dont know about urs

[twilit flax]

aight

uhm

i have 2 questions then i'm gonna go soon

[iron grotto]

okay

[twilit flax]

basically this question is uh

f(x) = x^2 + 1
-------
5

where do you start there

[iron grotto]

um

x is 0 here

cant write it in that form

[twilit flax]

the question is just like that

i dont know where to start

[iron grotto]

okay

its literally

oh my god why am i acting dumb

1/5(x+0)^2 + 1/5

[twilit flax]

oh

how about

f(x) = 2x^2
-----
3

[iron grotto]

same way

[twilit flax]

oh lol

2/3(x+0)^2 + 2/3

?

[iron grotto]

there's no constant term

no need to add 2/3 there

[twilit flax]

oh wait

how about this

f(x) = 4x^2 + 5x - 8

i did was uh

y + 8 = 4x^2 + 5

then i need to factor out 4 again

[iron grotto]

yes

take 4 common

you get 5/4 there

[twilit flax]

y + 8 4(x^2 + 5/4

[iron grotto]

and then complete the square

[twilit flax]

is it just gonna be like that

[iron grotto]

good

[twilit flax]

how would i do that

xD

[iron grotto]

ill tell you again

i think this example will you help you

[twilit flax]

Alright

[iron grotto]

i took 4 common

and now

as i said before

[twilit flax]

looks painful

i dont even get it

[iron grotto]

its not

[iron grotto]

this term

is 0 right?

[twilit flax]

yeah?

is that the H

[iron grotto]

so it doesnt make a difference

[twilit flax]

i dont which is which

[iron grotto]

no i didnt simply if yet

this is intermediate

https://cdn.discordapp.com/attachments/903463355619110912/1192472669703114843/image.png?ex=65a933b7&is=6596beb7&hm=0efc2f110416b318853e33093f05b5d4bc90eb437ccd5001864e50f8d07daa01&

this part is (X + 5/4 )^2

[twilit flax]

damn

wait

where did 2 came from btw

:)

[iron grotto]

4x^2 + 5x - 8 right

[twilit flax]

yup?

[iron grotto]

4(x^2 +(5/4)x - 2 )

the same thing.

[twilit flax]

whAt

[iron grotto]

multiply the 4 in each term

you'll get the same question

[twilit flax]

uh

[iron grotto]

these two are the same thing right

[twilit flax]

but where do i multiply the 4

where each term

[iron grotto]

dont

you might be thinking why did I do this right?

[twilit flax]

yea?

[iron grotto]

that's because

[twilit flax]

no i'm just confused where did you multiply to get 2

[iron grotto]

I re-wrote the whole equation

have a look at it again

the 2nd equation is same as the 1st

[iron grotto]

now is it fine?

[twilit flax]

oh

[iron grotto]

I'll do it in this way

[twilit flax]

but why is - 8 there

wouldn't it be like

y + 8 = 4(x^2 + 5/4

[iron grotto]

its in the question...

[iron grotto]

Exactly

take the 8 to the right hand side

isnt that -8?

[twilit flax]

why

cause you can't factor it anymore i guess?

am i right

[iron grotto]

you know what

youre right

ill do it in your way

youre getting confused

[twilit flax]

i am

[iron grotto]

okay so this the equation now

okay?

[twilit flax]

hmm

yeah

[iron grotto]

now ill be manipulating the right hand side

so

[twilit flax]

subtract

right?

to make 8 go in right side

idk my teacher's way

[iron grotto]

let it be there

for now

[twilit flax]

hmm

aight

[iron grotto]

in the 2nd step

[twilit flax]

oh

[iron grotto]

understood?

[twilit flax]

yeap

[iron grotto]

Nice!

[twilit flax]

but i'm just gonna act 5/8 isn't there since its gonna be 0

or smth

[iron grotto]

the reason why I did that was

this thing

this part is (x + 5/4) ^ 2

[twilit flax]

then

[iron grotto]

so h is -5/4

[iron grotto]

a = 4

and k is the constant term

[twilit flax]

yeah

but how 2

[iron grotto]

where 2?

[twilit flax]

thiS

or is it just gonna be 8

[iron grotto]

forget that

[iron grotto]

the solution starts from here

[twilit flax]

aight

[iron grotto]

understood?

[twilit flax]

how do you get the answer without completing the square

[iron grotto]

cant

trust me this is the easiest method

[twilit flax]

aight

[iron grotto]

you need practise

[twilit flax]

i can but i dont know where to start

[iron grotto]

to the point where you don't need pen

[thin kelp]

what is the questions?

[twilit flax]

i dont even make my own solution i just go with my brain

[iron grotto]

he wants to represent the quadratic equation in the form of
a(x-h)^2 + k

[thin kelp]

ah

[iron grotto]

basically completing square

[thin kelp]

yeah

[iron grotto]

so yeah

[iron grotto]

there are videos on yt

[twilit flax]

aight i watched

they just use the vertex form thing

[thin kelp]

yeah that is the vertex form?

[twilit flax]

what

[thin kelp]

a(x-h)^2 + k

where the point of the vertex is (h,k)

[twilit flax]

there is no vertex even mentioned in this topic

its next topic

[iron grotto]

ah

[twilit flax]

yea

idk how my book works

[thin kelp]

how does this change anything?

[iron grotto]

just learn method of completing square

[twilit flax]

aight

[twilit flax]

i dont know either

i just said it

@iron grotto

wait

hi

[iron grotto]

ok

[twilit flax]

uh

this

f(x) = 3x^2 - 4x - 7

will it be the exact thing

like

y + 7 = 3(x -4/3)^2 smth like that

[iron grotto]

Yesss

Wait

[twilit flax]

aight

[iron grotto]

NO

NO

[twilit flax]

what\

what happen

[thin kelp]

thats not how u complete the square

[twilit flax]

aight

then i just dont know how to do it

[iron grotto]

.

[thin kelp]

see this.

[twilit flax]

i cant complete the square when i cant factor it thats why

[thin kelp]

aight start from beginning

[thin kelp]

.

[iron grotto]

https://www.youtube.com/watch?v=0IFPixtQpYM

[twilit flax]

y + 7 = 3x^2 - 4x

then

[thin kelp]

we want to first pull out the 3

[twilit flax]

then y+ 7 = 3(x^2 - 4/3x

now what

[thin kelp]

no start with y = 3(x^2-4x) - 7

oh wait

[twilit flax]

huh

[thin kelp]

y = 3(x^2-4/3x) - 7

dont try to do it all in 1 step

so pull out the 3 from both terms with x

then

[twilit flax]

then

[thin kelp]

to complete the square take the 2nd term and half it

[twilit flax]

how can i half 4/3

[thin kelp]

half the numerator and if u cant then double the denominator

so in this case its 2/3

now ignore the x

now this becomes y = 3(x-2/3)^2 - 7

but you have to remember that when you complete the sqaure you have actually added an extra term

[twilit flax]

and that is?

[thin kelp]

because when you expand (x-2/3)^2 you get x^2-4/3x+4/9

[twilit flax]

ah

[thin kelp]

the 4/9 was added so to account for that we have to subtract it to stay even

so now we have y = 3(x-2/3)^2 - 7 - 4/9

[twilit flax]

wait

aight

[twilit flax]

then what do you do on the last constant/s

[thin kelp]

common denominator then you could subtract them

[twilit flax]

oh

[thin kelp]

so make the -7 into -63/9 -4/9

which becomes -67/9

so we should have y = 3(x-2/3)^2 - 67/9

then finally we can add it to the other side

y + 67/9 = 3(x-2/3)^2

[twilit flax]

then subtract 67/9?

[thin kelp]

oh did you want it all on one side

[twilit flax]

meh

nah

:)

[thin kelp]

this would be it with all on 1 side

[twilit flax]

oh

wait

me and zerome did this problem

im not sure if its still correct 🕴️

its this

4x^2 + 5x - 8

[iron grotto]

u understood?

[twilit flax]

on this part i did

[thin kelp]

try this problem for yourself

[twilit flax]

alright

[thin kelp]

what would be the first step?

[twilit flax]

uh

y = 4x^2 + 5x - 8

y + 8 = 4x^2 + 5- 8 + 8

then uh

[thin kelp]

hmm we want to factorise first

[twilit flax]

factor out 4

yea

[thin kelp]

yeah

[twilit flax]

y + 8 = 4(x^2 + 5/4

ok

[thin kelp]

y + 8 = 4(x^2 + 5/4x) , just fixing it up

[twilit flax]

oh

do i need to touch the 2nd term or no

[thin kelp]

yeah

[twilit flax]

half?

[thin kelp]

yep

[twilit flax]

then what would it be

[thin kelp]

well we cant half 5 so we will have to double 4, 5/8

[twilit flax]

then

keep doubling it?

[thin kelp]

not necessary

we are just looking for half of 5/4x

which is 5/8

[twilit flax]

oh

then

y + 8 = 4(x^2 + 5/8x)

[thin kelp]

hmm its going to be complicated but we have to do this all in one step

[twilit flax]

wait

[iron grotto]

no..

[twilit flax]

i have a question and its not related to this

[thin kelp]

aight

[twilit flax]

wouldn't be the x-2/3 be x+2/3

or no?

[thin kelp]

no, we started with -4x

we pulled out 3

-4/3x

then we halfed -4/3

-2/3

[twilit flax]

ah

i get it now

[twilit flax]

uh back to this

how does it work

[thin kelp]

so when we figure out the half

[twilit flax]

hmm

[thin kelp]

we can then complete the square by using the half, y + 8 = 4(x + 5/8)^2, but remember there is an extra term that we added

to find that extra term, we have to square the half number we worked out before

(5/8)^2

= 25/64

and then we have to subtract that

y + 8 = 4(x + 5/8)^2 - 25/64

[twilit flax]

then subtract 8 ?

its -25/64?

[thin kelp]

so we used to have (x^2+5/4x) in the brackets right?

[twilit flax]

yeah?

or parenthesis

[thin kelp]

when we complete the square we halfed the 2nd term to get (x+5/8)^2

[twilit flax]

yeah but why is the 25/64 negative

[thin kelp]

but when we expand that we get (x+5/8)^2 = x^2+5/4x+25/64

[twilit flax]

ah

[thin kelp]

see that extra 25/64 that we added

[twilit flax]

yup

[thin kelp]

to account for adding that, we have to subtract 25/64 to keep it equal

[twilit flax]

is the -25/64 negative or no?

[thin kelp]

x^2+5/4x+25/64 doesnt equal x^2+5/4x because the left side has an extra 25/64

[twilit flax]

its back to 5/4?

[thin kelp]

no that is just what we get when we expand (x+5/8)^2

[twilit flax]

ah

its still gonna be 5/4 then or 5/8

im confused

[thin kelp]

its this

but if we want it all on one side we are going to have to subtract 8

y = 4(x + 5/8)^2 - 25/64 - 8

[twilit flax]

oh

let me guess

the lcd

[thin kelp]

yeah

[twilit flax]

wait

[thin kelp]

?

[twilit flax]

what's the lcd gonna be

i was just thinking 25 or smth cause of 8

imaginary 1 skillz

[thin kelp]

well look at the denominators

-25/64 has a denominator of 64

and 8 has a denominator of 1

[twilit flax]

then 64

[thin kelp]

yeah

[twilit flax]

-25 / 64 - 8/64

uh

-33 / 64

right?

[thin kelp]

8/1 and we want a denominator of 64, we have to times both sides of the fraction by 64 to make it equal

[twilit flax]

huh

[thin kelp]

you cant just times the denominator by 64 because its not equal

1/2 doesnt equal 1/4

[twilit flax]

a

[thin kelp]

if we want 1/2 to have a denominator of 4 we have to times both sides by 2

so we have 2/4

[twilit flax]

in here?

[thin kelp]

-25/64 already has a denominator of 64

[twilit flax]

so what about the 8

[thin kelp]

well 8 = 8/1

[twilit flax]

we're not gonna do like this?

cause uhh

wait

[thin kelp]

not yet because you made the fraction wrong

[twilit flax]

oh

[thin kelp]

8/64 doesnt equal 8/1

because you have only multiplied the denominator

you have to also multiply the numerator by 64

[twilit flax]

damn

multiply where

the 8?

[thin kelp]

$\frac{8}{1} = \frac{64(8)}{64(1)}$

ah

[clever fjord]

Galaxy

[twilit flax]

the 25 is gone

[thin kelp]

yeah we arent worrying about the 25 because we still need 8 to have the same denominator

[twilit flax]

and that is

[thin kelp]

64

we want -25 and -8 to have the same denominator of 64

-25 alreadu has a denominator of 64

so there is only 1 number left that doesnt have a denominator of 64

[twilit flax]

then

[thin kelp]

make 8 have the same denominator of 64

what number would u get?

[twilit flax]

8

[thin kelp]

no

[twilit flax]

what

i got confused

[thin kelp]

look at this

u did this wrong because 8/1 is not equal to 8/64

they are completely different numbers

8/64 is equal to 1/8

and therefor you would be doing -25/64 -1/8

but that isnt what we are looking for

we are looking for -25/64-8/1

[twilit flax]

im just thinking of reciprocal tbh

[thin kelp]

how do you change a numbers denominator?

make 5/10 have a denominator of 40

[twilit flax]

whaT

[thin kelp]

what is confusing?

[twilit flax]

why 5/10

[thin kelp]

im just picking a random number since i feell like you arent getting this

[twilit flax]

im weak at fractions thats why

[thin kelp]

ok so i will now explain

[twilit flax]

alright

[thin kelp]

5/10 right? 5 is half of 10 so 5/10 = 1/2

if i want 5/10 to have a denominator of 40

[twilit flax]

then

[thin kelp]

in order to get to 40 we have to multiply 10 by 4

but

to keep the fraction equal, you must also multiply the top by 4

5/10 = 20/40

[twilit flax]

wouldn't it be the same

1/2

[thin kelp]

20 is half of 40 so 20/40 = 1/2

yes they are the same

[twilit flax]

hmm

then

[thin kelp]

now how do we apply this to 8

we want a denominator of 64

[twilit flax]

can you write it in like the fractions

let me if i get the denominator of 64

[thin kelp]

are u asking a question or are you wanting me to do it?

[twilit flax]

on this

which 8

is it 8/1

[thin kelp]

yes

[twilit flax]

then x64?

[thin kelp]

yes

[twilit flax]

then we'll get

512 / 64

[thin kelp]

right

so now put it back into the question

[twilit flax]

where did it go

[thin kelp]

.

[twilit flax]

this?

y = 4(x + 5/8)^2 - 25/64 - 8

[thin kelp]

yes

[twilit flax]

are you saying -25/64 - 512/64 or something else

[thin kelp]

yeah

[twilit flax]

so y = 4(x + 5/8)^2 - 25/64 - 512/64

?

[thin kelp]

yeah but its not fully simplified

[twilit flax]

-537 / 64?

[thin kelp]

what can we do with 2 numbers of the same denominators?

[thin kelp]

yes

[twilit flax]

then

is it just that

[thin kelp]

yeah

[twilit flax]

oh

that was painful

y = 4(x + 5/8)^2 -537/64 ?

[thin kelp]

yeah

[twilit flax]

wait

[thin kelp]

try a simple one f(x) = 2x^2+4x+7 to solidate this

[twilit flax]

is it ok if i go directly

y - 7 = 2(x^2 + 4+ 4)

then do we add 2 next to 7?

[thin kelp]

best to start slow because we are mixing up some steps

[twilit flax]

alright

[thin kelp]

first step?

[twilit flax]

y - 7 = 2x^2+ 4x + 7 - 7

then

[thin kelp]

no its to factorise

[twilit flax]

oh

factoring already

y - 7 2(x^2 + 4x)

oh

wait

y - 7 = 2(x^2 + 4/2x)

then

[thin kelp]

right but what is 4/2?

[twilit flax]

y - 7 = 2(x^2 + 2x)

[thin kelp]

yeah

[twilit flax]

and uhhhhh

[thin kelp]

so next step?

[twilit flax]

completing the square

like that

[thin kelp]

yeah

[twilit flax]

[1/2(b)]^2

[1/2(2)]^2 = (2)^2 = 4

[thin kelp]

i think yoy are missing something

half of 2 is 1

[twilit flax]

wait

oh ya

(1)^2 = 1

mb

then what i did to right side

im gonna do it on left side too

y - 7 = 2(x^2 + 2x + 1)

something's wrong

[thin kelp]

oh right i have forgotten i step

[twilit flax]

i need to add the 2 on the left side

[thin kelp]

yeah

[twilit flax]

right?

[thin kelp]

yeah

[twilit flax]

alright

y - 5 = 2(x + 1)^2

then subtract

f(x) = 2(x +1)^2 + 5

[thin kelp]

yeah

[twilit flax]

wait

how do i do uhhhh

when the coefficient is like

negative

like

-3x^2 -9x + 11

[thin kelp]

ok

[twilit flax]

im still confused on that problem

[thin kelp]

so same steps, we'll first pull out -3

-3(x^2+3x)+11

[twilit flax]

oh

wait

the 3x became positiev?\

oh yea

[thin kelp]

yeah

since -3*3x = -9x

[twilit flax]

oh yea

but

its still 11?

we're not gonna uhh

add

add -3 in left side

hold up

wait

[thin kelp]

no we havent gotten to that yet

[twilit flax]

wait

we dont add it in left side?

[thin kelp]

what are we adding?

[twilit flax]

the a is -3

we're not gonna add in left side

for 11

[thin kelp]

hmm i think you are mixing some things up

i will provide the solution

f(x) = -3x^2 -9x + 11

first step factorise out -3

f(x) = -3(x^2 +3x) + 11

[twilit flax]

wait

when do we add like numbers to the left side

[thin kelp]

what numbers specifically?

[twilit flax]

it's not x^2 + 3x^2

?

i did this problem and it's f(x) = 7x^2

and i answered f(x) = 7(x - 0)^2 + 0

[thin kelp]

yeah thats correct

[twilit flax]

?

[thin kelp]

vertex form is a(x-h)^2+k right

[twilit flax]

yep

[thin kelp]

7x^2

factor out the 7

[twilit flax]

oh wait

wrong reply

[twilit flax]

,.

[thin kelp]

look at -3x^2 and -9x

can you pull a -3 from both?

[twilit flax]

oh

aight then

[thin kelp]

continuing from this

[twilit flax]

is it the same as -x^2 - 4x + 7

let me try to solve it

[thin kelp]

aight

[twilit flax]

y - 7 = (-x^2 -4

then uhh

completing the square?

[thin kelp]

not exactly ur still missing things

[twilit flax]

y - 7 = (-x^2 - 4 - 4)

[thin kelp]

y=-x^2 - 4x + 7

we want to factor out -1

[twilit flax]

-1"?

[thin kelp]

y=-(x^2+4x)+7

yeah because if we want to get the form a(x-h)^2+k

if we dont factor out that negative from the start

we will have

a(-x+h)^2+k

which they are the same

but it depends on what ur teacher is looking for

[thin kelp]

when ur at this step we want to look at the 4x and find [1/2(b)]^2

which is [1/2(4)]^2 = 2^2 = 4

[twilit flax]

isnt it this

[thin kelp]

no because of multiply things

[twilit flax]

aaa

i want to go to sleep

[thin kelp]

first off you're missing the x

its -4x

[twilit flax]

oh

[thin kelp]

secondly its not -4 at the end

[twilit flax]

oh

oh yea

(-2)^2 = 4

i forgot about that

[thin kelp]

right

[twilit flax]

so

[thin kelp]

y-7=(-x^2-4x+4)

[twilit flax]

it's

y = (-x - -2)^2 + 7

or
1,-2,7

the ahk

[thin kelp]

not exactly

you forgot that u added 4 to the right side

[twilit flax]

oh ya

[thin kelp]

so you also have to add 4 to the left

[twilit flax]

i keep forgettingggggg

so 11

[thin kelp]

-7+4

[twilit flax]

oh

-3

then subtract

it's gonna be

f(x) = (-x - -2)^2 + 3

[thin kelp]

yes but double negative makes a positive

f(x) = (-x +2)^2 + 3

[twilit flax]

aight

[thin kelp]

everytime you see a negative sign you can think of it as -1

-2 = -1(2)

so --2 = (-1)(-1)(2)

= 2

[twilit flax]

aight

wait

im tryna work on this problem

3x^2 + 5x = 10

basically i got uh

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

oh wait

[thin kelp]

ok in this situation you have to treat it differently

[twilit flax]

aight

so

double denominator right

[thin kelp]

3x^2 + 5x = 10 we cant just add y since we dont have f(x)

[twilit flax]

aaaaa

[thin kelp]

with a question like this we are looking for an answer

[twilit flax]

im trying to solve this

but im stuck at 5/3 and im thinking to double the denominator like that

[thin kelp]

different approach to this question

3x^2 + 5x = 10

we dont have to complete the square

[twilit flax]

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

[thin kelp]

oh is this the question?

[twilit flax]

yeah

i'm stuck at the 5/3

[thin kelp]

aight mb

yeah

[twilit flax]

double denominator i guess

[thin kelp]

yeah

[twilit flax]

then the extra termmmmmmm

like that

[thin kelp]

you also forgot the x

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

[twilit flax]

oops

[thin kelp]

its y - 10 = 3(x^2 + 5/3x)

right so here we want to find [1/2(b)]^2 right

[twilit flax]

yeah

[thin kelp]

which is [5/6]^2

= 25/36

y - 10 = 3(x^2 + 5/3x + 25/36)

[twilit flax]

hmmmmm

then are we gonna yk uhh

[thin kelp]

but we just added 3(25/36) to the right side

[twilit flax]

add something in outside

[thin kelp]

so we have to also add it to the left

y - 10 + 3(25/36) = 3(x^2 + 5/3x + 25/36)

we can simplify it to y - 10 + 25/12 = 3(x^2 + 5/3x + 25/36)

then we can also complete the square

y - 10 + 25/12 = 3(x+5/6)^2

then common denominators and so on

its 3 am here, so im going to bed

[twilit flax]

so am i

im so tired

[twilit flax]

its back to 10/1 stuff like that

[thin kelp]

correcy

[twilit flax]

meh

im tired

i wanna sleep

night

[odd edge]

@twilit flax Has your question been resolved?

Channel closed

Closed by @twilit flax

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tardy thorn]

how do i solve b)? dont mind the language it is swedish. a) asked for det derivitive of f. But i cant figure out what f(theta(t)) is.

[echo ginkgo]

there's no mention of theta(t) before ?

[tardy thorn]

i guess they assume that theta(t) is the unite function

i think that is what is called but when t <0 it is 0 and t > 0 it is 1.

OH

[echo ginkgo]

I guess that's it yes

[tardy thorn]

i figured it out

I don't know what i was thinking but it is only f(1) they ask for

i feel dumb lol, but thanks anyways!

[echo ginkgo]

and f(0)

but yes

[tardy thorn]

hmmm but it shouldn't matter in this case right?=

the answer is just 4*theta(t) then or?

[echo ginkgo]

f(theta(t))= 4theta(t) yea

[tardy thorn]

nice ok thanks for the help! 🙂

.close

[odd edge]

Channel closed

Closed by @tardy thorn

Use .reopen if this was a mistake.

[odd edge]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[shrewd tiger]

the curve y=ax^2+bx+c has a tangent y=x in origo. the curve has a second tangent for the line y=2x-3. decide what the constants a, b, c are.

i managed to understand that since y=x c would be 0. but i couldn't find out the answer to b or a, so i checked the answers since i'm studying at home and don't have a teacher here. and the answer sheet says that the first step in finding out what b is that we know that y'(0)=1. but i did not know that. how do i find that out.

[shrewd tiger]

also sorry if i'm not using the wrong math words. english is my second language and i don't know the exact translation to every word.

[ornate inlet]

"has a tangent y=x at the origin" means y'(0) = 1

[shrewd tiger]

what? why?

[ornate inlet]

also this: "i managed to understand that since y=x c would be 0" is incorrect

[shrewd tiger]

not according to the answer sheets.

it says that the a=1/12 b=1 and c=0