help-10

[obtuse pebble]

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[chrome mesa]

It's not correct

[proper coyote]

.reopen

[obtuse pebble]

✅

[chrome mesa]

At least the derivative

[proper coyote]

Oh

[drowsy girder]

I mean you got right answer just not done right

[proper coyote]

Oh

Oh i shouldn’t have negative exponent in my derivative right?

[chrome mesa]

You can't differentiate the 2x and x^(1/2) separately. You have to use the product rule

[proper coyote]

Ohh

[chrome mesa]

The only reason something like d/dx 6x^2 = 6 d/dx x^2 is because d/dx of a constant is 0. But it's the product rule anyways

[proper coyote]

Oh so i shoudl group the 2x √ x

In an exponent

Instead of separate

And then product rule?

[chrome mesa]

Yes

[proper coyote]

Okay then i will fix it

But i have to go now

Thank you for the help

Have a nice day!!

[chrome mesa]

You can group the exponent into 2x^(3/2)

[proper coyote]

Ah yes i see

Then use product rule

Thanks 😊

Have a nice day, bye!

.close

[obtuse pebble]

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[drowsy girder]

Then you use power rule

[obtuse pebble]

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[wary sun]

Hey, does anyone know what I'm doing wrong in this problem?

[wary sun]

Here's what I did:

[obtuse pebble]

@wary sun Has your question been resolved?

[obtuse pebble]

@wary sun Has your question been resolved?

[obtuse pebble]

@wary sun Has your question been resolved?

[obtuse pebble]

@wary sun Has your question been resolved?

[lean wigeon]

In the answer in the problem, it only has 4 rows

If you can enter 5 rows, you should

[raven spire]

aren't a_1, a_2, a_3, a_4, a_5 column vectors? what do you think you're doing

You're supposed to rref this one ._.

[warm shale]

Ansh

[wary sun]

that worked, though I have no idea how you came up with that :/

[astral ivy]

Whoa is that an iPad

[wary sun]

yup

[obtuse pebble]

@wary sun Has your question been resolved?

[balmy mortar]

You probably read your vectors the wrong way or something?

[obtuse pebble]

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[timid silo]

hello currently stuck at this question

[burnt jungle]

This is one is rather easy

We have

The function that represents the freezing temperature with respect to salt percentage

Let's call it f(s)

We have that f(0) =0

[timid silo]

okay

[burnt jungle]

And f(23.3) =-21.1

Do you know whats the equation of a line?

[timid silo]

no i do not

wtf

[burnt jungle]

It's y=mx+b

Y in this case is f

And x is s

So it's f=ms+b

B represents the value of y coordinate when x is 0

[timid silo]

And this would be the equation for it correct?

[burnt jungle]

That means, the f value when s is 0

[burnt jungle]

Yep

It's called a linear

[burnt jungle]

Do you know what's this one?

The freezing point of 0℅ salt

[timid silo]

uhh no not rlly

[burnt jungle]

.. It's in the question

[timid silo]

it would freeze at -21.1

[burnt jungle]

Oh

At 0℅ salt?

[timid silo]

oh wair nvm it would freeze at 0.0

[burnt jungle]

Great

So b is 0

Now we need m

M is the slope

Ever heard of that?

[timid silo]

yeah

[burnt jungle]

Do you know the equation of a slope?

[timid silo]

m = y2 - y1

over x2 - x1

[burnt jungle]

Yes

The difference in freezing over the difference in salt

We need two freezing values and two salt percentages from. The question

One of both is 0

So x1 is 0 and y1 is 0

We need x2 and y2

A non-zero freezing point given in the question

The number you said earlier

[timid silo]

the x2 and y2 would be 0?

[burnt jungle]

No

[timid silo]

oh 21

-21.1

[burnt jungle]

We have the difference between two freezing points DIVIDED by the difference between their respective salt concentration

The 2 freezing points given are 0 and -21. 1

The respective salt concentration is 0 and 23.3

In order

[timid silo]

so x2 and y2 wouod be 23.3 ?

[burnt jungle]

X2 would be 23.3

Y2 would be -21. 1

Y is the freezing point

And x is the salt concentration

We have 0 freezing point for 0 concentration

And -21. 1 freezing for 23.3 concentration

We divide the freezing over concentration

So its

(-21.1-0)/(23.3-0)

[timid silo]

alrighr yeah

[burnt jungle]

You need to understand the slope equation

Take two values from y and the two values of their x

And do the difference then divide

Anyway

Here we are substracting 0

So it doesn't matter

-21. 1/23.3

Is our slope

So f=-21.1s/23.3

That's our equation

[timid silo]

yep got it

[burnt jungle]

You can plug more numbers to find other values

Like 34.2

[timid silo]

i see

[burnt jungle]

We need the freezing point for 34.2℅ concentration

Can you do that?

[timid silo]

would u have to plug in 21.1

since 23.3 would be the concentration

[burnt jungle]

S refers to salt

F refers to freezing

Which one do we have?

[timid silo]

F

[burnt jungle]

You sure?

I said 34.2℅

Is ℅ the unit for freezing?

[timid silo]

Oh S cus we need F

[burnt jungle]

Yeah

So we plug s

And solve for f

If we had freezing( coming right in the third question)

We plug f and solve for s

Anyway

Plug in 34.2 and solve for f

[timid silo]

would it be 21.1 / 34.2

[burnt jungle]

Look at the equation we made

So f=-21.1s/23.3

Plug in s

Replace s

Don't touch anything else

Just remove s and put your concentration instead of it

[timid silo]

so replace it with 34.2?

[burnt jungle]

Yeah

[timid silo]

34.2 /23.3

[burnt jungle]

Uh?

No

You have

(-21.1 × S ) ÷ 23.3

Only plug in s

Please

[timid silo]

ook i got it

[obtuse pebble]

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[obtuse pebble]

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[exotic sparrow]

T

[exotic sparrow]

Part e

[civic zealot]

$P(A|B) = \frac{P(A\cap B)}{P(B)}$

[warm shale]

Zybikron

[civic zealot]

So if $\mu$ is the mean and $m$ is the median then this is asking $P(\mu\leq x\leq m\mid \mu\leq x)$

[warm shale]

Zybikron

[obtuse pebble]

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@exotic sparrow Has your question been resolved?

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[tardy epoch]

Split the sum: $\sum_{i=1}^{52} (m_i-150) = \sum_{i=1}^{52} m_i - \sum_{i=1}^{52} 150$

[celest gorge]

How does that help

What would i do next

[tardy epoch]

do you know the formula for mean?

[celest gorge]

Sum of masses of apples / number of apples

[warm shale]

riemann

[tardy epoch]

write this in summation notation

[celest gorge]

I don't know how to use the discord bot to do that

[tardy epoch]

paper's fine

[leaden ibex]

or mspaint

[tardy epoch]

does your formula for mean look similar to something in this equation?

[celest gorge]

1 sc

i'll send

[tardy epoch]

Here, $i$ is the index of the 52 apples and $m_i$ is the mass in grams of the $i^{th}$ apple

[warm shale]

riemann

[leaden ibex]

Also, if you want to be cool and all and be able to use this bot, you'll need to learn LaTeX. (Although it might not be that useful to learn if you're not going to stay in STEM)

[celest gorge]

thats my equation for the mean

[tardy epoch]

write it in terms of your apple variables

what are x and n?

[celest gorge]

n = 52

[tardy epoch]

right

[celest gorge]

idk what x is just the mass

but idk what the mass is

of each apple

[tardy epoch]

x is mass of apple, so use m instead of x

[celest gorge]

yeah

[tardy epoch]

you don't need to know the mass of individual apples

[celest gorge]

ok

[tardy epoch]

re-write this with apple variables

[celest gorge]

k 1 sc

[tardy epoch]

not bad if this is really ms paint

[karmic cedar]

you can have straight lines in ms paint

[celest gorge]

thanks i guess lol

[tardy epoch]

right side should be $\overline{m}$ but close enough

[warm shale]

riemann

[celest gorge]

oh yeah

my bad

ok

I understand up to this point but Idk what to do next

[tardy epoch]

look here. do you see something close to $\overline{m}$ ?

[warm shale]

riemann

[celest gorge]

wdym by that

[tardy epoch]

compare the two and make a substitution

[celest gorge]

I don't understand

what am i comparing

[tardy epoch]

Yours

[tardy epoch]

and this

[celest gorge]

I don't see what you mean srry

[tardy epoch]

write it next to each other on paper

[tardy epoch]

and read this

[celest gorge]

do I divive it by 52?

to make it like my equation?

[tardy epoch]

yes!

[tardy epoch]

$\frac{1}{52}\left(\sum_{i=1}^{52} m_i - \sum_{i=1}^{52} 150 \right)= - \frac{182}{52}$

[warm shale]

riemann

[celest gorge]

ok

i understand that

[tardy epoch]

you're very close to getting the mean

[celest gorge]

but didn't we get the equation the same as mine?

im confused sry

[tardy epoch]

distribute the left hand side

a(b -c) = ab - ac

i think the rest is algebra

[celest gorge]

so I add 150 to -182/52?

[tardy epoch]

are you comfortable with the arithmetic?

[celest gorge]

i think so

but how do I calculate variance

[tardy epoch]

The definition:
$Var(m) = \frac{1}{52}\sum_{i=1}^{52} (m_i - \overline{m})^2$

[celest gorge]

dont you have to divide it by 52

or is that what the 52 above the sigma means

this notation is a little confusing srry

[tardy epoch]

ah yea i'll fix

[warm shale]

riemann

[celest gorge]

thx

but we dont have the masses of the apples so how are we meant to calculate it

[tardy epoch]

start with the left hand side of the last equation

[celest gorge]

?

[tardy epoch]

nope

[celest gorge]

i dont understand

[tardy epoch]

an equivalent definition could be
$Var(m) = \frac{1}{52}\left(\sum_{i=1}^{52} m_i^2\right) - \overline{m}^2$

[warm shale]

riemann

[tardy epoch]

you have to pick one and see which one is easier to manipulate and arrive at from the starting formula

[celest gorge]

wait what

but

[tardy epoch]

this is your starting formula

[celest gorge]

variance is this

[tardy epoch]

read

you should have seen that in class

[celest gorge]

I did but I don't know how to use it

I find this topic rly confusing

[tardy epoch]

you'll have to do some algebra and try

it's not straightforward. it takes trying and failing

[celest gorge]

i dont have the sum of the mass squared though

[celest gorge]

i've been on this problem for 3 days i don't know what to do..

[tardy epoch]

well now you know the right direction to go towards. use algebra and manipulate

[tardy epoch]

Last hint: expand (m-150)^2

[celest gorge]

m^2 - 300m + 150^2?

u mean that?

[tardy epoch]

Fixed
$Var(m) = \frac{1}{52}\left(\sum_{i=1}^{52} m_i^2\right) - \overline{m}^2$

[warm shale]

riemann

[celest gorge]

i don't understand any of this..

I still don't know how to rearrange with the sum/sigma sign

[tardy epoch]

that's why you're supposed to practice

[celest gorge]

how can I practice when I don't know how to do one?

[tardy epoch]

you can treat $\sum_{i=1}^{52} m_i^2$ as a variable, say $s$

[warm shale]

riemann

[tardy epoch]

re-do the mean calculation

[celest gorge]

s/52?

[tardy epoch]

keep going. use rules of algebra

https://www.cuemath.com/algebra/basic-of-algebra/

[celest gorge]

• 146.5^2?

[celest gorge]

i dont have m^2 I have (m-150)^2 in my question

[tardy epoch]

.

[celest gorge]

m^2 -300m + 150^2?

[tardy epoch]

You don't need help verifying every line

[celest gorge]

i don't know what im doing

[tardy epoch]

Follow the rules and you'll be good

[celest gorge]

i know algebra rules..

i dont know how to do statistics

i dont know how the the sigma symbol affects the question

[tardy epoch]

.

Or google some videos on sigma/summation notation

[celest gorge]

i did

as i said

i've been stuck on this problem for 3 das

days

I looked at so many videos and guides

i dont know what to do

literally makes 0 sense

[tardy epoch]

What videos

[celest gorge]

statistics,stand deviantion,how to calc mean and variance

none of them helped with this question

[tardy epoch]

None of those sound like what I told you to watch

[tardy epoch]

.

[celest gorge]

i watched a video but it just explaned what I already know I don't know how to put it into context of my question

I dont see why 1768/52 isnt the variance

because if I divide both sides of the last equation by 52 it looks like the variance equation

can you just explain what im meant to do clearly watching videos hasnt helped

[tardy epoch]

Keep going with this

[tardy epoch]

Because 150 is not your mean

Is it?

[celest gorge]

146.5 is my mean

[tardy epoch]

Then keep looking for more videos or ask a more specific question

[celest gorge]

my question is how to find the variance

I havent found a video witha question like mine

[tardy epoch]

"more specific"

What don't you understand about summation notation

[celest gorge]

for exampel idk what the 2nd equation is telling me at all

like I don't know how I can calculate the variance using that equation

[tardy epoch]

That's the same question from the beginning . Scroll up and read my explanations

[tardy epoch]

.

[celest gorge]

but I don't see why you cant just show me how to calculate it then I can practice it I don't care about getting the answer value I just want to know the method

[tardy epoch]

Because it's the same method as the mean

And you didn't try to apply it to the variance

[celest gorge]

I still dont get what you mean by that
I don't know how the squaring the brackets affects the problem

I have the correct answer of the variance it's 21.75 i literally dont care abt the answer I just want someone to show me the method

[tardy epoch]

Take 10 minutes and read this
https://tutorial.math.lamar.edu/classes/calci/summationnotation.aspx

[obtuse pebble]

@celest gorge Has your question been resolved?

[tardy epoch]

@celest gorge did you read this yet

[celest gorge]

yeah but im still confused

[civic zealot]

$a^2+b^2 \neq (a+b)^2$

[warm shale]

Zybikron

[tardy epoch]

confused about what. be specific

[tardy epoch]

what questions do you have about this chapter

then you haven't read it and you're just wasting everyone's time

"looked at" meaning you opened the tab and not read it?

because you have summations!

you know this is a summation, right?

It's just algebra and you haven't even tried

it's the same method as I showed you for the mean

EXACTLY THE SAME

alright i'll stop talking

nope. i assume you know algebra because you said so

more confusing than what?

if you know a simpler way to do it, go for it

[civic zealot]

You can find variance with $E(m^2) - [E(m)]^2$. Looks like you already found $E(m) = 146.5$. So now you just need to find the expected value of $m^2$

[warm shale]

Zybikron

[civic zealot]

that's where the second equation is useful

E(m) = 146.5

[celest gorge]

oop

i meant

146.5^2

is E(m^2) 146.5^2

[civic zealot]

Nope, $[E(m)]^2 = 146.5^2$

[warm shale]

Zybikron

[celest gorge]

ok nice

so How do I find E(m^2)

[civic zealot]

And just for reference if you haven't see the notation $E(m)$ is the average. So $E(m) =\frac1n\sum m$ and $E(m^2) = \frac1n\sum m^2$

[warm shale]

Zybikron

[celest gorge]

OH

I see

Yeah I was alittle confused by the notation

[civic zealot]

Here you said $(m-150)^2 = m^2-300m+150^2$ so you have $\sum(m-150)^2 = \sum m^2 -\sum 300m + \sum 150^2$

[warm shale]

Zybikron

[celest gorge]

Ok I think I might be able to solve it by myself now i'll let you know if I have any problems

thx

.close

[obtuse pebble]

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[timid silo]

hey

[timid silo]

is my answer right?

[gloomy valve]

???

[timid silo]

one sec

@gloomy valve

@green verge

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

.close

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[forest sinew]

so idk if theres a nice answer for this but

[forest sinew]

I'm trying to interpret what P could be in this model

S is a variable, the average size of trees

and E is a variable, the total energy in the forest

It must almost certainly be some kind of parasitism term

but i cant really track the units or what id expect it to be

any uhh intuition or guidance?

[obtuse pebble]

@forest sinew Has your question been resolved?

[forest sinew]

.close

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[steel goblet]

is the answer C?

[obtuse pebble]

@steel goblet Has your question been resolved?

[obtuse pebble]

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[fair abyss]

could you please help me with the problem tan(theta/2) = sqrt(3)?

[dense gulch]

I would first do tan(theta) = sqrt 3 and find theta

then just multiply that number by two and bam you get the answer

[hybrid gull]

@fair abyss ^^

If you have an interval that you're restricting your solutions to, then you'll have specific solutions you're targeting.

If you are looking for all real solutions, then you'll have a general solution that models all possible solutions.

[obtuse pebble]

@fair abyss Has your question been resolved?

[obtuse pebble]

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[white rapids]

Oops

With the question I'm not sure how I should separate the b⁵ from the 2.5

Would it be logb ((5/2) b⁵)

Nvm i got it

.close

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[drowsy iris]

I just want to check my answers as i am not too confident

a) A = (x)(x^2)(1/2)
= tan^3(theta)/2

dA/dt = 3/2 tan^2(x)sec^2(x) d theta/dt

so at theta = pi/3, dA/dt = 6

for b im not too sure but i calculated 5/3sqrt(3)cos^2(sqrt2)

<@&286206848099549185>

um

how to do 9b

help

.close

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[timid silo]

@upbeat hazel

[upbeat hazel]

yo

damn I've done integration

but not with cos and sin

cos sqrt is the same as cos^1/2

[timid silo]

So what would the answer be?

[upbeat hazel]

do yk how to do it?

[spiral maple]

If you just want the answer, use a calculator.

[upbeat hazel]

fr

[timid silo]

What calculator does this?

[spiral maple]

Also don't ping random users, it's poor netiquette.

Get googling

[upbeat hazel]

nah he dmd me

[timid silo]

I asked him before

[upbeat hazel]

so I was like sure

[timid silo]

But what calculator has this?

[spiral maple]

Lots

[upbeat hazel]

just use the internet

[timid silo]

What’s it called?

[spiral maple]

If you put some effort into googling, you'd find some

[upbeat hazel]

google

just google any calc

[timid silo]

I tried Mathway it was wrong

[upbeat hazel]

searching for the answer won't help tho

try see on yt how to do it

and similar qs

it'll help you answer such questions with ease

[spiral maple]

But if you're struggling that hard to google, post your attempt at doing the integral

Oh you tried to get the answer to this already

[timid silo]

do you need help or the answer?

[upbeat hazel]

Idek tho Icl

[spiral maple]

They want the answer, hence why nothing is happening

Cause giving the answer is shit help.

[upbeat hazel]

it's 2:16am rn

[spiral maple]

(dare I even call it help)

[upbeat hazel]

and I'm watching vinland saga

[timid silo]

I’ll use a calculator

Like u recommended

[spiral maple]

ok, .close the channel then

[timid silo]

Okay how?

[spiral maple]

.close

[timid silo]

do .close

[spiral maple]

and next time open a channel if you actually want help, not just the answer.

[upbeat hazel]

oops

[timid silo]

neither would you learn anything but alright

use a calculator

.close

[obtuse pebble]

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[upbeat hazel]

https://www.youtube.com/watch?v=M0WcSCxYl2Y

bro

just use that

https://www.youtube.com/watch?v=3pXALn2ovIE

[obtuse pebble]

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[little sandal]

I was trying out this problem and I got average revenue per passenger as 15.7 $ and SD as 19.95 $ which is correct. In the second part, revenue expected of 120 passengers, I did 15.7 * 120 = 1884 which is also correct.

In the case of SD in b part, should I multiply 120 with the Standard deviation (19.95)?

In a) part I am finding SD per person right? so in b) part, for 120 people, It must be multiplied right?

[obtuse pebble]

@little sandal Has your question been resolved?

[little sandal]

<@&286206848099549185>

[obtuse pebble]

@little sandal Has your question been resolved?

[obtuse pebble]

@little sandal Has your question been resolved?

[obtuse pebble]

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[wicked wren]

what do i do next..?

[tranquil rain]

Do u have the original question

[wicked wren]

that’s the og, i just copied it on paper and did a bit

wait

that’s not the og og

take away the colored lines and that’s the og

[tranquil rain]

Ok

[misty cedar]

try midpoint theorem

[wicked wren]

i’d love to, if i knew what that was..

[misty cedar]

basically midpoint theorem states that
if a line joins any 2 midpoints of the sides of a triangle, then the line is half the length of the remaining side and parallel to it
the converse also holds true

[wicked wren]

i don’t see any line that joins 2 midpoints of any triangles though

[tranquil rain]

AEG and CFG

[wicked wren]

what line joins 2 midpoints though?

[tranquil rain]

Midpoint of AC and FE

[wicked wren]

i don’t know if that’s the midpoint tho

that’s what im tryna figure out

if it’s the midpoint, that means FG and GE and congruent, and AC bisects FE

but i don’t know that yet

<@&286206848099549185>

[obtuse pebble]

@wicked wren Has your question been resolved?

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[timid silo]

<@&286206848099549185>

Is this right

[raven spire]

[timid silo]

WEONG PIC

[desert sparrow]

You can delete it

Hover over it with the 3 dots

And press the trash can

I'm not sure what the procedure is for mobile

[raven spire]

,calc (15.1^2 + 12.3^2 - 14.3^2)/(2 * 12.3 * 15.1)

[warm shale]

Result:

0.47060248748183

[tranquil rain]

I can't really read what's on the board

[raven spire]

,w arccos 0.47060

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Ansh#3502

[raven spire]

Nezuko chaaaaaaaaaaan(oops ping )

[desert sparrow]

Calc also has arccos

[tranquil rain]

Uwu

[raven spire]

bruh be flexing that hairstyle

[forest sinew]

the taper is nice

[timid silo]

do u like

[raven spire]

[forest sinew]

i always wanna taper

but i havent learned how to do it right

[timid silo]

what happened to the neck 😭

[tranquil rain]

Correct

[forest sinew]

its the only thing that makes my cowlicks look good tho

[timid silo]

look at the neck

[timid silo]

thank u

[raven spire]

Use #chill for making conversations

.close

[timid silo]

ok

[tranquil rain]

Lol

[tranquil rain]

This too

[timid silo]

LMFAO

wyd 😭

[obtuse pebble]

@timid silo Has your question been resolved?

[idle thunder]

damn u ok

[obtuse pebble]

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[misty cedar]

Let ABC be a triangle with AB = 16 and AC = 5. Suppose the bisectors of angle ABC and angle BCA meet at point P in the triangle's interior. Given that AP = 4, find length of BC.

[idle thunder]

draw a diagram

[misty cedar]

i did

wait lemme send

[idle thunder]

Can we see

[obsidian isle]

BC > 11

[misty cedar]

uhhhhh yeah? triangle inequality right?

[misty cedar]

sorry for the delay, my laptop's very slow

[obtuse pebble]

@misty cedar Has your question been resolved?

[broken bridge]

@misty cedar if AC=5, AP=4, PC=?

wait nvm

[misty cedar]

that's not a 90 deg angle tho

[broken bridge]

yea i realised that

im thinking if you can find the radius of circle and area of the triangle then we can use (perimeter*r)/2=area

but i cant figure out what AP can do for us

[misty cedar]

same

[obtuse pebble]

@misty cedar Has your question been resolved?

[obtuse pebble]

@misty cedar Has your question been resolved?

[raven spire]

is there absolutely nothing else given?

can you show the question?

[obtuse pebble]

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[vapid bay]

what is P(match)? im not good at english srry

[vapid bay]

<@&286206848099549185>

[obtuse pebble]

@vapid bay Has your question been resolved?

[obtuse pebble]

@vapid bay Has your question been resolved?

[tranquil rain]

@vapid bay Which part are u struggling with?

Match as in they're either both Q or both E

[grave kestrel]

How do we know that the area is increased four times by doubling the radius?

[glossy ibex]

this is true for all areas

take the area of a rectangle for example

area = w*h

now double the dimensions

area = 2w*2h

= 4w*h

[grave kestrel]

I am confused that the answer is 16 pi r^2 but they are saying that area is increased 4 times

[glossy ibex]

because the area started as 4pi*r^2

4 times that = 16pi*r^2

[grave kestrel]

Okay thanks

In this question I understood the first part but in the second part
I cannot understand why the answer is 1/8

[high lily]

$\frac{r^3}{8} = \frac18 \times r^3$

[warm shale]

ℝamonov

[high lily]

also dislike their liberal use of = signs

[grave kestrel]

Okay thanks

[obtuse pebble]

@vapid bay Has your question been resolved?

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[timid silo]

why the standard deviation cannot be negative (like -2)?

[timid silo]

the second statement

I feel like the standard deviation can be in both side negative and positive

Well ya it can be but there is a huge problem

I understand why u are saying +, -

It's because it's an sqrt

But dont forget that std is ment to show the variance in the data

I got it now

.close

[obtuse pebble]

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[proper coyote]

Function is given. Set up a formula of tangent line k in point A with Xa = 4.

Can someone check if my work is correct?

[timid silo]

Ur given a function

And u want to construct

The tangent at a particular point

That's all?

[proper coyote]

Yes

Could you check if i did it correctly in the above picture?

[timid silo]

That function is $f(x) = \frac {9x}{x\sqrt{x}+1}$

[warm shale]

CatHashira

[proper coyote]

Yes

[timid silo]

Hmm remember [I can prove it ] that if there is any function and you want to construct $t(x) = f'(a) * ( x-a) + f(a)$ where a is the point where you want to construct the tangent can you prove it?

[warm shale]

CatHashira

[proper coyote]

My teacher or book didn’t learn me how to prove it but i think you can prove it yes

[timid silo]

Do it yourself prove it try it atleast

[proper coyote]

Okay with the formula u gave me?

[timid silo]

Ya prove it

[proper coyote]

Okay

[proper coyote]

What do you mean by x-a ?

So just x - - 1/3

?

[timid silo]

Wdym by - -

[proper coyote]

My ‘a’ is negative

And u have negative sugn in the formula

So it becomes - - right

That’s +

[timid silo]

Ya

But the answer is not limited

To what u asked

This is valid for all functions

[proper coyote]

Yes i just asked for that part

Wait i’m stil lcalculating

Give me 3 misn

Mins

I mean

1-2

[timid silo]

Forget about the question just prove that formula

And you will be done

[proper coyote]

But to prove i have to insert -1/3 into a root

And thats impossible

[proper coyote]

For f’(a)

[timid silo]

I see

[proper coyote]

So that means my a that i found is wrong?

[timid silo]

Ur answer can be in imaginary numbers?

Probably

[proper coyote]

Noo we ddid not learn that

I will just see what my teacher says on monday then its okay

[timid silo]

I see I don't find any other way of solving it

[proper coyote]

Can u help me with how to find relative extrema?

Oh i should just do f’(x) = 0

?

.close

[obtuse pebble]

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[proper coyote]

A) Function is given. Set up a formula of tangent line k in point A with Xa = 4.

B) calculate relative extrema of f

Can someone check if my work is correct?

function is $f(x) = \frac {9x}{x\sqrt{x}+1}$

[warm shale]

blue™

[obtuse pebble]

@proper coyote Has your question been resolved?

[proper coyote]

<@&286206848099549185>

please, then i can do the rest if i know this is correct

.close

[obtuse pebble]

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[mystic saffron]

I am having trouble trying to figure out if i set up triangles for proportions correctly

my teacher says geometric mean is just ratio and proportions

do these triangles look right?

[balmy mortar]

to check, mark angles.

[mystic saffron]

ok

i think i got it thanjks

.close

[obtuse pebble]

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[timid silo]

I need help with 26, e part (ii)

I don't understand anything, pls help

<@&286206848099549185>

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[oblique fjord]

(3 x 10⁴) x (2 x 10⁹)
So far = 6 x 10¹³, which ain't equal. What do i do when the power figure is not a whole number?

[carmine bear]

you still apply the same principle, except you'll be adding fractional powers instead of whole number powers

say for example
$$3^{\frac{1}{2}} \times 3^{\frac{3}{2}}$$
you'll add the powers together such that you get $$3^{\frac{1}{2} + \frac{3}{2}} = 3^2$$

[warm shale]

I can't believe you've done this

[oblique fjord]

And in this case?

[brave bramble]

It isn't clear what your question is. "Which ain't equal"?

[oblique fjord]

Doesn't the power has to be a whole number to be correct?

[drowsy girder]

Nope

[oblique fjord]

So the ¹³ is fine?

[brave bramble]

13 is a whole number

[drowsy girder]

There is only 1 situation

Where

[oblique fjord]

https://tenor.com/view/buzz-lightyear-no-sign-of-intelligent-life-dumb-toy-story-gif-11489315

I apologise

[brave bramble]

If you are concerned with scientific notation, then yes 10ⁿ does have to be a whole number

[oblique fjord]

I will return to my forsaken lands

[brave bramble]

But your calculator will do that for you, in that case

[drowsy girder]

$$a^x * a^y ≠ a^{x + y}$$

[warm shale]

Pluton

[drowsy girder]

If a < 0

And x and y are fractions

But like really its just few cases

Wait actually nvm its other way

$$a^x * b^x ≠ (a * b)^x$$

[warm shale]

Pluton

[drowsy girder]

When a or b is a negative number

[drowsy girder]

Well technically if x and y are 1/2 and a = -1
$$(-1)^{2/2} = 1$$

[warm shale]

Pluton

[drowsy girder]

Well nvm

Rules for negative square roots are a little different

Thats all

[oblique fjord]

Thank you 😊

.Close

.close

[obtuse pebble]

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[tired talon]

Idk where to start w this any help?

[obtuse pebble]

@tired talon Has your question been resolved?

[obtuse pebble]

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[silk fossil]

Hello I need guidance with a partial fraction problem

[civic zealot]

whats up?

[silk fossil]

Hi

@civic zealot Are you able to help me see the light?

[broken bridge]

maybe try describing what you need help with

[civic zealot]

sure, but I need to know what exactly you're struggling with

[silk fossil]

Uh, the first step? I believe the formula goes (a_0/x) + (a_2x+a_1)/x^2+1

Im not certain. Struggling with this topic

[civic zealot]

yeah, that's correct

[silk fossil]

Right, not a clue how to get there

Sorry, not familiar with LaTeX on Discord.

[civic zealot]

I'm not sure what you mean. It's a bit of just using the formulation.

you're effectively un-combining fractions

for example, instead of turning 1/2+1/3 into a single fraction, your taking 5/6 and writing it as a sum of two fractions.

The factors in the left column are assumed to be irreducible or unfactorable

[silk fossil]

Ok I think I got it

.close

[obtuse pebble]

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[silk fossil]

Thanks

[obtuse pebble]

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[tardy gull]

dose someone know what the awnser to this i picked it woudlnt change but that was wrong.

[obtuse pebble]

@tardy gull Has your question been resolved?

[tardy gull]

<@&286206848099549185>

[civic zealot]

does it say that answer is wrong?

[tardy gull]

no, the awnser that was wrong was it would stay the same

[civic zealot]

so you're asking why it increases?

[tardy gull]

no, i dont know which one it is, im just asking how id figure it out

the awnser thats in yellow is a guess

[high lily]

draw some triangles

[tardy gull]

ok

[civic zealot]

specifically some right triangles where the ramp get's closer to the stair

[tardy gull]

ok

[civic zealot]

good, what happened to your angle?

[tardy gull]

it increased?

mabey

would it be increasing because as you got close to the stairs and the angle a the top got smaller and made the angle 5.7 larger?

[civic zealot]

yes, that's one way to look at it

[tardy gull]

ok

ty

.close

[obtuse pebble]

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[native pivot]

I did the work and I'm pretty sure I got the right answer

idk why its saying I'm wrong

[spiral maple]

no abs value bars in the logs

[native pivot]

The thing that I'm doing this one doesn't use abs value bars

[spiral maple]

wdym

You don't have abs value bars, so it's wrong

[native pivot]

No I would've put abs bars

but the website I'm doing this on doesn't use abs bars for some reason

idk why

[spiral maple]

"Remember to use absolute value where apparopriate"

[light sand]

Help

[spiral maple]

Im literally reading the instructions

@light sand #❓how-to-get-help

[nocturne minnow]

#❓how-to-get-help

[native pivot]

I'm so confused

[spiral maple]

yeah, that's a number

[native pivot]

But here I didn't put abs bars and it says its correct

[spiral maple]

yeah

cause you evaluated shit

$\int\frac{1}{x}\dd{x}=\ln(|x|)+C$

[warm shale]

Mosh

[light sand]

How do you Do you express the ratio x:y in simplest form

[nocturne minnow]

#❓how-to-get-help

[spiral maple]

How do you Read?

[native pivot]

Dang

looks like it was because of the abs bars

Thank you @spiral maple for the assistance

.close

[obtuse pebble]

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[craggy cairn]

help

[craggy cairn]

So basically we have for

arccos(√((1+cosx)÷2)) where x⋳ R

they at first asked to simplify it which I did

then obtained

either

arccos(cos(x/2))

or arccos(-cos(x/2))=arccos(cos(pi+x/2))

but then the x is in R so how to proceed?

[timid silo]

help, what does all of this mean?

I am new to all this stuff

[craggy cairn]

<@&286206848099549185>

<@&286206848099549185> ????

[obtuse pebble]

@craggy cairn Has your question been resolved?

[craggy cairn]

no

<@&286206848099549185>

[civic zealot]

well, arccos(cos(x)) = x when 0<x<pi

[craggy cairn]

yeah but

then

sould i find the solution of that equation?

0<x/2<pi???

and also we have the case of 0<x/2 + pi <pi

???

how do i Proceed

[civic zealot]

isn't cos(pi+x) = -cos(x)?

[craggy cairn]

yes

[craggy cairn]

<@&286206848099549185>

[short spruce]

are you daft

[craggy cairn]

yes

[craggy cairn]

<@&286206848099549185>

[obtuse pebble]

@craggy cairn Has your question been resolved?

[craggy cairn]

well gonna re-ask later c yall and yes I am dumb tnx

.close

[obtuse pebble]

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[timid silo]

hi friends! currently creating a notepad that you can draw in, ran into an issue where if you draw fast the pixels will start spacing out n stuff

in hopes of solving it, i researched it and found the viable solution is to create a line between the points, though i don't know how

i currently have the distance, midpoint, opposite line, rotation values as well as the coordinates for the last and current pixel though i've no clue what the formula is to create a line

can someone please hand me the formula to create a line from these factors? results are inconclusive online :c

[timid silo]

values are generated from this image if that helps

?

<@&286206848099549185>

Interesting

[timid silo]

Which values are you talking about?

[timid silo]

distance, midpoint, opposite line, rotation values

[timid silo]

I think u can just draw a line connecting the gap between the two points?

or will that lack performance

[timid silo]

i was trying to figure out the formula for that 😭

to generate a line of those values (distance, midpoint, opposite line, rotation)

[timid silo]

Umm well

Let's say $c_1$ and $c_2$

[warm shale]

CatHashira

[timid silo]

Are two points on the x, y grid

Ok?

Mhm

Now let's say the x component of $c_1$ is $x_1$ and for $c_2$ is $x_2$ in the same way y components are $y_1$ and $y_2$

[warm shale]

CatHashira

[timid silo]

Then the slope of the line connecting the two points, can you find it?

yes

(x_2-x_1)/(y_2/y_1)

Did u made a typo?

i've no clue how to use the bot

😭

Umm ur wrong

What is the change in y axis

Between the two points

oh oops

yeah typo LOL

i meant -

$(x_2-x_1)/(y_2-y_1)$

[warm shale]

calamixy

[timid silo]

No

? you asked for slope

$\frac {y_2-y_1}{x_2-x_1}$

[warm shale]

CatHashira

[timid silo]

U made a small mistake ig

oopsies

Anyways can you find the intercept now

Btw there are even better ways of solving this but I am showing the simplest now

$\frac b = {y}{mx}

$\frac b = {y}{mx}$

[warm shale]

calamixy

[timid silo]

that's not rigth

LOL

b = y/-(mx)

Dw u can right normally

[timid silo]

Eh I asked the intercept

y=mx+b describes the line, b is the intercept?

confused

Hmm I think it's getting hard to tell how to do this on plain text

Do you know how to draw a tangent to a function?

unfortunately no

Hmm

ok let's see $f(x) = mx+c$

[warm shale]

CatHashira

[timid silo]

We have computed for m

But we don't know about c

What if I edit this formula

$f(x) = m(x-x_1) + c$

[warm shale]

CatHashira

[timid silo]

Can you now find intercept

c is the intercept?

Yup

think of what

$x-x_1$

[warm shale]

CatHashira

[timid silo]

Does when x=x_1

$y-x+x_1/m = c$

[warm shale]

calamixy

[timid silo]

wait wait

$y-(x+x_1)/m = c$

[warm shale]

calamixy

[timid silo]

x-x_1 is shifting each x value by a factor x_1 left wards

I doubt if this will require u any algebra

If you can imagine what is happening inside the graph

same follows for y?

y-y_1

Probably no

It is shifting $c_1$ to 0 on x axis and the y coordinate of $c_1$ is $y_1$

Thus ur intercept is $y_1$ get it

[warm shale]

CatHashira

CatHashira

[timid silo]

Ye now it's structured

ah yeah

Is it clear?

yes thank you

c.close

The best possible solution to this will be even harder

Wait don't close

ah alr

Do you know calculus?

nah :c

Ah then I think this is the only way

👍

thank you so much

.close

[obtuse pebble]

Channel closed

Closed by @severe garnet

Use .reopen if this was a mistake.

[obtuse pebble]

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• 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.

[grave kestrel]

In this question they're using the formula pi r^2 divided by 2. I am confused that for what that formula is used. What are they finding by using the formula

[tardy epoch]

surface area of a cylinder

[forest sinew]

warning im p sure this books last formula was incorrect

if someone is answerin

so not a good track record

[tardy epoch]

what the heck is upper

[short spruce]

i think it used the wrong formula for surface area of the semisphere