help-39

[flint drum]

i still got one more quesion

right so i would answer this

4 = 3(1) + c

but is that even remotely right?

[plush moss]

Is that line supposed to be the tangent?

[flint drum]

yeah?

[cobalt hinge]

How are you supposed to tell the graph of the line here?

[plush moss]

Oh nvm

It's f'

[cobalt hinge]

Do they give coordinates?

[plush moss]

Yea the axes aren't exact

Then only give like 1 on the y axis

[flint drum]

so?

[plush moss]

So they just want you to estimate?

Welp in this case then you can use the point line formula

Take note of the value of f' and f at x=1

y= 3(x-1)+4

Where (1,4) is the point where the line is tangent to the graph

@flint drum

[flint drum]

uh

i should know this

but i dont

[plush moss]

Actually nvm did you write this as your final answer

[flint drum]

this is just a old exam

from a year or two ago

which im studying

but yeah

i wrote that

like 10 mins ago

[plush moss]

Well you're almost there

[plush moss]

you can calculate c from this

And the equation of the line is y=mx+c

[pearl pond]

@flint drum Has your question been resolved?

[flint drum]

ok t

ty

[pearl pond]

Channel closed

Closed by @flint drum

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.

[scarlet trellis]

At first I just tried using the equations tool on my calculator but it failed saying the system is non-linear (which makes sense because I don't see how this could be put into a matrix)

and I didn't want to try doing substitution here, this was on a timed test.

[tiny lintel]

Hello what's your grade ?

[scarlet trellis]

This is competitive Algebra 1 but I am taking Algebra 2

[pearl pond]

@scarlet trellis Has your question been resolved?

[scarlet trellis]

<@&286206848099549185>

[chilly hill]

i'm looking at your problem since 10 minutes and dont know what i would do xD

[scarlet trellis]

I've even tried creating a program like this:

for b in range(-50, 50):
    for c in range(-50, 50):
        for d in range(-50, 50):
            for e in range(-50, 50):
                a = (b+c+d+e)//128
                if b * (a+c+d+e) == 155 and \
                     c * (a+b+d+e) == 203 and \
                     d * (a+b+c+e) == 243 and \
                     e * (a+b+c+d) == 275:
                      print(a, b, c, d, e)
                      break

But it takes a while and still returns no answer (maybe these numbers are decimals or greater/less than +-50)

Also, the answer to the problem is 10, although it was unknown during the test

[pearl pond]

@scarlet trellis Has your question been resolved?

[chilly hill]

I suppose you should set the part in paranthesis as a linear function which is i suppose possible by transponing some vectors and the matrix. And the input of this function will be the vector (a, b, c, d, e)T
Idk if this is it but i can be a beginning

i guess this should be correct

first of all there is only one solution for this problem

[tiny lintel]

Your matrix product doesn't work

[scarlet trellis]

I'm not really sure what any of this means

[tiny lintel]

Have you done some linear algebra ?

[scarlet trellis]

No

[tiny lintel]

Hmmmm

[pearl pond]

@scarlet trellis Has your question been resolved?

[lone cypress]

Im just gonna try this, no guarantees

And might as well practice my latex

Zo all the variables share the sum x

[
\begin{cases}
1); a(b + c + d + e) = 128,\
2); b(a + c + d + e) = 155,\
3); c(a + b + d + e) = 203,\
4); d(a + b + c + e) = 243,\
5); e(a + b + c + d) = 275.
\end{cases}
]

[
\frac{(d + e)(c - b)}{a}
]

[
S = a + b + c + d + e
]

[
\begin{aligned}
& a(S - a) = 128, \
& b(S - b) = 155, \
& c(S - c) = 203, \
& d(S - d) = 243, \
& e(S - e) = 275.
\end{aligned}
]

[
b(S - b) - a(S - a) = 155 - 128
]

[
bS - b^2 - (aS - a^2) = 27
]

[
bS - aS = b^2 - a^2 + 27
]

[
(b-a)(S - (a + b)) = 27
]

[
(b - a)(c + d + e) = 27
]

[
(c - a)(b + d + e) = 75
]

[
(d - a)(b + c + e) = 115
]

[
(e - a)(b + c + d) = 147
]

[
4(b + c + d + e) = 128 \quad \Rightarrow \quad b + c + d + e = 32
]

[
b(4 + c + d + e) = 155
]

[
b(36 - b) = 155
]

[
b^2 - 36b + 155 = 0
]

[
\Delta = 36^2 - 4 \cdot 155 = 1296 - 620 = 676
]

[
b = \frac{36 \pm 26}{2} \quad \Rightarrow \quad b = 5 \text{ or } 31
]

[
c + d + e = 32 - 5 = 27
]

[
c(4 + 5 + d + e) = 203
]

[
c(36 - c) = 203
]

[
c^2 - 36c + 203 = 0
]

[
\Delta = 36^2 - 4 \cdot 203 = 1296 - 812 = 484
]

[
c = \frac{36 \pm 22}{2} \quad \Rightarrow \quad c = 7 \text{ or } 29
]

[
d + e = 27 - 7 = 20
]

[
d(4 + 5 + 7 + e) = 243
]

[
d(36 - d) = 243
]

[
d^2 - 36d + 243 = 0
]

[
\Delta = 36^2 - 4 \cdot 243 = 1296 - 972 = 324
]

[
d = \frac{36 \pm 18}{2} \quad \Rightarrow \quad d = 9 \text{ or } 27
]

[
e = 20 - 9 = 11
]

[
e(4 + 5 + 7 + 9) = 275
]

[
(9 + 11)(7 - 5) = 20 \cdot 2 = 40
]

[
\frac{(d + e)(c - b)}{a} = \frac{40}{4} = 10
]

[
\boxed{10}
]

[jolly parrot]

Aerith

[scarlet trellis]

Holy

That is a lot

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[sharp smelt]

Trying to do this using a substitution

[sharp smelt]

Kind of lost

The Original substitutions I had planned were $x+y=u; y-2x=v$

[jolly parrot]

What a wonderful world!

[sharp smelt]

Let the jacobian be $J$. Then the new integrand is $ u(v)^2 J du dv$

[jolly parrot]

What a wonderful world!

[sharp smelt]

The issue is I'm having trouble figuring out the new bounds

[hot canyon]

exactly the problem . How'd you figure bounds

Rewrite x and y in terms of u, v

[sharp smelt]

I was thinking I could start by finding the "origin" here

[hot canyon]

Put them into bounds of x, y

[sharp smelt]

wdym

[hot canyon]

x = (u - v)/3, y = (2u + v)/3

Now plug 0 ≤ y ≤ 1 - x, 0 ≤ x ≤ 1

Should get bounds

[sharp smelt]

hmm, okay

thanks

Ah

x+y=1 corresponds to u=1

and similarly I can obtain other bounds

cool

[hot canyon]

Yes, so u ≤ 1

[sharp smelt]

cool

Thanks

Trying to do this now

[hot canyon]

That's two lines

[sharp smelt]

Yeah, I know

I was thinking of -2x+4=u

and y+2=v

[hot canyon]

You have to evaluate integral? Or can use help of geometry?

[sharp smelt]

I have to use integrals

[hot canyon]

Welp, no need for substitution here then

[sharp smelt]

I think factoring the expression might help first

[hot canyon]

It's polynomial

[sharp smelt]

So (x-y)(2x-y)

,w (x-y)(2x-y)

oops

[hot canyon]

(2x + y)(x - y)

[sharp smelt]

yeah

got it

I now have to work out the new bounds

Let's start with 2x+y=u

and x-y=v

[hot canyon]

And Jacobian

[sharp smelt]

so v=2 and v=3. are two bounds

and u=12

and u=21

So the integral is $\int_{2}^{3} \int_{12}^{21} vu \cdot J du dv$

[jolly parrot]

What a wonderful world!

[sharp smelt]

Is that right so far?

The jaobian is 1

which feels sus

Yeah, I think I got it

thanks

.close

[pearl pond]

Channel closed

Closed by @sharp smelt

Use .reopen if this was a mistake.

[pearl pond]

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.

[fierce totem]

$1)\int_{0}^{1}\frac{\ln^{2}(x+1)}{x},dx\newline2)\int_{0}^{1}\frac{\ln(1-x)\ln(1+x)}{x},dx$

[jolly parrot]

TargetVN

[fierce totem]

I got these 2 integrals

I feel like I can throw Beta function in here but idk how

(btw, source: unknown)

[rough forge]

seems like the case if you substitute ln

[fierce totem]

u=ln(x+1)?

[rough forge]

yea try that

[fierce totem]

$\int_{0}^{\ln2}\frac{u^{2}e^{u}}{e^{u}-1},du$

[jolly parrot]

TargetVN

[fierce totem]

that looks quite worrying

[pearl pond]

@fierce totem Has your question been resolved?

[fierce totem]

<@&286206848099549185>

😭

[midnight haven]

let me revise integration

[fierce totem]

okay

[pearl pond]

@fierce totem Has your question been resolved?

[fierce totem]

<@&286206848099549185>

[pearl pond]

@fierce totem Has your question been resolved?

[plush bramble]

try expanding the denominator as a geometric series

$\frac{1}{1-y} = \sum_k y^k$

[jolly parrot]

riemann

[plush bramble]

then a bunch of integration by parts

[pearl pond]

@fierce totem Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[lucid osprey]

Can anyone fucking tell me what variance is?

[pearl pond]

Please don't occupy multiple help channels.

[open rivet]

!1c

[pearl pond]

Please stick to your channel.

[light blade]

In statistics?

[lucid osprey]

Obviously

[vagrant trout]

a measure of how far a set of numbers is spread out from their average value

basically

[light blade]

It is the square of the standard deviation

[lucid osprey]

THAT is standard deviation

[light blade]

There's nothing obvious about it

[light blade]

What is?

[lucid osprey]

The squared one is standard deviation

[light blade]

No

Variance is the square of standard deviation

[lucid osprey]

Fine

[sharp vigil]

standard deviation is $\sigma$, variance is $\sigma^2$

[lucid osprey]

Anyways

[jolly parrot]

cloud

[light blade]

Yep

[vagrant trout]

no

square root

[west sapphire]

pro tip, they are the same when sigma is 1 (or 0)

[vagrant trout]

oh mb

variance is the square

[light blade]

I'm very sure it is but let me check

[vagrant trout]

yes

nono

i thought u were talking

abt standard dev

[light blade]

It's ok

[lucid osprey]

Let’s say I have numbers

3, 7, 9, 12

The average number is 7,75

It’s a timeline

Now, standard deviation would be a number showing on average the distance between each numbers and the median (7,75)?

[vagrant trout]

Here's a table I found online.

It tells you the difference between the two.

[open rivet]

!nogpt ?

[pearl pond]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[valid peak]

doesn't look like gpt

[vagrant trout]

not gpt

[open rivet]

oki

[lucid osprey]

@valid peak

@valid peak

[open rivet]

dont spam ping

[lucid osprey]

Then answer

[open rivet]

its been 1 minute

chill

[lucid osprey]

No.

[light blade]

We're not here to do your hw sorry

[lucid osprey]

You’re not.

Also don’t do me a favor.

[light blade]

I told you the difference please try yourself

[valid peak]

I'm not obligated to and I won't -- I told you already to be respectful

[lucid osprey]

I don’t care about the difference

I want the meaning and usage

[light blade]

Well, please specify what you "want"

[open rivet]

$\sigma=\sqrt{\frac{\sum (x_i-\mu)^2}{N}}$

[jolly parrot]

Bonk

[valid peak]

meaning and usage

[lucid osprey]

From their average value, so 7,75?

[light blade]

Also please be a little nicer, we are trying to help you after all

[valid peak]

the standard deviation is used more than the variance because of the https://en.wikipedia.org/wiki/68–95–99.7_rule

[light blade]

Yess

[lucid osprey]

The standard deviation in this is 3,27

3+3,27 is 6,27

Not 7

So it’s not accurate

[light blade]

Why add 3?

[lucid osprey]

9+3,27 is 12,27 not 12.

[vagrant trout]

find mean of dataset -> find deviations of dataset -> square your deviations -> find average of squared deviations

that's your answer

[lucid osprey]

Because finding the distribution

[lucid osprey]

OKAY.

But like I want to know WHAT IS THE PURPOSE OF IT.

[open rivet]

how do you come to this conclusion?

[lucid osprey]

LIKE WHAT STATISTICS FORS IT SHOW

[light blade]

Ok lemme explain

[lucid osprey]

What do you NOT UNDERSTAND?

[light blade]

In a Normal Distribution any value within 2 standard deviations is likely (92%chance

So if a data is more than 2 standard deviations from the mean

We can investigate if something is wrong

in the data

Example

[vagrant trout]

mean of dataset: 3+7+9+12/4 - 19+12/4 = 31/4 = 7.75

deviations: (3-7.75), (7-7.5), (9-7.75), (12-7.75) = -4.75, -0.5, 2.75, 5.75

square these 4 and when you get the answers for the four, do a mean of the squared deviations, that's your variance

i told you the purpose

[light blade]

The intelligence scale (can't write quotient in front of it) is one such scale

Which has mean 100 and s.d. 14

So anybody above 128

[vagrant trout]

it serves the purpose of measuring data spread

[light blade]

There maybe something wrong in the data collection

[vagrant trout]

its also used to measure risk in finance

i believe

i'm not really a statistics expert to know every application

[lucid osprey]

Don’t understand it

[vagrant trout]

what do you not understand

[lucid osprey]

It is how much are the numbers distanced from median?

[vagrant trout]

no, it is to measure the spread of a set of data points relative to their mean.

[light blade]

From the mean

[lucid osprey]

What’s mean?

[light blade]

It is used for probabilities in a normal distribution

[vagrant trout]

average

mean value

[light blade]

The arithmetic average

x bar

Don't know how to write it in latex

[open rivet]

$\bar{x}$

[jolly parrot]

Bonk

[lucid osprey]

So for example

2, 2, 5

Avg is 3

1,41 is standard deviation

Why? If it’s early 1

[light blade]

Thanks man

[lucid osprey]

3-2=1

5-3=2

[light blade]

Ok what you are calculating is the mean-root deviation?

[open rivet]

wdym early 1?

[lucid osprey]

So is the standard deviation used to find the difference in distributions from mean?

[light blade]

From the mean. And no it's used to see how your data is dispersed

[lucid osprey]

Omg

[vagrant trout]

2, 2, 5

mean: (2+2+5)/3 = 9/3 = 3

deviation: (2-3), (2-3), (5-3) = -1, -1, 2

squared deviation: 1, 1, 4

variance: (1+1+4)/3 = 6/3 = 2

[static bloom]

pls put brackets

[vagrant trout]

ye just did

[open rivet]

the average is where the peak of the red line is, the standard deviation means how wide the red line is

[lucid osprey]

Why is variance 2 if 2-3 and 2-3 is -1?

[light blade]

What is @lucid osprey trying to ask exactly?

[open rivet]

you dont use the variance like that

[light blade]

This table is one of the uses of Standard deviation

[lucid osprey]

TJEN HOW DO YOU USE IT?

IN STATISTICS

[open rivet]

i just told you

[open rivet]

look at this

the blue is the real data

[light blade]

Are you trolling @lucid osprey

?

[lucid osprey]

MEDIAN, YOU USE IT FOR EXACTLY A JUKBER IN THE MIDDLE.
MEAN, MIDDLE NUMBER RESPONSIBLE FOR THE WHOLE GROUP
MODE MOST REPEATED NUMBER

[open rivet]

variance is the spread of the numbers

[light blade]

Have you learnt what Mean is?

[lucid osprey]

WDYM SPREAD?

[open rivet]

look at this

[lucid osprey]

Stop thinking that I’m disabled

[light blade]

What have you studied so far in statistics

[open rivet]

you see the red line?

[lucid osprey]

What the fuck is it?

[light blade]

Woah!

[light blade]

<@&268886789983436800>

[open rivet]

!volunteers

[pearl pond]

Helpers are just people volunteering their time to help you. Be polite and patient.

[open rivet]

no need to be rude

[light blade]

This person is being rude to us

[open rivet]

and disrespectufl

[lucid osprey]

@open rivet

What is spread of the numbers?

[open rivet]

we have been sitting here for 20 minutes now trying to explain to you

[light blade]

And very patiently too

[light blade]

What have you learnt so far in statistics?

[lucid osprey]

Everything

SPREAD

What is it

[open rivet]

the numbers 1,3,5 have a larger spread than 2,3,4

even though the have the same average

[light blade]

Ok this is a troll confirmed now

[light blade]

This example is useful

[valid peak]

you were told to keep it respectful and didn't, so you're muted. Helpers have put a lot of effort into trying to answer your convoluted questions

.close

[pearl pond]

Channel closed

Closed by @valid peak

Use .reopen if this was a mistake.

[light blade]

Thanks mod, finally like you guys/s

I just wish I could have 20 mins of my life back

[pearl pond]

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 hull]

how do i do number 61 bc i have a feeling i don’t just plug t into the given formula

[plush moss]

I think you have to find the accleration from the function of position

Then you can find the Force exerted with the mass and accleration

[vital hull]

okay that makes sense

[vital hull]

yeah it worked ty

.close

[pearl pond]

Channel closed

Closed by @vital hull

Use .reopen if this was a mistake.

[pearl pond]

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.

[median estuary]

need help

[median estuary]

so bad

how is this not

the answer

[west sapphire]

tangent = what over what?

[median estuary]

wym

bro

[west sapphire]

as in sohcahtoa

[lime carbon]

who can vc and help me with my hw

[median estuary]

boer

bro

shut up

im doin shit

right bnow

[median estuary]

idk what u mean

[west sapphire]

are you south african?

[median estuary]

yes

7/6

right

[west sapphire]

what is 7/6

[median estuary]

tan y

[west sapphire]

certainly not

[vivid stone]

.

[median estuary]

brio

[west sapphire]

go back to your sohcahtoa

[median estuary]

bro

[vivid stone]

ws

[median estuary]

i do online math'

[vivid stone]

wsg

[median estuary]

you think

i actually

do it?

i use gauth brother

gauth ai

or chatgpt

[vivid stone]

hats 2+2

whats*

[west sapphire]

then you are doomed to failure

[vivid stone]

i use chat gpt fror my exams

fo*

for*

[west sapphire]

ask chat gpt how to open your own help channel

[median estuary]

deadass

bro why cant ppl just tell us the answer

like

ur not our teacher

just pls

help us

[west sapphire]

that's not how it works

we can guide you to find the answer yourself

[median estuary]

bro

every ai

[west sapphire]

you don't learn anything if someone just tells you the answer

[median estuary]

says this is the answer

bro

this isnt gonna help me

[west sapphire]

i don't believe you

[median estuary]

as a sport athletics

[west sapphire]

they can't all be that stupid

[median estuary]

i swear 😭 🙏

ill show u

they are all

so stupid

[west sapphire]

well if all the world's AI's say it's true then it must be true, what do you need us for?

[plush bramble]

!nogpt

[pearl pond]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[west sapphire]

it's right that tan = opp/adj

[west sapphire]

but it completely screwed up what is opposite and what is adjacent

look at the picture yourself, what side is opposite the angle Y?

[median estuary]

Z

[west sapphire]

side

Z is an angle

[median estuary]

bro

i meant

85

,/85

[west sapphire]

well that's wrong in a different way

[median estuary]

_/85

[west sapphire]

which side is the hypotenuse here?

[median estuary]

bor

bro

i dont know?

[west sapphire]

well you have to understand these things in order to get the answer right

[median estuary]

ok

nbere

heree

about

you teach me

this

then ill try

a different

concep

t

[west sapphire]

the side opposite the RIGHT angle is the hypotenuse

which angle is the right angle?

[median estuary]

X

[west sapphire]

good

and which side is opposite it?

[median estuary]

im guessing 85

[west sapphire]

yea sqrt(85)

[median estuary]

squirt

[west sapphire]

opposite is the side that doesn't touch the angle

[median estuary]

wth

yes

[west sapphire]

ok so sqrt(85) is the hypotenuse

[median estuary]

alr

[west sapphire]

now what side is opposite Y

[median estuary]

6

[west sapphire]

yep

and the adjacent side is the one that's not opposite and not the hypotenuse

[median estuary]

85/6

[west sapphire]

so adjacent = ?

[median estuary]

uh

6

[west sapphire]

no 6 is opposite

[median estuary]

7

[west sapphire]

the adjacent side DOES touch the angle

yes 7

[median estuary]

is there only

one

adjacent side

[west sapphire]

so opposite/adjacent = ?

[west sapphire]

yea the one that is not the hypotenuse and touches the angle

[median estuary]

7

opposite

adjacent

bro

what

you

said

[west sapphire]

opposite = which one

[median estuary]

oppisite/adjacnt

then

if you go up

u say its not

6

is opposite

[west sapphire]

6 is opposite

7 is adjacent

[median estuary]

yes

85 is opposite

to x

[west sapphire]

85 is opposite to x, but we don't use that terminology for the right angle, we call it the hypotenuse

(i don't make the rules, but those are the facts haha)

[median estuary]

oh igjt

ight

[west sapphire]

so tangent of Y is what

you have the numbers you need

[median estuary]

wel

l

i dont know what

the hell

the tangent is

is it the adjacent

the opposite?

[median estuary]

ik

[west sapphire]

plug those into the formula

[median estuary]

so its 6/7

bro

[west sapphire]

tan Y = opposite / adjacent

yes, 6/7

[median estuary]

is that the forumla

right there

[west sapphire]

yes it is

of course you have to use the opposite and adjacent corresponding to that angle

[median estuary]

k now

that

i dont understand

how th ehll

[west sapphire]

so for tan Z it'll be different

[median estuary]

its not

53

[west sapphire]

what trig function relates the two given sides and the angle you want to find?

[median estuary]

uh

cos

tan

[west sapphire]

which one?

[median estuary]

cos

[west sapphire]

ok

[median estuary]

nice

ez guess

[west sapphire]

so cos(unknown angle) = what ratio?

[median estuary]

:

?

💀

what

[west sapphire]

sohcahtoa

the "cah" part

[median estuary]

dude

u keep saying that

[west sapphire]

cosine = adjacent / hypotenuse

[median estuary]

i have no idea what sohcahtoa is

[west sapphire]

wth

what cretin is teaching trig without sohcahtoa

it's the most useful mnemonic in all of math

[median estuary]

cretin

what the fuck is cretin

[west sapphire]

i am not gonna google it for you

[median estuary]

i googled it

[west sapphire]

but it's not a favorable term

[median estuary]

bungo

get this

into your mind

ok

im online math

i go to school

sophomore in hs

i dont have math

in teacher

she gives us an assignment

with a video

im not watching a stupid ass video

on some boring useless shit

[west sapphire]

what she doesn't actually stand there and teach you?

[median estuary]

no?

[west sapphire]

what is this, covid?

[median estuary]

she gives us a video

basically

[west sapphire]

tell her lazy ass to get up to the board and teach

[median estuary]

thats what that fat ass dooes

you should hear

her voice

when shes talking

makes we wanna

ykyk

buit

this is why

[west sapphire]

all right

anyway

[median estuary]

i dont know shit

[west sapphire]

this term:

[median estuary]

and im failing

act

and all state tests

[west sapphire]

sohcahtoa
is taught by ALMOST all trig teachers

[median estuary]

🙂

[west sapphire]

all it means is this:

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

[median estuary]

bet

[west sapphire]

take the first letter of each word, you get sohcahtoa

[median estuary]

uh

why isnt it called

sincostan

[west sapphire]

because that doesn't help remember what sides you need for those

[median estuary]

and sohcahtoa does?

[west sapphire]

yea

[median estuary]

alr ig

[west sapphire]

soh = "sin = opp/hyp"

cah = "cos = adj/hyp"

toa = "tan = opp/adj"

once you get it burned into your brain you never forget it even after years

[median estuary]

yo im not gonna lie

my

test

ends

in like

15 minutes

i dont got all day

[west sapphire]

so back to your picture

[median estuary]

and i gopt like 5 questions

left

...

so im cooked gng

[west sapphire]

this is a test?

[median estuary]

no

lol

[west sapphire]

you said test

[median estuary]

yeah

i get mixed up

forget it

next

[west sapphire]

show the whole screenshot

don't crop out the part where it says test

[median estuary]

time remaining

was a joike

but

hurry

i have to leave soon

too

test/assessment is samething

my teacher calls all homework assessments

ok @west sapphire

we gonna keep teaching

or

[west sapphire]

i dunno, if <@&268886789983436800> say ok then yes, it's not my call to make

[median estuary]

<@&268886789983436800> hurry

dont got time to waste

[valid peak]

if it's a timed assessment I'm going to assume that you're expected to complete this by yourself. We don't allow cheating in exams, personal assessments, etc. here #rules

.close

[pearl pond]

Channel closed

Closed by @valid peak

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.

[solemn rover]

someone just help me with these

[solemn rover]

i understand how to do them but my instructor has put completely different answers than mine

[grim fractal]

what were your answers

[solemn rover]

a) 161.7

b) 104

c) not sure

d) 512

[hollow oak]

how did you end up with a decimal number

a is composed by a square and a triangle

you can sum their areas and find the total area

how would you calculate their areas?

[solemn rover]

i used a2 + b2 = c2 to find the unknown side for the triangle

[vagrant trout]

yes

and after?

what did you get for the unknown side?

what does it equal?

[solemn rover]

17.7

[vagrant trout]

how?

if the hypotenuse is 13

one side is 12

[grim fractal]

The unknown side can't be larger than the hypotenuse

[vagrant trout]

what's the unknown side

[solemn rover]

isnt it

13 squared and 12 squared = c2

[vagrant trout]

nono

[grim fractal]

No dawg c is the hypotenuse

[vagrant trout]

the hypotenuse

[vagrant trout]

you don't have to be harsh about it

[steep valley]

c. 321.5

[grim fractal]

How am I being harsh?

[vagrant trout]

"dawg"

😭

[vagrant trout]

c represents the hypotenuse

[grim fractal]

😵 my bad

[hollow oak]

I would leave it as 400 - 25π

[vagrant trout]

in this case 13 is the hypotenuse

[vagrant trout]

but r = 10

for the circle

isn't it 400 - 100pi?

[grim fractal]

yes r=10

[vagrant trout]

yeah so it's 400 - 100pi

20^2 - r^2 * pi

[solemn rover]

is the unknown side 5?

[hollow oak]

nope

that's a quarter of the total area of the circle

so it is 20² - ¼(π10²)

which is 400 - 25π

[solemn rover]

Ah, i understand the first one

[vagrant trout]

oh right

mb

[hollow oak]

no problem

[solemn rover]

The unknown variable in part a) is 5, and the area of the square is 144 so I'd get 174

5 + 12 + 13 = 30

30 + 144 = 174

[hollow oak]

wait what is 5 + 12 + 13

[solemn rover]

30

[hollow oak]

no I mean, are you calculating the area?

that's the perimeter

[solemn rover]

*12 x 5 / 2

Nonetheless it's still 30

[hollow oak]

yes, just luck and coincidence

[solemn rover]

is the area of the last one 544?

[hollow oak]

I don't think so

how did you calculate it

[solemn rover]

so, LxW which is 24 x 16 = 384

and for the left triangle 12 x 16 /2 which is 96

and the right triangle which is 4 x 16 / 2 = 32

384 + 96 + 32 = 544

*512

[hollow oak]

are you sure about the last assumption?

[hollow oak]

now it's ok

[solemn rover]

yeah, but my instructor put the answer as

"atleast 100"

without a specific answer

[hollow oak]

ahahah Idk why

I can tell you that you did it correctly tho

[solemn rover]

alright, thanks

my math examination tomorrow and im just revising over my exam preperation sheet

thats why

so to clarify

area formula = a sqrd + b sqrd = c sqrd

perimeter formula = c sqrd = a sqrd + bsqrd

[hollow oak]

what?

area's formula of what

[solemn rover]

like the overall unknown side formula

[hollow oak]

why did you put "area formula" then

c² = a² + b² yes

nothing to do with area and perimeter tho

[solemn rover]

oh so the formula is same for both?

[hollow oak]

bro you might be a little confused

that formula c² = a² + b² has nothing to do with areas an perimeters

it's just the relation between the sides of a rectangular triangle

[solemn rover]

it depends on the conditions of the sides?

so if a shape had two known variables which were the same value it would be a2 + b2 = c2

but if it had two different values which one of them were larger than the other it would be c2 = a2 + b2

[gray lantern]

did you learn about the pythagorean theorem

and/or how to use it

[solemn rover]

yeah id learnt about it this semester and im reviewing it currently

i understand how to use it, just some questions are tacky for me

its used mainly whenever there is an unknown variable and two known variables which can be used to indicate it using the formula

[gray lantern]

well under the condition of it being a right triangle

not in all cases

[solemn rover]

yeah, for some reason we mainly worked on right triangles this sem

could have done other shapes but idrc

[gray lantern]

do you remember which sides correspond to what letters in a right triangle then

(letters aka variables in a2 + b2 = c2)

[solemn rover]

Yeah

largest variable is always c2

[gray lantern]

yes otherwise known as the hypotenuse

[solemn rover]

secondary variable is the one put into the equation with the unknown variable

[solemn rover]

yeah

[gray lantern]

so you know how to solve those

[solemn rover]

basically yeah

again im reviewing mostly

[gray lantern]

i see

so where is the confusion located

if any

[solemn rover]

let me go over a few questions with you

[gray lantern]

sure

[solemn rover]

so for this composite figure

i'd locate the unknown variable through the theorem, being 13 sqrd = 12sqrd + b sqrd

which equals 169 = 144 + b sqrd

144 is missing 25 to become equivalent in value to 169, so id do 5 sqrd due to it amounting to 25

end equation =

169 = 144 + 5 sqrd (25)

which is 169 = 169

so, knowing the unknown variable is 5

id use the regular triangle formula doing 12 x 5 / 2 = 30

then for the square, 12x12 = 144

hence being 30 + 144 = 174

overall area = 174

for a)

[gray lantern]

that's correct

though i would probably suggest solving for b equation-wise first just for convenience

[solemn rover]

yeaht reu

true

[gray lantern]

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

[solemn rover]

to find the unknown variable, id do 12 sqrd = 5 sqrd + b sqrd

so, 144 = 25 + b sqrd

[gray lantern]

is that the longest length?

[solemn rover]

Yes

the known variables in the triangle are 5 and 12

[gray lantern]

the hypotenuse will always be opposite to the right angle

[solemn rover]

ah

i thought it was the largest value

[gray lantern]

it would be the hypotenuse if you knew it

so that's what you're solving for

[solemn rover]

let me do it the other way

[gray lantern]

you have a and b

[solemn rover]

5 sqrd + 12 sqrd = c sqrd

yeah

[gray lantern]

yes

[solemn rover]

25 + 144 = c2

169 = c2

13 = c

[gray lantern]

yes

[solemn rover]

so i use the formula i just used whenever i have a known a and b

[gray lantern]

identical to the previous problem basically

[solemn rover]

yeah

[gray lantern]

generally, use pythagorean theorem if you have 2 of the sides known in a right triangle

[solemn rover]

okay

triangular formula: 8 x 6 / 2 = 24

rectangular formula = 8x 10 = 80

24 + 80 = 104

[gray lantern]

yep

[solemn rover]

overall perimetre = 104

okay

[gray lantern]

area not perimeter

[solemn rover]

*area

yeah

(finidng perimetre_)

circle formula = 3.14 x 8 / 2 = 12.56

triangle formula: 10 + 10

= 20

12.56 + 20 = 32.56

[gray lantern]

good

[solemn rover]

also, on my examination we'd be going over slopes and such

(gr 9)

just to give you the level im doing

[gray lantern]

i see

[solemn rover]

these are simpler questions

buit

a) y = 2000x + 10000

b) y = 2000 x 5 + 10000

(20000)

[gray lantern]

yep

[solemn rover]

a) i) initial val = 1

ii) ROC = 9/3 = 3

iii) y = 3x + 1

b) i) initial val = 0

ii) 40 / 20 = 2

iii) y = 2x + 0

c) i) initial val = 70

ii) ROC = -40 / 80 = -0.5

iii) y = -0.5x + 70

[gray lantern]

i mean you seem to have a pretty good understanding of all the concepts

everything here is good

[solemn rover]

yeah i was mainly having a bit of difficulty on the composite shapes, but that had been due to the fact that i had forgotten the formulas for them and when to use them

[gray lantern]

ah

[solemn rover]

the rest is polynonmials and expressions

also exponent laws with questions like b3 + b5

monomial - 1 term

binomial - 2 terms

trinomial - 3 terms

quadrinomial (four termed polynomial) 4 terms

4 - 3p + 2 = p - 10

4 + 2 -3p = p - 10

6 - 3p = p - 10

6 + 10 = p + 3p

16 = 4p

16 / 4 = p

4 = p

[gray lantern]

yes

[solemn rover]

ok, thank you for staying here with me

i think im okay now

[gray lantern]

im sure you'll do fine

[pearl pond]

@solemn rover Has your question been resolved?

[pearl pond]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[pearl pond]

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.

[tawny cypress]

how do i solve intergal of e^x/e^8x

[bitter lodge]

Dyk about u-substitution

[tawny cypress]

no

[bitter lodge]

Ok uh

[tawny cypress]

we didnt learn it

yet

[bitter lodge]

Can you try simplifying $\frac{e^x}{e^{8x}}$

[jolly parrot]

King Leo

[tawny cypress]

isnt it like 1/e^7x

but im not sure

ok ty

[bitter lodge]

$\int \frac 1{e^{7x}} \dd{x}$

[jolly parrot]

King Leo

[tawny cypress]

then I move it up and divide e^-7x by -7 right

[bitter lodge]

$$\int \frac 1{e^{7x}} \dd{x}$$
$$\int e^{-7x} \dd{x}$$
$$\frac{e^{-7x}}{-7}$$

@tawny cypress youre missing one thing

[tawny cypress]

oh yh

i forgot

its e^-6x

[jolly parrot]

King Leo

[tawny cypress]

then divide by 6

?

hm

[tawny cypress]

do we add an exponent?

for this

[bitter lodge]

No

Instead, you must add a Constant of Integration

[tawny cypress]

yea ik

ty i understand it now

[bitter lodge]

No, thats the power rule

[tawny cypress]

ya i forgot it doesnt apply for this

[bitter lodge]

!done

[pearl pond]

If you are done with this channel, please mark your problem as solved by typing .close

[tawny cypress]

.close

[pearl pond]

Channel closed

Closed by @tawny cypress

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.

[quartz yoke]

could someone please help me on number 13

ive done these problems before i just cant remember the rest

im pretty sure you're supposed to use similar triangles but my stuff gets messy later on

[deft bough]

so (4-x)+x= a^2, y+3-y = b^2??

[lunar atlas]

you can identify the hypotenuse 5

[lunar atlas]

bc of perfect triangle theorem

[quartz yoke]

yea

idk why i didnt realize that

[lunar atlas]

wait

nvm

[quartz yoke]

sorry, i dont really get whats happening here

[lunar atlas]

im wrong

[quartz yoke]

rly?

[lunar atlas]

nvm

im correct again

[deft bough]

Based on the information you have labeled, one side is equal to 4-x+x, one side is equal to y-3+y…

That doesn’t seem so accurate

[quartz yoke]

wdym

4-x+x=4

one side is 4

3-y+y=3

thats the other side

[deft bough]

Im not reading the question properly

💀

[quartz yoke]

💀

[lunar atlas]

yo use congruency

[quartz yoke]

congruency?

where do we use it

[zenith cipher]

The area of the triangle would be..

[lunar atlas]

you can tell 4/3 =4-x/y

[quartz yoke]

yea

[quartz yoke]

12

[lunar atlas]

jesus what grade is this

[quartz yoke]

wdym

bro

my fault

im sorry

6

[plush moss]

Bro sold with the half

[zenith cipher]

Calculate the area of the triangles and rectangle inside

[lunar atlas]

i was thingking using tthe herons formula

[zenith cipher]

Correct

[lunar atlas]

ig im too far

[quartz yoke]

so like we go xy+(4-x)(y)/2 + x(3-y)=6?

idk

[lunar atlas]

bro

i use all the option

and 7 is the perfect one

idk

[quartz yoke]

wait what

so you got a fraction?

7 is odd

[zenith cipher]

Correct.
Now try to find y int of x.
And then
Perimeter of rectangle is x+y.
Now put y here and differentiate

wrt x

[lunar atlas]

i got 4x-4/3x2 = 12

with that i got x= 3/2

and y= 2

and then use the perimeter formula

to get 7

[quartz yoke]

wait so how did you get your end equation

[lunar atlas]

so

[zenith cipher]

You'll get 3x+4y=12

[quartz yoke]

okay

do we make a system of equations?

[lunar atlas]

i think im wrong

[zenith cipher]

From here,
You want maximum area right?

[quartz yoke]

yes

[zenith cipher]

I'll find y in terms of x.
like y=(12-3x)/4

[quartz yoke]

ok yeah

[zenith cipher]

Area would be x*y=x(12-3x/4)

Now differentiate wrt x and set it to zero to get the value of x

For which the area will be maximum

I found x=2

Finally, Get y and find the perimeter

[quartz yoke]

wait so we find the derivative

and then the max

[lunar atlas]

wth

[quartz yoke]

yuh

[lunar atlas]

dayum

i dont even think about derivative

thats why im asking what grade is this

[quartz yoke]

im in 10th grade

[lunar atlas]

i think im cooked

im an 11 grader and we dont even talk about derivative

[quartz yoke]

bro why did i get 0

am i stupid

[lunar atlas]

youre not alone

what is this supposed to be

[quartz yoke]

like a math tourney

[lunar atlas]

ah

thats why]

bro why the diffrence in difiiculty of number 13 and 14 is so high

[quartz yoke]

ikr

[lunar atlas]

is 14 d ?

[quartz yoke]

thats what i got

[lunar atlas]

okay