help-13

[frail iris]

huh?

so the base function that graphs the line is f(x)

[spice kraken]

yes

[frail iris]

we evaluated

$\int{0}^3f(x)dx=3+4+(-9)

[spice kraken]

$\int_{0}^3f(x)dx = \int_{0}^3F'(x)dx \ = F(x) |_{0}^3 =F(3)-F(0)$

[frail iris]

ok

[wraith dagger]

_wherewolf_

[frail iris]

so I need to find F(3) somehow?

[spice kraken]

what did we calculate in a

part

[frail iris]

we know F(0)=7

[frail iris]

oh shoot

since we evaluated from 0 to 3 there, it is F(3)

[spice kraken]

we know the whole thing equal -2 from part a

so F(3)-F(0) = -2

[frail iris]

this @spice kraken ?

[spice kraken]

easy right

the integral is not needed

[frail iris]

ok

so what about for this one?

wouldnt the area be 0

because it is an even function above and below the x axis?

[spice kraken]

the whole area from 0 to 2 is 0

[frail iris]

yes

so

now

F(1)-F(0)=0

F(1)-3=0

F(1)=3

?

[spice kraken]

how do it = 0

[frail iris]

it says it

[spice kraken]

?

[frail iris]

Up top

It says F(0)=3

[spice kraken]

I'm asking why F(1)-F(0)=0

[frail iris]

huh?

oh

wait

F(2)-F(1)=0

[spice kraken]

still no

[frail iris]

wait

[spice kraken]

remember that $\int_{a}^bF'(x)dx=F(b)-F(a)$

[frail iris]

its from 0 to 2

[wraith dagger]

_wherewolf_

[frail iris]

F(2)-F(0)=0

0-F(0)=0

F(0)=0?

wait

I am dumb

F(2)-3=0

F(2)=3

but how do I find F(1) now?

[spice kraken]

good job but no one asked for F(2) lol

[frail iris]

B does

lol

[spice kraken]

oh

ok

what about F(1)-F(0)

[frail iris]

I thought we couldnt do that?

F(1)-3=0?

F(1)=3

[spice kraken]

it's not equal to 0

what is it equal to

[frail iris]

wdym?

I am so confused

[spice kraken]

$F(1)-F(0)=\int_{0}^1F'(x)dx=\int_{0}^1f(x)dx$

[wraith dagger]

_wherewolf_

[spice kraken]

which is area from 0 to 1 of f(x)

find the area

[frail iris]

-1?

[spice kraken]

yep

[frail iris]

bc its just (-2*1)/2

ok

so

F(1)-3=-1

F(1)=2

[spice kraken]

correct

[spice kraken]

don't forget the dx

and write the right side as an integral too

[frail iris]

oh right

[frail iris]

?

[spice kraken]

$\int_{0}^2f(x)dx$

[wraith dagger]

_wherewolf_

[spice kraken]

also it should be f(x) not f(1)

[spice kraken]

that's no what I meant..

[frail iris]

im sorry

I am exhausted

cant think straight and just need to get this done

logical thinking is not my strong suit tn

What do you mean

I am very lost

and still have to do C and D

[spice kraken]

main takeaway: $\int_{a}^bf(x)dx$ means the area of f(x) from x=a to x=b

[wraith dagger]

_wherewolf_

[spice kraken]

and $\int_{a}^bF'(x)dx=F(b)-F(a)$

[wraith dagger]

_wherewolf_

[spice kraken]

that's the things you need to learn from the question

[frail iris]

ok

but I am still trying to figure out how you wanted me to structure my answer

[spice kraken]

so $\int_{0}^1f(x)dx=-1 \ F(1)-F(0)=-1$ and so on

[wraith dagger]

_wherewolf_

[spice kraken]

in this structure

[frail iris]

ok

now how would I answer these 2?

F(x) is just referring to area right?

[spice kraken]

and the third takeaway for questions c and d: F(x) is increasing if F'(x)>0 and decreasing if F'(x)<0

[frail iris]

So the area is increasing from 0 to 1

[spice kraken]

that's because F'(x) means the rate of change of F(x)

[frail iris]

and decreasing from 1 to 2

or

[spice kraken]

wdym by area is increasing

[frail iris]

well

isnt that whats its asking

I am so lost man

I just need to finish these 2

[spice kraken]

F(x) is increasing if F'(x)>0 and decreasing if F'(x)<0

where is F'(x)=f(x) > 0

and f(x)<0

[frail iris]

so

it is increasing if f(x)<0

[spice kraken]

increasing if f(x)>0

and decreasing if f(x)<0

[frail iris]

so the increasing interval is (1,2)

and the decreasing is (0,1)

[spice kraken]

good job

that's it

[frail iris]

ok

shit

I missed a problem

so start by taking the deriv of xcos(x^2) right?

d/dx(x cos(x^2)) = cos(x^2) - 2 x^2 sin(x^2)

[spice kraken]

you don't need to calculate that

[frail iris]

huh

can I just plug sqrt(pi) in and solve?

and plug 0 in

and solve

then subtract them?

[spice kraken]

remember the first takeaway $\int_{0}^{\sqrt{\pi}}F'(x)dx=F(\sqrt{\pi})-F(0)$

[wraith dagger]

_wherewolf_

[frail iris]

yes

right

so I plug each value in

solve

then subtract

[spice kraken]

yes

yes

this is an important lessons to learn about derivatives and integrals so make sure you understand them

[frail iris]

that seem good?

[cedar kiln]

@frail iris Has your question been resolved?

[cedar kiln]

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[astral gazelle]

I’m stuck what I’m doing wrong here

[crimson sedge]

the picture of the question is really blurry for me, can you send another one?

nevermind i see it once i zoomed in

[ancient valley]

your y-intercept is wrong

[obsidian coral]

,rotate

[obsidian coral]

What Judgemental Snail said

[astral gazelle]

my y int is wrong?

[obsidian coral]

When you were using point slope formula, you're supposed to use one of the coordinate points, not use a mix of both

[astral gazelle]

ohhhhh

thank you thank you

i appreciate the help guys

.close

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[wet elbow]

#help-13 Hi, can anyone answer me if subjectivity refutes mathematics in any way? (Sorry for this stupid question of mine) but I need the answer

[wet elbow]

<@&286206848099549185>

[quartz frost]

i think i cant follow what you are asking

could you explain what you mean?

[crimson sedge]

it doesn't but if you're reffering to like 1/2 a dog youu either got the question wrong OR the question was formatter strangly

if that is what you mean/are talking abt

[wet elbow]

In some way, you can use subjectivity to refute mathematics, for example. Subjectivity is an individual phenomenon. If I have a different view of mathematics than you do.

For example, "I think math is flawed", does that somehow refute it?

[spice kraken]

subjectivity refutes everthing

if you ask if P is true, you can always subjectively argue P is flawed

[quartz frost]

i dont think so

since subjectivity is not objective, therefore not fundamentally true, it can't prove and therefore also not disprove something

[wet elbow]

Can you explain why?

[quartz frost]

i think

[spice kraken]

subjective view is more like personal opinion

[quartz frost]

i mean that is the fundamental idea behind math is it not?
to not make any subjective assumptions

so since there are no subjective assumptions, different subjective opinions don't matter

[wet elbow]

This is quite confusing. But a good answer

[cedar kiln]

@wet elbow Has your question been resolved?

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[hasty echo]

I'm stuck between the first and 2nd

My friend got 10

I got 190 and I can't choose now because I'm not sure if he did it right or I did

[vestal bear]

,w compute cos170

[wraith dagger]

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Requested by Arctic#1647

[vestal bear]

wheres another point this close to -1

[hasty echo]

So it's 190?

[vestal bear]

yes

[hasty echo]

Alright ty

[vestal bear]

,w compute cos10

[wraith dagger]

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[vestal bear]

,w compute cos190

[wraith dagger]

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[hasty echo]

Makes ok

Sense*

[vestal bear]

lol

[hasty echo]

.close

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[torn jolt]

i got sum of all numbers until -173 = 6808

is that all its asking me to find

and if so can someone check if im correct? thankms

[fallen moat]

im thinking the sum should be negative

[torn jolt]

oh

i messed up

-80956

[dreamy sleet]

yes, because you can factor out tan 60

[cedar kiln]

@torn jolt Has your question been resolved?

[torn jolt]

so i got sim of all terms is -2323

[dreamy sleet]

How did you get that

[torn jolt]

,rotate

[torn jolt]

do i just take this result and multiply by tan 60

[dreamy sleet]

Looks right

[torn jolt]

ok ty

.close

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[limber snow]

Let f: [0, 2] -> [5, 6]

where one of the values from codomain is mapped to two diff elements from domain

Can this still be surjective?

[limber snow]

I couldnt find anything in my book related to this

so lets say 5 maps back to 1 and 2 and 6 maps to 0

its still surjective right

[tropic oxide]

did you get that backwards?

also why so much spacing

anyway like

as far as i understand your question is this:

Let f: [0, 2] -> [5, 6] be a function satisfying f(1)=f(2)=5 and f(0) = 6. Is it possible for f to be surjective in this circumstance?

confirm or deny that my understanding of your question is correct

@limber snow

[cedar kiln]

@limber snow Has your question been resolved?

[tropic oxide]

[cedar kiln]

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[azure marsh]

can someone send working for this

[azure marsh]

Part B especially

(simple way if possible pls)

[obsidian coral]

We're not here to do your work for you

[azure marsh]

no as in

idk how to

i found two equations

but what do i do from there

[cedar kiln]

Show your work, and if possible, explain where you are stuck.

[azure marsh]

Equation one: 1/4 = A(1-e^-5k)

Equation two: V= A(1-e^-10k)

they want us to find how much is filled btween these 5 min

what do i do next?

[cedar kiln]

@azure marsh Has your question been resolved?

[azure marsh]

<@&286206848099549185>

[cedar kiln]

@azure marsh Has your question been resolved?

[dreamy sleet]

you can subtract the volumes before and after the 5 min

[crimson sedge]

Ya I will

[dreamy sleet]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[dreamy sleet]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[crimson sedge]

Ok

[dreamy sleet]

can you delete your messages?

[crimson sedge]

@azure marsh solve other parts

[crimson sedge]

I solved only one

[cedar kiln]

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[celest heath]

is this correct?

[crimson sedge]

,w 15 choose 6

[wraith dagger]

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[crimson sedge]

yep seems right

[livid hound]

what's the method of selection?

does order matter?

[celest heath]

but is it permutations or combinations?

[crimson sedge]

well i had assumed it would be choosing them since ordering 6 members doesn't sound realistic

[celest heath]

yea

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[celest heath]

is this correct?

[fair geyser]

of course

[celest heath]

its good?

[thin roost]

,w 2^13

[wraith dagger]

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[thin roost]

Yes

[celest heath]

thanks

[celest heath]

this correct as well?

[thin roost]

What is a(n)

[celest heath]

a or an 4 answer multiple choice test

[thin roost]

Ye then

[celest heath]

its correct?

[thin roost]

Correct...

Yes

[celest heath]

thank you

.close

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[solid dragon]

Rectangle ABCD has AB = 10sqrt(2) and AD = 10. Point M is chosen on side AB so that angle AMD = angle CMD. Find angle AMD

[solid dragon]

i wasn't able to make any progress

😭

i genuinely have no idea how to solve it

[tropic oxide]

have you made a diagram

[solid dragon]

yes

[tropic oxide]

show the diagram

[solid dragon]

it's a very horrible diagram

[tropic oxide]

probably better than no diagram at all.

[tropic oxide]

,rccw

[tropic oxide]

better than i was bracing myself for

may wanna mark the two equal angles tho

also your $10 \sqrt{2}$ looks too much like $\sqrt[10]{2}$ --- you understand those arent the same thing, right?

[wraith dagger]

Ann

[solid dragon]

yeah

i understand the diff

this question needs us to extend the diagram?

[tropic oxide]

may wanna mark the two equal angles tho

dunno about 'extending' anything yet

[solid dragon]

do you want me to send the diagram again with the angles marked?

[tropic oxide]

if you wnt

want*

im thinking of reflecting point A across line MD

that might lead to sth interesting

not sure

[solid dragon]

like extend line MC?

[tropic oxide]

dunno, if you think itll help then sure

brb

[sinful ocean]

Can you use trigonametry?

[solid dragon]

i don't think so

because no angles were given

or at least my trig is not good enough to calculate it

[sinful ocean]

But you alliwed to use?

[solid dragon]

yeah

[sinful ocean]

Ok then i can help

Let angel AMD=x

What is angle ADM

[solid dragon]

there were no angles given

[sinful ocean]

Yes but in terms of x

[solid dragon]

uh

i think 90-x

[sinful ocean]

Yes

[solid dragon]

assuming angle amd is x

[sinful ocean]

Yes correct

Now what is angle CDM

[solid dragon]

90-(90-x) which is x?

[sinful ocean]

Yes

And Angle CMD is also x by definition

What kind of trinagle CDM is?

[solid dragon]

isoceles?

[sinful ocean]

Yes

Can you continue?

[solid dragon]

uh

nothing

[sinful ocean]

What is the length of DC?

[solid dragon]

10sqrt(2)

[sinful ocean]

And MC

[solid dragon]

whats Anf

i can't calculate

[sinful ocean]

CDM is isoceles

[solid dragon]

OH

it's 10sqrt(2)

[sinful ocean]

Yep

What is CD?

[solid dragon]

also 10sqrt(2)?

[sinful ocean]

No

Ohh sorrs

BC i wanted to ask

[solid dragon]

10

[sinful ocean]

Yes

[solid dragon]

pythagoras' theorem?

[sinful ocean]

Yep

You can find BM

[solid dragon]

Bm is sqrt(100)

[sinful ocean]

Wich is..

[solid dragon]

so M is in the

M is the midpoint

is it?

[sinful ocean]

Can you repost the image it takes a lot time to scroll up

[solid dragon]

.

ok wait

theoretically M is the midpoint unless im wrong

[sinful ocean]

,rccw

[solid dragon]

is it 60

[sinful ocean]

M is not a midpoint

[solid dragon]

BM is sqrt(100) and AB is sqrt(200)

oh wait nvm

[sinful ocean]

BM=10

Sqrt 200 not 20

But we can find AM

Because we know AB and BM

[solid dragon]

10(sqrt(2) - sqrt(1))

or is there a better way to simplify

[sinful ocean]

Its good

Now you can find tangent of AMD

[solid dragon]

tan AMD = 10/10(sqrt(2) - sqrt(1))?

my trig is weak

[sinful ocean]

Yes

And you can put it in a calculator to find arctangent

Wich is the angle

[solid dragon]

wait how do I do reverse of tan

[sinful ocean]

Use calculator

[solid dragon]

tan AMD is 2.4142...

how do I reverse tan now???

[sinful ocean]

Youre doing it on an online calculator or on yours?

[solid dragon]

on mine

[sinful ocean]

The send a picture of your calculator

The button should look like this $tan^-1$

[wraith dagger]

Balint

[solid dragon]

oh i do have the button

67.5

[sinful ocean]

Yes

I got the same

[solid dragon]

ok tysm

[sinful ocean]

Np

[solid dragon]

.close

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[cedar kiln]

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[jade abyss]

\

[jade abyss]

so far

1/ sin + cos / sin

1/sin = csc

and ik that cos/sin = tan

but idk how to make that into cot

[south tundra]

You meant sin/cos = tan?

Because cos/sin is cot

[jade abyss]

yeah mb

[jade abyss]

how ?

[south tundra]

It's defined to be

[jade abyss]

its one of th elaws

right

[south tundra]

Right

[jade abyss]

ok thanks

.close

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[crimson sedge]

is this correct?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

.close

[cedar kiln]

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[compact storm]

Its a bit general but how do you work out rate of change of a liquid through a cone?

[solemn torrent]

You workin on related rates?

water pouring into the cone?

[compact storm]

Yee

[solemn torrent]

what's the exact q

[compact storm]

I saw an example where they differentiated it but some numbers would disappear and I got confused

[solemn torrent]

are we workin on volume?

[solemn torrent]

show

[compact storm]

We have a conical vessel with a maximum diameter of 5 metres and a height of 10 metres. If the small end is downwards and liquid is pouring into the vessel at 1000 litres per second what is the rate of change of depth when the depth is 2 metres?

[unkempt depot]

dy/dx problem

[unkempt depot]

If you are familiar with implicit differentiation then you’ll be able to find a constraint as well as an equation to differentiate by solving for the variable dy/dx. Since the small end is pointed downwards, we know that the liquid is filling from the bottom at the small end to the top, so height of the liquid (V) is increasing as does the area (pir^2) and diameter. I forgot to mention that you may also have to use V=1/3pir^2 as well.

[compact storm]

In this dx would be dtime?

[unkempt depot]

dV/dt = 1000 liter/s

you want to find dh/dt when h= 2m

[buoyant latch]

^^

that's the stuff you want to write down

the goal is to find dh/dt at h = 2

[unkempt depot]

Apologies for earlier wrong variables

[buoyant latch]

you absolutely will need to use V = 1/3 pi r^2 btw

because if you dont know the shape of the vessel

there would be no way to know what's happening

you can handwave some things and go we need dh/dt, and we have dV/dt

so we just need to find dh/dV

so we have dh/dt = dV/dt * dh/dV

[compact storm]

Ah I understand

Thanks you two

[bitter narwhal]

can this server help with 8th grade maths

[cedar kiln]

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[pure summit]

How do I do these limits?

[cedar kiln]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[pure summit]

1

[cedar kiln]

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[crimson sedge]

Help please

[cedar cypress]

!status

[cedar kiln]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[crimson sedge]

1

[cedar cypress]

What do you know about the sides of this triangle?

One relation provided in the question is AB=BD.
Can you find relations between BD and AD and/or AD and AB

Try using the info that D is the centre of the circle

[pure summit]

.reopen

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

so its an iscoscles right triangle, correct?

[cedar cypress]

Why do you think so

[crimson sedge]

not a right triangle

i meant triangle

sorry

[cedar cypress]

It being iscoscles was already known to us

D is the centre

[crimson sedge]

so if angle a is x degrees then angle d is also x degrees

[cedar cypress]

What does that tell you about DB and DA

[crimson sedge]

both radii

[cedar cypress]

Yes, and that means ?

[crimson sedge]

they are equal to the diamteter

[cedar cypress]

? Why do you think the radius is equal to the diameter now

[crimson sedge]

im saying them combined

[cedar cypress]

Why are you combining them

[crimson sedge]

oh my mistake

[cedar cypress]

They're both radii so they're equal

[crimson sedge]

yes

OHH

that

means

its

really

an

equilateral

so is x 60

[cedar cypress]

Yes

[crimson sedge]

wow i see

thank you friend

i appreciate it

.close

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[zenith igloo]

how do i solve the top question and the 95% interval

[zenith igloo]

<@&286206848099549185>

[cedar kiln]

@zenith igloo Has your question been resolved?

[wide lintel]

For the first one, you are testing if the sample means are equal

For the second one, I only know how to do it on calculator. There’s a setting to construct a “T~interval”

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[dusk monolith]

<@&286206848099549185> This is Statistics based. Help me out the best you can please!

[cedar kiln]

@dusk monolith Has your question been resolved?

[dusk monolith]

<@&286206848099549185>

[cedar kiln]

@dusk monolith Has your question been resolved?

[upbeat forge]

Use table to find x for which disttibution equals to 98%

I will show you now

then compute deviation of mean value

last step is to use next

in total

Hope it will help

[upbeat forge]

do you have any further questions?

[cedar kiln]

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[crimson sedge]

How is this wrong?

[short blade]

why did your 1/12 turn into 1/2

[crimson sedge]

good question

i dont know

i fix

[crimson sedge]

it would be this then right?

-9.05

[short blade]

plug it in and see

[crimson sedge]

uhhhhhh is it right LOL ive been stuck on it if i get it wrong i need to do 2 problems instead of 1

[short blade]

plug it in and see

[crimson sedge]

ok

[short blade]

oh

i mean plug it into the equation

[crimson sedge]

ok thx

i got it right

[short blade]

not the answer box

ok

[crimson sedge]

thx

.close

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[shut wadi]

Hello

[shut wadi]

Why is it when switching from inequality form to slope intercept form that the inequality switches sometimes from greater to lesser or vice versa

[short blade]

did they multiply by a negative when switching from one to the other?

[shut wadi]

It switching like this

[sonic thistle]

because you divided by a negative number

[shut wadi]

Oh

So like

If it’s a positive number

It won’t switch

Like if the -4y was 4y

It would have not changed

[sonic thistle]

if the -4 was 4

you divided by -4

[shut wadi]

Yeah

[shut wadi]

So that’s why it switches

[sonic thistle]

yes

[shut wadi]

Ok

[sonic thistle]

same when you miltiply by a negative number

multiply

[shut wadi]

I’ll try it a few times then I’ll close if I’m doing good

Thank you

[sonic thistle]

np

[cedar kiln]

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[odd ice]

can someone help me through this

[cedar kiln]

Please don't occupy multiple help channels.

[dire geode]

did you draw a picture

[odd ice]

this is all i have so far

im struggling with the 3d shape

do i intergrate with respect to x or y?

@dire geode am i doing something wrong?

<@&286206848099549185> can anyone help me please

[earnest robin]

You first need to calculate where your two functions intersect

[odd ice]

at 1,1

[earnest robin]

ok now you integrate

[odd ice]

with respect to y?

[earnest robin]

First $$\int_{0}^{1} \sqrt{x} dx$$ and then $$\int_{1}^{2} 2-x dx$$

[wraith dagger]

homelama

[earnest robin]

i would do x

[odd ice]

alright thanks

im kinda confused about that

since its top-bot right

[earnest robin]

what do you mean?

[odd ice]

top function - bottom function

[earnest robin]

don't you simply first calculate the base?

[earnest robin]

Oh but i think it is easier to split it up or am i dumb?

[odd ice]

i dont quite understand

[earnest robin]

like this

and add it

[odd ice]

i get it now

2 seperate integrals

[earnest robin]

Yes

because both of them are really quick

[odd ice]

but for 0,1 wouldnt it be the function 2-x -(sqrtx)

[earnest robin]

No because you want the area between the x-axies and sqrt(x) and not between 2-x and sqrt(x)

[odd ice]

okay thank you

[earnest robin]

did you calculate it yet?

[odd ice]

1/2+2/3

[earnest robin]

yes

[odd ice]

thank you sm

[earnest robin]

you got the height also already?

[odd ice]

height?

[earnest robin]

don't they ask you to calculate the volume?

[odd ice]

ohhhhhhhh

how would i calculate the height

would it be *2

[earnest robin]

Oh i just realized that we had to comput some other intgrals

because you can cut it up into slices and each of them are squres

I am sorry i thought at the beginning we had to compute a cuboid

[odd ice]

im thinking i solve for

x

and integrate with respect to y

from 0,1

[earnest robin]

Now its the same just squared $$\int_{0}^{1} \left(\sqrt{x}\right)^2 dx$$ and then $$\int_{1}^{2} \left(2-x\right)^2 dx$$

[wraith dagger]

homelama

[earnest robin]

No we just forgot to incoperate the height, which is always the same as the distance from the x-axies

so its the same just squared

i am very sorry if this is now confusing

[odd ice]

let me try this

1/2+1/3?

[earnest robin]

wait

[earnest robin]

yes

should be correct

[odd ice]

thank you so much

[earnest robin]

np

[odd ice]

have a great day

[cedar kiln]

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[simple flare]

May I know to solve (e)(i)?

I got the answer but I don’t know how to solve using adj

Is it using det(A) times identity matrix?

.close

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[pallid silo]

Still having trouble with this question, I think the only way to solve this is with graphing the functions?

Anyway, any help is appreciated. thanks.

[cedar kiln]

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[pallid frigate]

help meeeeee

idk how to

[cedar kiln]

@pallid frigate Has your question been resolved?

[pallid frigate]

😥

oh wait its been 15 minutes

<@&286206848099549185>

[pallid frigate]

its been 40 minutes 💀

[lucid cloud]

what's a right prism

[pallid frigate]

💀

like a pyramid

[lucid cloud]

a pyramid is not a prism

or does it mean a prism with a right triangle as base?

but anyway

it does not matter

do a ratio between the areas of the prisms

take the sqrt of the ratio

cube the ratio

[pallid frigate]

yea but thats the hard part

[lucid cloud]

then use it for the big one

wdym

[pallid frigate]

try it

[lucid cloud]

lets do big/small

Abig : Asmall = 25:9

length_big : length_small = 5:3

volume_big : volume_small = 125/27

Vbig = Vsmall • 125/27

no?

375 units^3

[pallid frigate]

what

375 is the asnwer?

[pallid frigate]

no cause u get big decimals

[lucid cloud]

yeah

[lucid cloud]

?

[pallid frigate]

i got 315.3361557...

[lucid cloud]

how?

[pallid frigate]

18sqrt36qrt2/50sqrt100sqrt2=81/x

??

yello?

sadge

[lucid cloud]

huh?

why you taking those sqrts?

[pallid frigate]

cause the square root of the thing cubed is the volume thingie

[lucid cloud]

so this is not how you solved it?

then where did you do something different

[lucid cloud]

no, it's the cube of the sqrt ratio

[cedar kiln]

@pallid frigate Has your question been resolved?

[cedar kiln]

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[crimson sedge]

\

[crimson sedge]

help please

[hearty arch]

what have you tried so far

[crimson sedge]

@hearty arch my progress

i notice they are similar

wait

is it 20?

[hearty arch]

let me calculate, but probably

[crimson sedge]

k

[hearty arch]

yes!

sorry google tried correcting my asin to sin

nice job!

you didnt even need me lol

[crimson sedge]

thanks bro

i appreciate it

.close

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[cursive path]

This is a triangle, how do I show that y = 12 - 0.75x

[cursive path]

That is a rectangle inside

Is it something to do with triangle similarity?

[vestal bear]

I'd try to use pythag to find the total hypotenuse then individual hypotenuses and add them up then equate them to each other

that might make something complex though

oh wait

these triangles are isosceles

[cursive path]

How do we know they are isosceles

[vestal bear]

look at the top right edge of the rectangle

we gave a 90 degree angle

[hearty arch]

it doesnt matter if they're isoceles as long as they're right triangles

[vestal bear]

a 180 degree angles from the flatline

[hearty arch]

this

[vestal bear]

which means the angle has to be 45

[cursive path]

But it can always be something other than 45

[vestal bear]

making them isosceles right triangles and their legs ewual

[cursive path]

maybe 60-45-30

[vestal bear]

oh wait they looked diagonal mb

yeah I'd just do my first method

[cursive path]

Pythagoras the equations are too complex lol

i Get a squareroot( x and y terms) + squareroot (x and y terms) = squareroot(400)

I have to show y =12-0.75x

I think it should be a simple solution but cant see it

Can we employ similar triangles for both triangles?

Oh wait we can

Thanks similar triangles work

[hearty arch]

yea they're similar. that is easier

[cursive path]

(12-y)/x = y/(16-x)

👍

.close

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[pallid silo]

Hello, I am having trouble with this cubic polynomial question, I'm not sure how I am supposed to solve this if I can't find it via systematic guessing

[cedar kiln]

@pallid silo Has your question been resolved?

[slate lintel]

with difficulty, there's a lot of theory behind this and almost none of it is taught in schools

there should be a rational root available here

[pallid silo]

This is a grade 12 math course

like highschool, so idk.. I don't know any algorithms to solve the roots from a cubic function if it isn't an integer

I'm pretty sure they just want us to graph it?

usually i would do "systematic guessing" to get the first root then do polynomial division and then it would be good. but that didn't work here

[slate lintel]

you tried all the factors of 735?

[pallid silo]

dont think so, what do you have in mind?

well, is what i have there correct so far?

also the other thing that doesn't make sense is "between" 300 and 900. is that <= or just < ? Kind of a open question tbh

[slate lintel]

that depends on the rest of your question

[slate lintel]

look up the rational root theorem

[pallid silo]

Is that a higher level math course? this is highschool stuf. only learnt about the factor and remainder theorems.

[slate lintel]

it says that any rational root of a polynomial is in the form a/b where a is a factor of the constant term and b is a factor of the highest power

i learned it in algebra 2 i think

[pallid silo]

interesting 🤔

[slate lintel]

so like in your case for $x^3 + 19x^2 + 103x - 735$ any rational root will be $\pm$ a factor of $735$

[wraith dagger]

Hayley

[pallid silo]

alright, well thanks alot i appreciate your help.

I've got somewhere to look.

have a good night/ day 🙂

[slate lintel]

ty!

[pallid silo]

.close

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[pallid dagger]

can i use {lim (x->0) sin(x)/x =1} 2 times in 1 equation? like the photo, or i should solve using l’hopital rule

[dense hornet]

yes, that is fine.

or you could also view it as 2*(sin(1/2u)/[1/2u])^2 and then bring the limit inside the square, this is because x^2 is continuous near infty

[pallid dagger]

thx

.close

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[crimson sedge]

Suppose $X$ and $Y$ are random variables. A sample of size $n_X=20$ for $X$ and a sample of size $n_Y=25$ for $Y$ are recorded. The parameters are given below.
$$\bar{X} = 100$$
$$s_X = 2.5$$
$$\bar{Y} = 105$$
$$s_Y = 4.9$$
Supposing these samples are unpaired and not normal, how would one do a t test comparison at a 5% confidence interval?

[wraith dagger]

brotherimusttalk1234

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

.close

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[buoyant crow]

can someone help me with question 11 b

[buoyant crow]

i know the answer for b but i’m not sure how to use the a part’s answer to get it

[vestal bear]

,w differentiate 2x^(3)*lnx

[wraith dagger]

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Requested by Arctic#1647

[vestal bear]

maybe its just a continuation

since 6x^2lnx is solved the same way as x^2lnx

and integration of 2x^2 is straightforward

[buoyant crow]

i’ve done the first part of the question but im not sure how to use the answer for the b part

[vestal bear]

.

i dont think you have to

[buoyant crow]

what do you suggest i do?

in the previous questions u’re sort of supposed to integrate the answer of the first part

by substitution in some cases

[vestal bear]

oh i guess you can just say that int(x^2lnx) =2x^3lnx

and go from there

or uh

[vestal bear]

get the part of this that is x^2lnx?

idk I would just integrate what you have

[buoyant crow]

yea alright, thanks i think i sort of have an idea

[vestal bear]

or even just say 2x^3lnx=int(2x^2(3ln(x)+1))

ooo yeah thats how

[buoyant crow]

i’m new to integration, why do exactly add a one?

[vestal bear]

^

its just the derivative of 11a

or

your answer

[buoyant crow]

ohhhh

i got it

thanks

[vestal bear]

,w integrate x^2lnx

[wraith dagger]

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Requested by Arctic#1647

[buoyant crow]

yea that’s the one

i got it too

[cedar kiln]

@buoyant crow Has your question been resolved?

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[cedar kiln]

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[spice kraken]

What rule do the sequence follow?

[vagrant elbow]

Check the difference between two successive terms

You'll notice a pattern

[spice kraken]

We have $a_{n+1}=a_n-(\frac{243}{3^{n-1}})$

[wraith dagger]

WhereWolf

[spice kraken]

And a_1 = 364

So $a_n=364-\sum_{i=1}^n\frac{243}{3^{i-1}}$

[wraith dagger]

WhereWolf

[spice kraken]

Then you just calculate the sum

Easy one

[cedar kiln]

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[errant phoenix]

I looked at it

[errant phoenix]

And I found out that I could say 0 and +/- 2 works

But I don’t know what other solutions there are

And how to throughly explain that in logic

[gritty galleon]

You have to consider the cases when x<0, x>0, x=0 (perhaps even x=1 and x=-1)

that will give you all possible values of x

[cedar kiln]

@errant phoenix Has your question been resolved?

[errant phoenix]

But I don’t think I can just go infinitely

What I think I need is the logic that will help me to determine the x values

Like I can’t just plug in all values to find solutions

[long arrow]

you don't have to plug all values

it doesn't work that way

we consider following cases:
x - 1 = 0 --> x = 1
x + 1 = 0 --> x = -1
and hence we examine:

1. x < -1
2. -1 <= x < 1
3. x >= 1

[errant phoenix]

Actually

The only possible answers are probably just 0 2 and -2

[long arrow]

for the 1):
-(x-1) + (x+1) + x = 0
-x + 1 + x + 1 + x = 0
x + 2 = 0
x = -2 < -1 --> we have a solution

etc.

it's simpler than you think

just three linear equations

[errant phoenix]

Well its |x-1|

[long arrow]

what's |x-1| when x < -1 ?

according to the definition of absolute value

[errant phoenix]

3+

[long arrow]

what?

[errant phoenix]

The value is

At least 3

[long arrow]

I mean this

[errant phoenix]

In this case

[long arrow]

are you familiar with this?

[errant phoenix]

Not rly

[long arrow]

okay, so look at this

we have |x-1|

and we assumed x < -1

for example let's take x = -1000

(obviously -1000 < -1)

now we plug it into |x-1| and we get |-1000 - 1|

and hence

[errant phoenix]

1001 would be the answer

[long arrow]

|-1000 - 1| = |-1001| = 1001

yes

and you can see that sign changes

[errant phoenix]

And now that i think about it

[long arrow]

and that logic works for every x < -1

and hence we have |x-1| = -(x-1)

[errant phoenix]

Bc of |x+1|-|x-1|+x=0

[long arrow]

in other words absolute value puts "-" sign before the result if the inside is negative

[errant phoenix]

The diff between the two values must be 2

Therefore it can only be plus or minus 2 and 0

Yes

Now i got it

I think

Ty

.close

[cedar kiln]

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[wild spear]

if $p\mid a^q+1$ and $q\mid a^p+1$ for $p,q$ odd primes and a natural number $a$, prove that $p\mid a+1$ or $q\mid a+1$.

[wraith dagger]

nicholas

[wild spear]

it's trivial for p = q, but how do i solve it if p =/ q?

[cedar kiln]

@wild spear Has your question been resolved?

[cedar kiln]

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[elfin otter]

What I got so far:\
i) $$ y = 1000 + 5x $$
ii) $$ y = ( 1000 + 5x ) + 40x $$

[wraith dagger]

Kai

[ancient valley]

i think your second equation is wrong. you confused profit with revenue. the revenue is the total amount of income generated by the sale of the tickets before deducting costs.

[elfin otter]

i) $$ y = 1000 + 5x $$
ii) $$ y = ( 1000 + 5x ) + 40p $$

Liek this?

[ancient valley]

1000+5x is the cost of hiring the coach for the event. we should be deducting the cost if were looking for profit. but were looking for revenue

also use a different variable for ticket cost

[wraith dagger]

Kai

[tropic oxide]

notation could be a lot better there

for one you need to define your variables clearly

[elfin otter]

x = per km
p = tickets sold

[tropic oxide]

x = per km

bad

x is the distance travelled with the coach, in kilometers

and p is the number of tickets sold

and even still you need to distinguish between cost and revenue, which you currently do not in your variables -- they're both y

[elfin otter]

Ah

Hold on

i)

Cost
\
k = distance travelled with the coach, in kilometers

$$ C = 1000 + 5k $$
ii)

Revenue
\
p = tickets sold
$$ R = 40p $$

[tropic oxide]

ok, that'll do

er

except that revenue is just 40p

the 1000+5k is a cost, not a revenue...

it's money you spend, not money you gain.

[wraith dagger]

Kai

[ancient valley]

yep looks good now 👍