help-17

[grand frigate]

I don't know where to start.

[ornate ember]

the larger function subtracted by the smaller function

and where the intersect is your bounds

[wary bolt]

Hi, I have an algebra question, at least I believe it is

[grand frigate]

doesn't that give the area enclosed between the two equation?

[ornate ember]

hi there, can you open a new channel? This one is occupied.

#❓how-to-get-help

[ornate ember]

correct. Is that not what you're asking for?

[grand frigate]

that would gice this no?

[ornate ember]

yeah correct

[grand frigate]

I need the area enclosed by the curve, the line, and the x axis

is that possible?

if it's too advanced, i'll probably just get back on this problem in the future.

[ornate ember]

just curious, what course is this for?

I don't know if I grok what you're asking for. 😦

Can you highlight what area you're actually lookin for like you did above?

[grand frigate]

Wait, nvm

it's just the area of the curve and the x axis - the area i highlighted.

.close

[vocal sleet]

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[ornate ember]

ah ok that makes more sense lol.

Sounds like you got it!

[vocal sleet]

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[woven jungle]

could someone help me with this problem? honestly i have no idea what im doing rn

[high frost]

this is asking you to find the second derivative of f(x^2)

[vocal sleet]

@woven jungle Has your question been resolved?

[woven jungle]

this actually makes sense now

thank you so much <333

[vocal sleet]

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[silk ember]

Yo

[silk ember]

Lemme take a pic real fast

,rotate 270

[silk ember]

Technically the question is a physics type of question

but it isnt part of physics class

nor have I taken physics before

Its more of a figure process physics thing for engineering class

So my question is about the conversion

The equation PE/1 • 1/m • 1/deltaH = g (considering PE = m * g * deltaH, and that I need to solve for g)

And g needs to be in ft/s^2

on the left I replaced J with kg•m^2/s*2

and on the right I replaced J with Nm

So either way

I'll get kgm in some sense

but I feel the right side is easier to understand my question

So if I take out the m

I have 901N

then I can replace N with kg mass and to 1m/s^2

so I was looking at how I can change / get rid of lbm and I was thinking

if I switch N to kg mass, is that the same as lbm?

so I could convert pound mass to kg mass

and would that cancel out or would that leave me with a kg/mass answer?

Honestly these problem sets with units are out of my repertoire so I really struggle with them for some reason

Actually better yet

if someone could explain to me the connections I'm missing with lbm and lbf that'd be nice

because I feel those are a bit confusing to me

[vocal sleet]

@silk ember Has your question been resolved?

[vocal sleet]

@silk ember Has your question been resolved?

[vocal sleet]

@silk ember Has your question been resolved?

[vocal sleet]

@silk ember Has your question been resolved?

[vocal sleet]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[vital latch]

sorry last trigonometry question i promise

[vital latch]

so if we have sin(2x) = cos(x)

i got help before to say sin(2x) = sin(pi/2-x)

[quick estuary]

or you can expand

sin2x

using double angle formula

[vital latch]

yes! i saw a video on this just now

and i was wondering

if i do this

3x = pi/2,
x = pi/6

[quick estuary]

i think from this you only get answers in 1 quadrant

not a general solution

[vital latch]

i think you can do this though

[quick estuary]

if it asks general solution then no

[vital latch]

3x = pi/2 + 2'pi'n
x = pi/6 + 2/3'pi'n

[quick estuary]

2npi/3??

thats incorrect

[vital latch]

no like (2/3)pin

i think

[quick estuary]

same as what i said

[vital latch]

🤔

ah wait

[quick estuary]

for n = 1 you will get 5/6pi

which is wrong

[vital latch]

i wrote wrong i think

[quick estuary]

ye

[vital latch]

or no i didnt

nvm im so confused

[quick estuary]

your first line is wronf

wrong

[vital latch]

because we have sin(2x) = cos(x)

[quick estuary]

in this

[vital latch]

which we convert to sin(2x) = sin(pi/2-x)

and then we can move the x over and get 3x = pi/2

[quick estuary]

it can also be - pi/2

[vital latch]

and then we have 3x = pi/2 + 2 pi n

[quick estuary]

thats a part of the solution yes

[vital latch]

so x should be pi/6 + 2/3 * pi * n for all solutions no?

[quick estuary]

no

because you have not taken

the solutions from 4th quadrant

[vital latch]

ah ok yeah

[quick estuary]

3rd

i mean

not 4th

where both negative

this answer you got from both positive

for the other answer

i would not the substitution method but

[vital latch]

ok so the better way to do it then is to do

sin(2x) = cos(x)

[quick estuary]

2 sin x cos x

[vital latch]

2sinxcosx = cos(x)

[quick estuary]

sin x =1/2

yep

[vital latch]

move it over

2sinxcosx-cosx = 0

cosx(2sinx-1)=0

cosx=0 and 2sinx-1 = 0

cosx=0 gives x = pi/2, 3pi/2

sinx = 1/2 gives x = pi/6, 5pi/6

[quick estuary]

ye

[vital latch]

and then on that we have to add 2'pi'n?

' being *

[quick estuary]

u can use union

or not use 2npi

instead

[vital latch]

what would the union look like? i thought union only was a thing in graphing when expressing the range/values?

although I guess this is values too

[quick estuary]

2n+1 pi/2

this is always a solution

and

ok

[vital latch]

oh yeah because you ust add 2

and get 3pi/2

but the other one is not the same no? because pi/6 + pi would give 7pi/6?

[quick estuary]

yea its not

union i was talking about was

one solution is 2n+1 pi/2

other is n pi +(-1^n) pi/6

because when n is even

we are adding pi/6

when its odd

we are subtracting

if we get that we use this form

[vital latch]

okok

[quick estuary]

i cant seem to think of a way to write them together rn

[vital latch]

its fine

but if i were to do it the way i did it originally

[quick estuary]

youll miss solutions

[vital latch]

at that point i would have to not only do sin(2x) = sin(pi/2-x)

but also

[quick estuary]

5pi/2-x

[vital latch]

cos(pi/2-2x) = cos(x)

[quick estuary]

no thats same thing

[vital latch]

and then in the unit circle look for where those values occur again?

[quick estuary]

you would have to do 5pi/2

to get the 5/6 solution

and for pi/2 and 3pi/2 uh

[vital latch]

couldn't I just say that sin(x) = 1/2 which also occurs at 5pi/6?

and the same for cos?

[quick estuary]

your equation wont support that tho

this is what you know

[vital latch]

or no it's gonna equals the same thing

[quick estuary]

but your eq says 3x=pi/2

[vital latch]

ok yeah

[quick estuary]

so its not convincing

[vital latch]

in that case

if you got this question

sin(3x) = cos(2x)

[quick estuary]

just expand

[vital latch]

what would you do then?

[quick estuary]

this is. 💀

convert everything to sin

you get a cubic

find its roots

[vital latch]

but sin(3x)

is not equal to 3sinxcosx

right?

[quick estuary]

its not

its

[vital latch]

that's what i suspected

[quick estuary]

3sinx - 4 sin^3x

[vital latch]

wait what

[quick estuary]

youll learn it

once you are taught

or just use angle addition if you know

[vital latch]

i do not know but would like to know ;D are there any videos online for this?

[quick estuary]

idk

[astral shadow]

Khan academy.

[quick estuary]

and then expand cos2x

1-2sin^2x

[vital latch]

yeah that one i know

[quick estuary]

you get a cubic in sin x

using sin x as y

3y-4y^3+2y^2-1=0

you solve this

and use the solutions lying strictly between -1 and 1

[vital latch]

legit have no idea how to solve that with the 1 being there imma be honest with you

otherwise i could probably factor out the y

[quick estuary]

its a normal cubic equation

4y^3-2y^2-3y+1=0

and if u dont get rational roots

[vital latch]

like the only way i know to solve those is long division

[quick estuary]

then solution doesnt exist

[vital latch]

but there's no denominator(?)

[quick estuary]

for a cubic you hit and trial a bt

bit

[vital latch]

yeah i think thats what my uni teacher said to

[quick estuary]

like look here

[vital latch]

you just guess and hope for the best

try 0 -1, 1, -2, 2

[quick estuary]

whenever sum of coeeficients is 0

x-1 is always a factor

so you will get y=1

[vital latch]

oh like -3x^3 + 3x^2 ?

[quick estuary]

which will give a solution

[vital latch]

-3 + 3 = 0?

[quick estuary]

ye

factor theorem

[vital latch]

got it

thats a good one to know

[quick estuary]

after one solution

u divide make quadratic continue

the usual

[vital latch]

okok that checks out

but if i were to get sin(3x) = cos(2x) tomorrow on my amazing test that i don't feel prepared for

and i will check out angle addition but like yeah

[quick estuary]

you wont

if sin 3x expansion

hasnt been taught yet

[vital latch]

do you think they'd hang me alive if i do sin(3x) = sin(pi/2 - 2x)

[quick estuary]

idk i have literally never used that method

[vital latch]

i mean its university level and we're probably expected to know this, issue is i didnt do math for 5 years and remember 0

[quick estuary]

for trig eqns

[vital latch]

well lets see if it works ,D

[quick estuary]

this is in class 11

for me

[vital latch]

then we'd have 5x = pi/2

x = pi/10

[quick estuary]

which is one solution

from the cubic youll get

root 5 -1/4 as a root

which is sin 18

18 degree

[vital latch]

yeah the same

cause pi/10 is 18

and then i think i can say

• 2 pi n

and also do 2/5 pi n

to get the other solutions

[quick estuary]

hmm

adding 2pi/n doesnt give all solutions tho

[vital latch]

better than 0 XD

[quick estuary]

nevermind

no

from cubic youll get a root 5 +1/4 aswell

2pi/5 yes

youll also get pi/2

[vital latch]

wouldn't we get pi/10 + 2pi/5 -> 5pi/10 which is pi/2

[quick estuary]

as a solution

[vital latch]

hmm

[quick estuary]

pi/2 coming from the fact that the root of the cubic was 1 aswell

[vital latch]

ok so what solution am i missing?

[quick estuary]

cubic will guarantee you all answers

[vital latch]

i have pi/10, pi/2

[quick estuary]

2pi/5

[vital latch]

ok so we set n to 2

[quick estuary]

n?

[vital latch]

pi/10 + 4pi/5 = pi/10 +8pi/10, = 9pi/10

[quick estuary]

2npi/5 isnt correct

2pi/5 is one solution

[vital latch]

yes but when n is = 1 you get that

i think

wait

look

pi/10 + 2pin/5

when n is 0

we get pi/10

when n is 1

we get pi/2

when n is 2

we get 9pi/10

[quick estuary]

9pi/10 hm

cos 18pi/10

sin 27pi/10

[vital latch]

which is uhh.. 162 degrees?

but sin(18) = sin(162)

i think

[quick estuary]

cos 18pi/10 is 4th quadrant

cos pi/5 youre getting from this

sin 27pi/10 gives you

cos 7pi/10

sin*

cos 3pi/10

definately not equal

cos 3pi/10 and cos 2pi/10

using cos (-x) = cos x and sin (pi-x) =sin x

oh wait

sin 3pi/10

ok youre right

its is 2/5n

[vital latch]

IT DOES WORK!?

[quick estuary]

ye

[vital latch]

holy macaroni

[quick estuary]

had to check

[vital latch]

ok that's good news

i will still try to learn angle addition because i want to use the "good" techniques

but while im trying to learn this one is a little easier :p

[quick estuary]

for trig equations factoring is the best methof

[vital latch]

yeah it does seem to be very good

do you have any recommendations for good geometry problem videos?

[quick estuary]

my own gemetry is 💀

[vital latch]

because we're expected to know all these formulas but when i tried to look online for like precalc / calculus geometry it's really lackluster compared to the problems in the last exams..

like this one

[quick estuary]

these are 11th grade problems

can translate?

[vital latch]

im not entirely sure what the idea is here

a chord in the unitcircle is seen from a point on the circle with the degree of 120, (see figure), decide the chords length

so there is the "randvinkelsats"

[quick estuary]

thats doable

you just

[vital latch]

Inscribed angle

?

[quick estuary]

make the centre

youll get angle in centre

and use sine law

and done

[vital latch]

wait so what i did

is this

[quick estuary]

oh bruh

this is straight observation

[quick estuary]

answer is 1

you find the wrong angle

[vital latch]

is this correct?

[quick estuary]

that too incorrect

💀

[vital latch]

that's what i was afraid of

[quick estuary]

look

both those are radii

and

[vital latch]

my lines u mean?

[quick estuary]

its a cyclic quadrilateral isnt it

ye

[vital latch]

yes they are 1

uhh

quadrilateral

lemme google rq

ah

well yes it is

[quick estuary]

then by its property

a cyclic quads opposite angles

are supplementary

[vital latch]

but are there rules that the opposite corner in a quadrilateral always is opposite angle?

[quick estuary]

so middle angle 60

[vital latch]

oh

supplementary

[quick estuary]

and radii are 1

[vital latch]

got it

[quick estuary]

so its equilateral

wait

i have commited error

my bad

[vital latch]

no problem dear sir

[quick estuary]

your angle is correct

thats not a cyclic quad

all 4 points have to touch circle

[vital latch]

so can i use the inscribed angle?

but i think they do

[quick estuary]

so what you do is you join it to the top

yes b=2x is correct

then you apply sine rule

[vital latch]

cos no?

[quick estuary]

cos?

use sine for this

[vital latch]

c^2 = 1+1 -211 cos(120)

[quick estuary]

so complex la

use sine rule

much easier

sin 120 /x = sin 30

[vital latch]

c^2 = cos(120) which is sqrt1/2?

or?

[quick estuary]

you get imaginary

how

wait

[vital latch]

ah wait

[quick estuary]

its 1+1

2(1-cos 120

use sine law

search it up

[quick estuary]

its 1/2

[vital latch]

its the a/sin A = b/sin B = c/sinC right?

[quick estuary]

ye

2 x 3/2

is c^2

c is root 3

sdone

[vital latch]

and how would you apply it here then? say that 1/sin(30) = x/sin(120)

uhh

[quick estuary]

just plug values

sin 120/sin 30 =x

sin 120 is cos 30

cot 30 =x

x is root 3

same answer

[vital latch]

ohh ok

i think i see

wait is sin120 cos30?

🤔

oh yeah

[quick estuary]

yes

[vital latch]

or no

wait wat

isnt sin(60) = cos(30)

uhhh

[quick estuary]

and?

you know the graph of sine?

sin90+x is cos x

[vital latch]

i know it's a bit further ahead

[quick estuary]

ok so

[vital latch]

isnt sin90-x also cos x?

[quick estuary]

from this

yes

why cant both be true

[vital latch]

it just feels wrong

but ok

[quick estuary]

once u see the graph

it will clear out

[vital latch]

ok but then i think i understand this one

as long as the point in the middle connects to the same lines as the other angle it's gonna be double?

[quick estuary]

wut?

[vital latch]

like to get the angle

using the inscribed angle theorem

[quick estuary]

thats a theorem?

lol

[vital latch]

im not sure how you get it otherwise

[quick estuary]

oh this

[vital latch]

https://www.houseofmath.com/encyclopedia/geometry/geometric-constructions/angles/how-to-prove-the-inscribed-angle-theorem

but im having issues seeing how it works with this problem..

[quick estuary]

angle at centre is double angle inscribed

[quick estuary]

this is correct

[vital latch]

ok awesome

[quick estuary]

you just find the other angle using this

360-240

then sine/cosine rule

[vital latch]

okok

and how would you approach this one for example?

translation on its way

20 meters of steel wire must be used to enclose a flowerbed in the form of
a sector of a circle with an angle α between 0 and π and radius r (see figure). For
which radius of the circle sector is the area of the discount the largest, and what is it
maximum area?

i assume we want to set up a function right?

[quick estuary]

area of discoiunt?

oh got it

[vital latch]

uhh

[quick estuary]

so

[vital latch]

is the area of the flowerbed the largest

[quick estuary]

yeah got it

[vital latch]

rabatt means flowerbed and discount XD

[quick estuary]

2pir * theta

is circumference

[vital latch]

yeah so 2pir is circumferenece

[quick estuary]

+2r

[quick estuary]

,thats whole circle

[vital latch]

yep

[quick estuary]

for a sector you multiply theta in radians

that +2r is 20

[vital latch]

ohhh ok

[quick estuary]

write that down kek

[vital latch]

i think i can remember it

[quick estuary]

2r(1+pitheta)

=20

r(1+pitheta)=10

you have to maximize

[vital latch]

ok so normally entire circumference is 2pi*r

[quick estuary]

yep

[vital latch]

and then in this scenario when its a circle sector we have

2pi*r * theta

[quick estuary]

yes

you underdtood why the theta multiplied?

[vital latch]

and you set that equals to 20 for the length of the steel wire?

[quick estuary]

adding twice the radius

then yes

because thats how much wire we have

now

r+ rpitheta=10

r pi theta = 10-r

theta = 10-r /rpi

okay?

[vital latch]

and wait wait you say r twice because of the radius apart from the circlesector right

just making sure im with you

[quick estuary]

yes

[vital latch]

liek this

yeah

ok

[quick estuary]

yed

[vital latch]

im with you then

[quick estuary]

.

k?

[vital latch]

yes

[quick estuary]

now

area is pir^2

of whole circle

[vital latch]

yep

[quick estuary]

so for sector

pi r^2 theta

[vital latch]

so then we get

pi r^2 * (10-r/rpi)

[quick estuary]

also from here just r theta = 10-r/pi

[quick estuary]

well this works

so it cancels

pi and r

r(10-r)

when is this maximum?

[vital latch]

low r

?

[quick estuary]

if u know a little bit of quadratic eq

no

10r-r^2

u know differentiation?

[vital latch]

i probably do but i do not know that word

derivative?

[quick estuary]

derivative

minima

[vital latch]

yeye

[quick estuary]

yes

[vital latch]

so this would be

10 - 2r

right?

[quick estuary]

yes

u know when maxima or minima occurs?

[vital latch]

when you factor and its equal to 0?

i think?

thats the turning point?

[quick estuary]

uhh

close

when dy/dx is 0

so 10-2r=0

r = 5

put this r

[quick estuary]

here

[vital latch]

ohh alright

and then get 25?

[quick estuary]

you get 25

yes

you can find this maxima in many many ways

[vital latch]

ok then i think im with you all the way

[quick estuary]

using AM GM inequality

using quadratic

but its okay

[vital latch]

am gm inequality, another term i've never heard of ;D

thank you so much for all of this help btw

[quick estuary]

np

its just practice for me

[vital latch]

did you have any recommendation for videos that target these kind of geometry problems?

[quick estuary]

i dont study from videos kek

[vital latch]

XD

[quick estuary]

books>

[vital latch]

like the issue with my uni books is that the problems dont have the steps to the solution, just the answers

[quick estuary]

all this was in my school curriculum kek

uni for me means different kek

uni is after college

these problems are my grade 10

[vital latch]

ah yeah this is probably college for you

[quick estuary]

no lmfao

[vital latch]

like 19 year olds?

[quick estuary]

these are elementary

no

15

[vital latch]

XD

i mean we did have this back then too

its just that we're supposed to still know it

[quick estuary]

bro frogor

[vital latch]

big time

5 years without math

it all went straight out of the head

[quick estuary]

lo

[vital latch]

literally was wondering what happened when i multiply negative values

i was 90% sure it was gonna be positive

[quick estuary]

💀

[vital latch]

but now i have to continue as if i were just in grade 11 or w/e u said it was

[quick estuary]

ye

[vital latch]

ok if you want more practice that would help me enormeously with the understanding

[quick estuary]

💀

probably dm now

[vital latch]

oh yes

.close

[vocal sleet]

Channel closed

Closed by @vital latch

Use .reopen if this was a mistake.

[vocal sleet]

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.

[long flame]

finding gradient using limit method of $ y = \frac{1}{x^2}, x = 2$

[long flame]

$ y = \frac{1}{x^2}, x = 2$

[twin meteor]

chlamydia

[grizzled halo]

any progress?

[long flame]

it's a bit messy but wait

w' rotate

[long flame]

the problem is that what I call D, the y of x delta minus y of x, gives a fraction

so D / dx is complicated and i get lost trying to get to the answer which should be -2

i can however tell the pattern that when we expand y of delta x, and subtract y of x, we have the coefficient of delta x being -2. This coefficient is always also the final answer

but for the previous exercises i was able to get to the final equation through algebra and then plotting limit of dx -> 0 to get the answer but for this exercise I wasn't able to

basically we have $\frac{\frac{-2dx - dx^2}{1+2dx+dx^2}}{dx}$

[twin meteor]

marty

[long flame]

how can we solve this to become -2

(after having dx = 0)

[magic surge]

(-dx(2+dx)/(1+dx)^2)/dx = -(2+dx)/(1+dx)^2 = -2/1

algebra

what's gradient

[long flame]

slope

[magic surge]

isn't it like

3d

oh ok

ah slope

[vocal sleet]

@long flame Has your question been resolved?

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[languid venture]

How can you solve an arg like that?

[vocal sleet]

@languid venture Has your question been resolved?

[languid venture]

<@&286206848099549185>

[languid venture]

I dont understand what that even means

Usually i calculate arg of a and b

[languid venture]

Ok this is useful but here its Zi

Not just Z

[cursive turret]

arg(ab)=arg(a)+arg(b), so arg(iz²)=arg(i)+2arg(z)

i is just a complex number.

[languid venture]

Ahh ok I try

[languid venture]

What about the fact that its all =1?

[cursive turret]

what should be? its just an equation. 1 = arg(i)+2arg(z). solve it.

[languid venture]

Rught ok I try

[vocal sleet]

@languid venture Has your question been resolved?

[languid venture]

Since z=x+yi how can I calculate arg without knowing x and y

[cursive turret]

the point is: you posted just a small part of the exercise, so it is nearly impossible to help you. What is asked in your example?

[languid venture]

It gives me options to reply about the solutions of the exercise

[cursive turret]

you know the left side, you should know arg(i) so you should be able to calc arg(z).

[languid venture]

Like this?

[cursive turret]

yes, so you can calc arg(z), but you still havent said what the goal of the example is.

[languid venture]

It asks if the solutions are a line a circle or a uhh

Not full line

It also says there are many solutions?

[vocal sleet]

@languid venture Has your question been resolved?

[languid venture]

<@&286206848099549185>

[manic lava]

Yeah?

[languid venture]

Can you help me choose the right answer

It asks if the solutions to that arg are a line a circle a not full line

[manic lava]

Lemme check

Should be a circle I think

[languid venture]

Why?

[manic lava]

Which book is it from?

[languid venture]

Its a old exam not book

[languid venture]

How do u get a circle from this

[manic lava]

Ok wait I'm thinking

U have the question pic somewhere?

[languid venture]

Yeah but italian

[manic lava]

No worries send

I'll try to solve it

[languid venture]

Question 2

[manic lava]

Yeah I'm thinking

[languid venture]

I can tell vorrect option

[manic lava]

??

[languid venture]

Did u figure out

[manic lava]

Not yet

Explain no

[languid venture]

?

[vocal sleet]

@languid venture Has your question been resolved?

[vocal sleet]

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[formal gazelle]

So if we are converting the parent function $\frac{6}{x-3} + 5$ to the child function $\frac{6}{-3x-3} +5$ . IS THIS reflection over the y axis or the x axis. And is it a vertical dilation of 3? Or is it a horizontal dilation by a factor of 1/3? Or is it horizontaly dilated by 3?

[twin meteor]

ahaan

[formal gazelle]

<@&286206848099549185>

Had posted this an hour ago

in a diff channel

<@&286206848099549185>

[dapper jay]

they have the same y-intercept

both expressions

[formal gazelle]

so?

That doesmt say anything useful?

[dapper jay]

it does

you can use that information to determine what axis its reflected over

[formal gazelle]

how?

[dapper jay]

think about it

[vocal sleet]

@formal gazelle Has your question been resolved?

[vocal sleet]

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[formal gazelle]

.reopen

[vocal sleet]

✅

[formal gazelle]

I tried

Idk hoiw

[vocal sleet]

@formal gazelle Has your question been resolved?

[formal gazelle]

<@&286206848099549185>

Kinda getting annoying

[hollow thunder]

so basically for this question if you cant rememeber it, I try to roughly sketch it

[formal gazelle]

Its kinda hard to sketch this ngl

[hollow thunder]

I would just plug in points

[formal gazelle]

still its kinda confusing

I dont get it

[hollow thunder]

hmm ok so the parent function x is a -3x in the child function so y-value when x is -1/3 would be the same as y value when x is 1 in the parent so if any arbitrary point on the parent were like (x,y) then a point on the child would be (-x/3,y)

so then you can see how it changes from the (-x/3, y)

does that kinda make sense?

[formal gazelle]

no?

[hollow thunder]

wait a sec lemme see if I can find something

basically use that

does that help?

if not I can help break it down

look at your parent function as f(x)

how would you represent you child function in terms of f(x)??

[vocal sleet]

@formal gazelle Has your question been resolved?

[vocal sleet]

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[daring sinew]

How can one calculate trigonometry functions without a calculator?

[hushed pewter]

painfully

But it depends on the function and input

[final bridge]

what question is it?

[daring sinew]

Lets say for an example cos 800° = 800-360*2 = 800-720 = cos 80°

so cos 80° without a calculator

[final bridge]

damn

[daring sinew]

.close

[vocal sleet]

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[grand void]

I'm not sure how to define x in terms of theta, can anyone offer any insight?

[late ingot]

$\cos^{2}\theta+\sin^{2}\theta=1$

[twin meteor]

b0ngl0rd

[late ingot]

that has a radius of 1

the integrand has a radius of 16

[grand void]

I factored out the 16.

[late ingot]

so you got the 1 - sin^2 as the identity, which works

you gotta find what you replace x with.

[grand void]

As to how this is derived I am very confused.

Not sure how to put x in terms of theta

[late ingot]

trig sub.

[grand void]

Somehow it's 4sin(theta)?

How was that calculated?

[late ingot]

x/4 = sin theta

x = 4 sin theta

[grand void]

Where did we know the value was going to be sin?

And that it was equal to x/4?

[late ingot]

look at your work

you'll see x/4 appears

but thats slightly confusing, thats why i was trying to show through the identity how to get it

$16\cos^{2}\theta+16\sin^{2}\theta=16$

[twin meteor]

b0ngl0rd

[late ingot]

square root the whole thing

$\sqrt{16\left(\cos^{2}\theta+\sin^{2}\theta\right)}=\sqrt{16}$

[twin meteor]

b0ngl0rd

[late ingot]

$4\sqrt{\cos^{2}\theta+\sin^{2}\theta}=4$

[twin meteor]

b0ngl0rd

[late ingot]

that constant is the multiple you need for the substitution

$\sqrt{r^{2}-\left(r\sin\theta\right)^{2}}$

[grand void]

I do see x/4, how do we know that was equal to sin? (thank you for showing me this other clever trick as well).

[late ingot]

because the identity matched the form, all that we needed to do was scale the identity by the radius of the semicircle we are working with

sqrt(16) = 4 = radius

[twin meteor]

b0ngl0rd

[grand void]

Is that because somehow the 4/x matches the reciprocal identity for sin?

[late ingot]

no. the reason is exactly what your work shows, that the radius scales x, specifically by a factor of 4

thats why we take x/4 = sin theta

then to get x we multiply

[grand void]

So basically x is always going to be a*sin(theta)?

[late ingot]

no

it depends on the identity

[grand void]

These.

Okay gotcha

[late ingot]

[vocal sleet]

@grand void Has your question been resolved?

[grand void]

Did the top need to be simplified to 4cos(theta), and then make the subsition or should I just make the subsitution from the very beginning on x?

[late ingot]

if you know the substitution you should be able to do it from the beginning with no work done.

[vocal sleet]

@grand void Has your question been resolved?

[vocal sleet]

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[junior adder]

Need help with combinatorics

[junior adder]

Is there a formula to find how many different variations of two dice equaling a certain number

say I want to find how many ways I can roll two dice to equal the number 7

is there a formula for that?

[regal bane]

There's a method called "stars and bars", which can solve it, and some problems like it

[junior adder]

could i use lets say 6 choose 2?

or something like that

[regal bane]

What's your thought process?

[junior adder]

welll

to determine the total amount of combinations two dice have

i did 6 *6

[regal bane]

But I thought you wanted the number of ways to roll a 7

[junior adder]

yea

im hitting a road block

I havnt learned stars and bars yet

[regal bane]

In this case, it's also pretty easy to count all of the cases

1+6,2+5,3+4,4+3,5+2,6+1

[junior adder]

yea but

using math would be cooler

[regal bane]

Sure. So to connect this to a more common problem:
You want the number of positive integer solutions to the equation x + y = 7

[junior adder]

right

x being dice 1 and y being dice 2

if x 1 is = 1 then y has to be 6

[regal bane]

Let's say I take 7 stars and 1 bar, and put them in a row like this:
***|****

That permutation of stars and bars corresponds to the solution 3 + 4 = 7

So every arrangement of stars and bars corresponds to a solution to the equation

The question is NOW:
How many ways can I arrange 7 stars and 1 bar?

[junior adder]

5 ways?

wait

6

[regal bane]

Oh wait I am making a mistake. 0s are allowed in the solution, when using this method

|*******

Is 0 + 7 = 7

[junior adder]

thats impossible

[regal bane]

But obviously that can't happen with dice

[junior adder]

I was given this from the lecture

bayes rule

[regal bane]

This seems to be a pretty different question

[vocal sleet]

@junior adder Has your question been resolved?

[vocal sleet]

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[faint matrix]

Hey can i get help for a linear algebra question?

[hollow thunder]

sure I can try to help

[faint matrix]

so i can send you my work

but warning its a whole page long

but please tell me if i was on the right track

and these are the answers for this question:

[hollow thunder]

ok

[faint matrix]

this is my work

but i checked and im pretty sure my answer doesnt line up with the answer given in the answer key

and i sent the answers above

[hollow thunder]

Right so you just want to change it into I think it's called identity matrix

[faint matrix]

yes thats what I thought shoulvde been done in this question

I wrote it in terms of a augmented matrix or you could say identity matrix

[hollow thunder]

is the bottom one the final matrix?

[faint matrix]

yes

but im not sure if its right

[hollow thunder]

you want to make the ones at the top also 0

[faint matrix]

thats why I need help from someone who could help solve this questionb

[hollow thunder]

so you can get top row 1 0 0 0

next 0 1 0 0

and so on

the matrix is basically a system of equations

[faint matrix]

but i dont know how I could do that

it seems too complicated to get the top row 1 0 0 0

is it possible if you could show me the proper steps to solve this system of equations?

then I could compare it with my work?

[hollow thunder]

you have to work you down from the first row make the numbers under the first ones all zeros

[faint matrix]

I did that

until i got all the way down to 823/105

[hollow thunder]

you want to make it one so it's easier to cancel out the ones below

[faint matrix]

one more thing I think I could do here is turn that 823/105 in to a 1 and i know how to do that

[hollow thunder]

yes exactly

[faint matrix]

could you show me the steps?

[faint matrix]

im gonna do that right now to see what answer I get for w.

[hollow thunder]

so divide the first row until first is 1

[drifting jackal]

Btw I do suggest simplifying your fractions

[hollow thunder]

that too

[faint matrix]

Yes thats one thing

[drifting jackal]

Like you wrote in 60/90, that equals 2/3

Makes the math a tad easier

[faint matrix]

ah yes

I tried to do that sometimes

but then i stopped simpliyfying

overall do all my steps seem correct?

cuz if they do Im pretty sure my final answer will still be wrong.

[hollow thunder]

try to get the diagonal ones to 1 and all the others below that to 0

[faint matrix]

bro

[hollow thunder]

then you have to get all the ones above it to 0 too

[faint matrix]

thats too difficult i feel

i have no idea how

[drifting jackal]

What's this number here?

[faint matrix]

1760/90

[drifting jackal]

No need for RREF, you can back substitute

[faint matrix]

thank god lol

but overall do you guys think my steps seem correct and on point?

and if not could someone maybe try this question and show me their steps?

[hollow thunder]

you need to finish but other than that I think so

[faint matrix]

id really appreciate it

[hollow thunder]

I can't really show you rn but I can walk you through it step by step

[faint matrix]

on call?

like can i screen share

[hollow thunder]

like can you take a picture of where your final matrix is now?

[faint matrix]

yes one sec

doing that right now

[hollow thunder]

first step is to simplify the fractions

[faint matrix]

i got an insane number

final matrix is bottom right

[hollow thunder]

can that be simplfied?

[drifting jackal]

That number?

[hollow thunder]

I think it would be best if you simplified before going forward

right

so that way the numbers are easier to work with

[faint matrix]

that says 2800/90

[hollow thunder]

so that could be simplified

[faint matrix]

i cant go back and simplify tho now

[drifting jackal]

That's the first mistake

[faint matrix]

shit

could you explain how

[hollow thunder]

It might be a calculation error

[faint matrix]

or let me check

[drifting jackal]

,calc 2 * (625/90) - 5

[twin meteor]

Result:

8.8888888888889

[drifting jackal]

,calc 2800/90

[twin meteor]

Result:

31.111111111111

[faint matrix]

fuck

fuck

i give up

[hollow thunder]

chill

[faint matrix]

yea your right

my bad

i cant

ive been working on this for 20 mins

or 15

or even 30

i made a calculation error

[hollow thunder]

it fine I make them all the time

[faint matrix]

i know but i have a midterm on this tmmrw

[hollow thunder]

try simplifying the fractions to make calculating easier

[faint matrix]

thanks your right

[drifting jackal]

Definitely the not simplifying fractions messed you up

[faint matrix]

yea hundred percent

i shouldve simplified right away

[hollow thunder]

yeah

[faint matrix]

but anyway i gotta ask

if on a midterm

or sorry

[hollow thunder]

if worst comes to worst just write out a system of equations

[faint matrix]

if i was trying to row reduce, could i still find the values of each vairable with a matrix that looks like this

[hollow thunder]

thats basically all it is

[hollow thunder]

wdym

[faint matrix]

so this is the final matrix i got

but with using the info in this final matrix

can i still derive the values of x,y,z,w

[hollow thunder]

not if they are calculated incorrectly

[drifting jackal]

If you did algebra correctly

[faint matrix]

so is it not possible to derive the values of x,y,z,w if I did the algebra wrong?

[hollow thunder]

you can think of it like 0x+0y+0z+1w=(number)

[faint matrix]

shouldnt i still be able to derive the values

even if it gives me the wrong answers?

[hollow thunder]

the matrix is sorta just a system of equations

[faint matrix]

like if i use subsitition method i could get the values of x,y,z,w

no?

[drifting jackal]

You'll get wrong values that wouldn't satisfy the system

[faint matrix]

yea ik thast

[drifting jackal]

You'll get a set of values for x, y, z, w but it wouldn't be correct

[faint matrix]

ohh thats what i wanted to know. So therefore, I would get the values, but the values just wouldnt be right

ok thanks

thats what i wanted to know

[hollow thunder]

unless your teacher specifically asks for using the matrix I would just use a system of equations

[faint matrix]

Because I was just confused as to whether or not a system of equations has to be in rref in order for you to derive the values of varaibles

[faint matrix]

oh you mean like simply using subtituion method or elimination?

[hollow thunder]

exactly

thats really all the matrix is

[faint matrix]

cuz yea im def gonna do that

[hollow thunder]

substitution and elimination

[faint matrix]

but he most likely will ask us about ref and rref

[hollow thunder]

well if you think about it like the first row is 90x+90y+80z+12w=124 (im making up numbers) and the other rows like that and your just solving it in a different way

[faint matrix]

yea that makes sense

[hollow thunder]

you can think of it like a fancy way of writing it

[faint matrix]

ref and rref is the cancer way to solving for variables i feel like

[hollow thunder]

it's different

[drifting jackal]

Elimination is just gaussian elimination

[faint matrix]

gaussian elimination?

isnt that what we use for ref and rref?

[hollow thunder]

what your doing basically

[faint matrix]

oh wtf

i didnt realize that for sum reason

[hollow thunder]

its just the row reduction things

[faint matrix]

also I have one more question I'd like solved before I go

if possible

[hollow thunder]

sure

[faint matrix]

this one will also be on my midterm tomorrow and it involves financial mathematics

[hollow thunder]

I can try but i might not know how to solve

[faint matrix]

Is there someone who might know financial mathematics?

but yea please try if you can

i need help with specifically b

and d

for this question all i know is that you can use annuity formulas or you can use sigma notation to solve this.

[drifting jackal]

Yeah with gaussian elim, you multiply some row then add/subtract it to another, same thing with general elimination because you would take one equation, multiply it by some value to then add/subtract with some other equation to eliminate variables. The matrix is just the value form of general elimination

[hollow thunder]

yeah imma be honest im in middle school idk how to solve financial mathematics

[faint matrix]

ur in middle school and u know how to do ref and rref?

[hollow thunder]

uh yeah