help-13

[crimson sedge]

?

[fallen heath]

for what values of a are they integers

[crimson sedge]

why divide by 4 and 2

[fallen heath]

._.

._.

[crimson sedge]

oh yeah

oke

[fallen heath]

Now, your terms are $$a, \frac{a}{4}, -\frac{a}{2}$$

[fallen heath]

AND THEY NEED TO BE INTEGERS

[crimson sedge]

its

wait

why

does it need to be integers

@fallen heath

hm?

[fallen heath]

READ

THE

QUESTION

LET a, b, c be three integers

a, b, c are integers by definition

they were integers since the day they were born

it's us who redefined them for our measly purposes

and according to our convenience

[crimson sedge]

oh ok

ye

[fallen heath]

so

THE QUESTION IS

for what values of a

are these terms $$a, \frac{a}{4}, -\frac{a}{2}$$

[fallen heath]

INTEGERS?

[crimson sedge]

2 or 4

wait no

its 4

[fallen heath]

._.

not for 8?

16?

24?

32?

64?

[crimson sedge]

its smallest tho

[fallen heath]

[crimson sedge]

?

YES DID I GET IT

[fallen heath]

for a = 4, c = -2 but a < b < c

[crimson sedge]

[fallen heath]

so you're

[crimson sedge]

oh wait

damit

[crimson sedge]

this is for GP or AP

[fallen heath]

THIS IS FOR BOTH

[crimson sedge]

wHAT

[fallen heath]

we accounted FOR BOTH conditions

[crimson sedge]

HOW

[fallen heath]

WE CONSTRUCTED a, c, b SUCH THAT THEY FOLLOW THE GP CONDITION

and then

plugged them in so that they follow the AP CONDITION

and finally

[crimson sedge]

HOW DID WE PLUG IT IN SO IT FOOLLOW THE AP CONDITION

?

I FORGET

[fallen heath]

.

[crimson sedge]

oh ok

everythings coming back now

[fallen heath]

defenestrates

so uhh

[crimson sedge]

HMMM

[fallen heath]

do we understand that

these terms $$a, \frac{a}{4}, -\frac{a}{2}$$

[fallen heath]

are in A.P., and the a, c, b combination is in G.P.?

[crimson sedge]

wait what

[fallen heath]

[crimson sedge]

how

when

[fallen heath]

._.

[crimson sedge]

wait nvm

uh

its the ahem like the a + b = c^2

right

[fallen heath]

a + c = 2b

and ab = c^2

[crimson sedge]

a + c = 2b

ye ok

and we plugged that in with the GP

yes

continue pls

[fallen heath]

Yes, so

again

do we understand that

these terms $$a, \frac{a}{4}, -\frac{a}{2}$$

[fallen heath]

are in A.P., and the a, c, b combination is in G.P.?

[crimson sedge]

ofc

👍

[fallen heath]

finally ._.

Now

[crimson sedge]

um

yes

[fallen heath]

for a/2 is integer whenever a/4 is integer

Yes?

[crimson sedge]

um

yes

[fallen heath]

so

you need to make a/4 an integer

so just plug

a = 4k for some integer k

and your terms are

$a, b, c \equiv 4k, k, -2k$

[crimson sedge]

and a<b<c

?

[fallen heath]

Yes

[crimson sedge]

is it 1

?

[fallen heath]

so k must be negative

Yes

k = -1 is the smallest number

[crimson sedge]

oh -1

[fallen heath]

for which these are integers

[crimson sedge]

I said 1

lol

[fallen heath]

and a < b < c

[crimson sedge]

just by guessing

[fallen heath]

SO

[crimson sedge]

lets do a summary pls

[fallen heath]

c = 2, b = -1, a = -4

[crimson sedge]

cause my brain is completely fried

wait is the answer not -1 cause I just put -1 as answer and submitted

[fallen heath]

lmfao

[crimson sedge]

[fallen heath]

of course not

k = -1

but a, b, c were

$a, b, c \equiv 4k, k, -2k$

[crimson sedge]

so its 2

??

[fallen heath]

are we doing a test Q?

[crimson sedge]

?

what

[fallen heath]

is it an exam?

+_+

[crimson sedge]

um

lets say

[fallen heath]

YES

omg

[crimson sedge]

what why

[fallen heath]

🏃

no?

[crimson sedge]

its a practice

question

👍

[fallen heath]

@ moderator, please check the mod log

[crimson sedge]

bruh

joke

joke

joke

.-.-.-.

[fallen heath]

XD

[crimson sedge]

ok

[fallen heath]

do yeah

[crimson sedge]

back to problem

[fallen heath]

c = 2 works

a = -4

b = -1

[crimson sedge]

but the GP

-4, 2, -1

nvm

lol

wew that problem was so hard I couldn't never got it by myself

@fallen heath can you help me summarize it

[fallen heath]

Summary

[crimson sedge]

so we have AP and GP

a, a + r, a + 2r

a, ar, ar^2

[fallen heath]

OKAY

[crimson sedge]

ok

[fallen heath]

NO

[crimson sedge]

what

[fallen heath]

WTF

YOU HAVE A AP

or A GP

[crimson sedge]

you do the talking and I do the assimilating

[fallen heath]

you pick terms accordingly

AND

plug into the conditions for another

Not create TWO SEPERATE LIST OF TERMS

AND TWO SEPERATE LIST OF VARIABLES

[crimson sedge]

how did we combine the 2 conditions into one thing again

?

[fallen heath]

a, b, c in A.P. => a, a + r, a + 2r is fine

but then you'd just have to plug this into the conditions for GP

a, c, b in G.P. means ab = c^2

so pick the terms(that you assigned for the A.P. condition) here

a(a+r) = (a+2r)^2

THAT'S IT

[crimson sedge]

a(a+r) = (a+2r)^2

I don't remember doing this

[fallen heath]

because in the previous solution, we picked our construction from G.P. condition

[crimson sedge]

we did this not that

[fallen heath]

We assigned a, c, b = a, ar, ar^2

but you're using the A.P. condition

so you've assigned, a, b, c = a, a+r, a+2r

[crimson sedge]

oh ok

so we used the GP condition not the AP condition which we are using AP condition in the sumary

[fallen heath]

dummary, yes

Also, as you can see

using the G.P. condition to construct the terms and then plugging to A.P. conditions work better than vice versa

both of which are way better off than using the two conditions separately and introducing a third variable

[crimson sedge]

alright I get it now

now summarization for the end

[fallen heath]

towards the end

we just solved the second condition

and derived the terms in terms of one parameter

then applied integer condition

[crimson sedge]

how we were suppose to know that it was -1 without just guessing

[fallen heath]

and replaced with another parameter

and then, we finally concluded that our terms must look like

$a, b, c \equiv 4k, k, -2k$

[fallen heath]

NOW

if -2k > k > 4k

then k Must be negative

so the biggest negative number of -1

or smallest value for -2k is 2

and we're done

[crimson sedge]

BOOM

💥

I DID IT

also

[fallen heath]

I did it

[crimson sedge]

this problem is super easy once you are organized

so I got this formula $$ 5 * 2^x $$

[wraith dagger]

痛苦

[crimson sedge]

where x is the generation thing

but idk how to model the sum of people from previous 11 generations in quantitative reasoning

@fallen heath any thoughts?

[fallen heath]

just sum all the generations

it's a geometric series

[crimson sedge]

what how

is my formula I pulled from my ass not any good

I'm confused it says siri has 5 siblings so thats 6 right

@fallen heath I'm comparing $$ 2^12 vs 6(12)^11 $$

[wraith dagger]

痛苦

[crimson sedge]

2^12 and 6(12)^11

[cedar kiln]

@crimson sedge Has your question been resolved?

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[median creek]

Are there any alternative terms for "dependencies" and "dependents" in a directed graph? I find that these terms are a little ambiguous. For example, take node A's dependents. Does that describe the nodes that depend on it or the nodes it depends on?

[cedar kiln]

@median creek Has your question been resolved?

[cedar kiln]

@median creek Has your question been resolved?

[cedar kiln]

@median creek Has your question been resolved?

[cedar kiln]

@median creek Has your question been resolved?

[cedar kiln]

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[rich sandal]

.close

[cedar kiln]

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[tawny ivy]

sup

[tawny ivy]

can antone help

[cedar kiln]

@tawny ivy Has your question been resolved?

[rigid ridge]

what have you tried?

[mint sable]

use the formula for area of sector and formula for arc length and try equating the two

[cedar kiln]

@tawny ivy Has your question been resolved?

[cedar kiln]

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[tawny ivy]

yo

[tawny ivy]

can i do
4/x = rx
and
27 = 1/2 (r^2) x
would that work?
and then we arrange them
right???

[trail jackal]

sounds fine to me

[tawny ivy]

k thanks

[cedar kiln]

@tawny ivy Has your question been resolved?

[cedar kiln]

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[chrome agate]

i have a formula but im not sure how to exactly do it

cause the formula is 2 pi and r

[dire geode]

2* pi *r = circumference

[chrome agate]

yeah

but what is exactly is the order of operations

[dire geode]

Plug in r

[chrome agate]

we have r already

31 1/2 yards

we're solving for circumference

[dire geode]

You only have multiplication. Do it in any order you want

[chrome agate]

oh alright

i was just confused because i know how to do diameter just not radius

thank you sm

.close

[cedar kiln]

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[steady imp]

That is a question yes

[spark idol]

cant seem to find a way to start with the solution

[steady imp]

Well it has to be a square first of all

What information does that give you

[spark idol]

that it has to be a square

[steady imp]

That’s true!

[spark idol]

u trolling?

[steady imp]

What is the formula for the area

[spark idol]

s^2

[steady imp]

Okay so then how long is each side if the area is 10

[spark idol]

yeah thought of that

but u have to use the grid given with each square being 1 cm^2

[fallen heath]

answer only what's asked

how long is each side if the area is 10

[spark idol]

√10

[steady imp]

Okay so then what’s the issue here

[fallen heath]

How to use the grid of squares with sides 1cm each, to construct √10cm

[spark idol]

u have to abide to the given squares so the sides have to be integers

√10 is 3.16

[livid hound]

consider pythagoras

[steady imp]

Maybe you can rotate the square?

[spark idol]

wdym

[steady imp]

So can you construct a triangle whose hypothenuse is sqrt 10

[spark idol]

the sides of the square should be traced on the grid

[steady imp]

Using integers

There’s one that’s pretty easy

[fallen heath]

where is it written?

[steady imp]

I’ll draw an example for you

[spark idol]

last sentence @fallen heath

[fallen heath]

Use the grid to construct the square with area 10cm²

No where is it written that you must trace the square on the grid

[steady imp]

That’s a rotation

[spark idol]

given from the teacher

ngl that makes it seem impossible

so im pretty confused

[livid hound]

consider pythagoras

[steady imp]

It’s not impossible

[fallen heath]

Are you allowed to use compass?

[spark idol]

nope

[livid hound]

would you be able to construct a (right) triangle with a hypotenuse of sqrt(10)

[spark idol]

lemme try

[fallen heath]

then throw the question down the trash ._.

no compass and you need to trace the square on the grid

it's not possible

[steady imp]

Dude you just need a straight edge

Which is like, the basic requirement for making any rectangle

[fallen heath]

how does a straight edge solve the problem? okay fine you draw 3² + 1 = 10, say... da heck do you do to translate it on the grid

[livid hound]

they seem to have misinterpreted that the square needs to be on the pre-existing horizontal and vertical lines, which it does not

[mint sable]

by trace, surely they mean a rough square

[spark idol]

i dont think so

[steady imp]

Okay dude I’ll draw it out for you

[fallen heath]

no need

[livid hound]

you can draw it anywhere within that grid as long as you can justify that the sides lengths are sqrt(10) without external measurements and that it's a square

[spark idol]

but I guess i can try to solve it with a rotated square and see if its correct tmrw

[fallen heath]

tell me, how do you plan on rotating this square, so that the sides coincide within the grid?

[steady imp]

There’s like no other way to solve it

[fallen heath]

EXACTLY

[steady imp]

Okay

[fallen heath]

If this is true,

[fallen heath]

and this is true

[steady imp]

I feel bad that we ruined this problem for you in a dick measuring contest @spark idol

[fallen heath]

then I suggest give up on the Q

[livid hound]

you most likely misunderstood them

[spark idol]

.

i'll try to solve it like u suggested

and check

[fallen heath]

very good :D there's more than 1 such squares in the grid

please find them all ^^"(as a bonus Q ofc)

[spark idol]

alright then thats all

I'll close now

.close

[cedar kiln]

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[tulip raptor]

help someone

[tulip raptor]

<@&286206848099549185>

[tulip raptor]

They are telling me to Find
Every possible Answer of A

[glad kestrel]

• After 15 minutes, feel free to ping @Helpers.

[south tundra]

So that the inequality is true for all x?

For that you'd need x^2 - 4x + a to have 1 or 0 roots

(because if it had 2 roots, it'd somewhere be negative)

So you just need the discriminant to be <= 0

[tulip raptor]

i cant understand

[south tundra]

Just say that 4^2 - 4a <= 0

[tulip raptor]

yea i get it but why discriminate is below 0

[south tundra]

Because if it was positive

Then the parabola would have 2 roots

Meaning that somewhere it goes below x axis

But we don't want that to happen

[tulip raptor]

How do you see how many roots does parabola have

[south tundra]

Because it depends on the discriminant

[tulip raptor]

but How do you know disceiminant when you dont kNow A

[south tundra]

You don't need to know a

[tulip raptor]

Then discriminant = 4a

OHH

i get it

[south tundra]

4^2 - 4a *

[tulip raptor]

IT IS POSITIVE YEA??

4a

thats why it have 2 roots

[south tundra]

Pretty much the opposite, discriminant should be <= 0

Again, if it was positive then it'd have 2 roots meaning somewhere it goes below x axis

So x^2 - 4x + a >= 0 wouldn't be true

[tulip raptor]

@south tundra What if X²-4x+a<=0

[south tundra]

That's impossible, because look

Coefficient of x^2 is 1

So the parabola goes upwards

So somewhere it'll be above x axis

[tulip raptor]

i get itt

Close

@south tundra

finnaly get it after 4 hour of work

[south tundra]

That's nice

Btw it's .close

[tulip raptor]

.close

[cedar kiln]

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[vapid cliff]

heyy can i ask, how can i explain number 8??

[rigid ridge]

see #help-14 message, do you have any questions about that?

[vapid cliff]

Can i say that the only modification done every second step is swapping the objects on the same line

I got confused at first! thanks againnn!

[rigid ridge]

well, you could say like

"alternating between mirroring across the vertical line and showing a new symbol"

[vapid cliff]

ohhh okayy that sounds better, thank you!!

.close

[cedar kiln]

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[steel ledge]

hi! I have another question about angles - i was given the alpha angle inside the grey triangle. I don't understand why we can claim that the angle between the y axis and the vector mg is also alpha ?

[cedar kiln]

@steel ledge Has your question been resolved?

[upper garnet]

okay

[cedar kiln]

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[upper garnet]

.reopen

[cedar kiln]

✅

[upper garnet]

$\Phi$

[wraith dagger]

The Fractalogist

[upper garnet]

is 90 as you can see

let's say alpha is 25

then u can find angle T

65

and as u can see phi is alpha + T

25+65=90

@steel ledge

[steel ledge]

yes i see

[upper garnet]

nife

nice

[steel ledge]

thank you !

[upper garnet]

.clise

[steel ledge]

.close

[cedar kiln]

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[astral dagger]

d/dx this ln(sin^2(x))
so I did d/dx(sin(^2(x))) / sin(^2(x))

[astral dagger]

why is this wrong?

i thought it was u' / u

[clear glen]

https://socratic.org/questions/how-do-you-differentiate-ln-sin-2-x this gives you the full derivation

[astral dagger]

we got the same answer i think

[upper abyss]

It's not wrong.

[astral dagger]

letsss go!!

[upper abyss]

It's not finished but it isn't wrong

[astral dagger]

would 2cos(x) / sin(x) be a fine answer?

[clear glen]

nope 1 more step

[astral dagger]

what

[clear glen]

remember sohcahtoa

[upper abyss]

Yeah that's right

[eternal comet]

cos(x) / sin(x) is a common trig function

[clear glen]

^

so cancel out the H in sohcahtoa and you get a trig function

[upper abyss]

Oh I mean you could write it as 2ctg(x) but ehh

[astral dagger]

never heard of it

but thanks

[eternal comet]

Ey, someone else who uses tg, not tan

[clear glen]

so sohcahtoa is a math acronym for sin(Opposite/Hyp)= theta

cos (adj/hyp)=theta

[astral dagger]

right?

[clear glen]

and tan(opp/adj)= theta

and any co function is just the reciprocal of that

[graceful karma]

You say it as ctg not cot?

[eternal comet]

In my country we do too

Not common I believe

[clear glen]

so when you do cos/sin

[upper abyss]

I normally just do cot, but I forgot kek

"Three letters for cotangent? Must be ctg"

[clear glen]

its (A/H)/(O/H) which the H's cancel to give A/O

[graceful karma]

[clear glen]

and we know Tan=O/A so cot=A/O

[upper abyss]

Why does that follow?

[clear glen]

or wait co functions are different than arc functions my bad definition wise

[graceful karma]

coCat

[clear glen]

need anything else @astral dagger ?

[astral dagger]

no im alllll good

thanks

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[dim gull]

hopefully it’s clear!!

All of them! Sorry it’s quite a lot

Alright!

not much to be honest

I’m so stuck on it

I’ve says had a problem with this part of maths

5 yes

mhm

10mm

15?

It’s okay:)

Wait does it add on each time

If that’s so would that be 8

Oh alright

Yep

20?

mm

35

omd

I’m so dumb

So there’s 27 blocks

Not there’s 5

Yep

Whatever you said is correct

25mm

50mm

I think we add them up

huh

20mm

We add that up?

70

5blocks

So 25

We add that 95mm

Which is*

135mm

Right okay

Now what?

Is there another step or

Oh okay

Next one?

I understand! It’s quite late for me so can I ask tomorrow?

Thanks for helping btw!

I have to go now!

I’m so sorry!

Bye bye good night!

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[limpid grail]

.

im learning integration by substitution and im a little confused

[limpid grail]

i've been told to differentiate u = and rearrange to make dx the subject

Then i've been told to substitute into the integral

But then it goes from -du to du without any explaination

just wondering what's going on here.

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[crisp trail]

how do i do number 23

[cedar kiln]

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<@&286206848099549185>

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[coarse smelt]

help please :(( i really need it and i would really appreciate if you help 😊

[dire geode]

• After 15 minutes, feel free to ping @Helpers.```

[coarse smelt]

sorry! i did not notice

[flint plinth]

There are ten questions here, which one do you need help with?

[coarse smelt]

4 to 7 , im already done with the rest

im having trouble with indirect proportion

<@&286206848099549185>

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[crimson sedge]

Im having a brain fart while studying physics

[crimson sedge]

Ok so

[hollow osprey]

Hello fellow gigachad

[crimson sedge]

Oh hi you again

anyway

Heres the problem?

[eternal comet]

same

[hollow osprey]

Yo it’s a physics major

[crimson sedge]

We got a car racing. It needs to finish 2.88km in 65s. If its speed in the first half is 60m/s then what is the speed needed to finish the second half?

I can take a pic but yall probs dont understand french

[granite ridge]

(ive learnt french)

[crimson sedge]

#14

[granite ridge]

well how long is the first half

[crimson sedge]

Distance is 2880m
Time is 65s
Initial speed is either 0 or 60m/s
Final speed is what we looking for
No acceleration

You dont get it

You know the whole course

2880m

Or 2.88km

[bright surge]

does "the first half" mean "the first 1.44km" or "the first 32.5s"?

[crimson sedge]

What

[granite ridge]

i imagine the former

[crimson sedge]

First half of the.. course?

Yeah course

Oh thats what i was missing

My dumbass cant read

Gimme a sec

[bright surge]

either way you know 2 of v, d, t

[crimson sedge]

Yeah.

Thing is

Is the inital speed 0m/s

Or 60m/s

We start a race at 0

Or wait this is a two step thing aint it

Wait i might have it

Starting with the first part of the coursd

I need to know how long it took to complete half the course

$v=D/t$

[wraith dagger]

Serious Metrapolis

[crimson sedge]

How do i make a division

[bright surge]

$v=\frac{D}{t}$

[wraith dagger]

ryc for mod⁴ (meg)

[crimson sedge]

Why is it so complicated

Anyway with that formula i got 24s for the first half

Now i just need to find the speed with the 24s substracted from 65 yeah?

[bright surge]

that's the time

[crimson sedge]

Yeah

I need the time to know the speed

It was a two time thing

[bright surge]

yep

[crimson sedge]

Thanks

Stupid headache gonna make me fail

Bah

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[visual raptor]

now i have successfully prooved this with a true false table but im trying to do it algebraically and seem a bit lost in the weeds. does anyone have an insight of where i should go from here?

[cedar kiln]

@visual raptor Has your question been resolved?

[cedar kiln]

@visual raptor Has your question been resolved?

[crimson sedge]

Ping the helpers

[visual raptor]

<@&286206848099549185>

[visual raptor]

like i can't seem to transform the following statement

$\neg{P}\wedge{R}$ into ${P}\rightarrow{Q}$

[wraith dagger]

Sir Raftalot

[cedar kiln]

@visual raptor Has your question been resolved?

[violet flume]

is a truth table too much work

[fallen heath]

the idea at the first step should probably have been: \ $(P \rightarrow Q) \land (Q \rightarrow R)$ $$= [(P \rightarrow R) \lor \neg(P \rightarrow R)] \land [(P \rightarrow Q) \land (Q \rightarrow R)]$$

now, some manipulations in the center expression in the parentheses so you can make the parentheses from that.. into: $$[((P \rightarrow Q) \land (Q \rightarrow P)) \lor ((Q \rightarrow R) \land (R \rightarrow Q))$$

[visual raptor]

what law let you jump straight to that?

[fallen heath]

jump straight to what?

[visual raptor]

from the lhs to your first p->R

[fallen heath]

Give me a second, I probably typo-ed sth

[fallen heath]

does that make sense now?

which law do you think I used :o

[visual raptor]

no because i haven't learned wahtever law let you move from the LHS to p->R

[fallen heath]

Hey c'mon, it's not always about the laws

Here:

[visual raptor]

or rule that let you do that

[fallen heath]

I used: $c \lor \neg c = T$

[visual raptor]

i learned that p->q become notPorQ

ohhhh right

ok ill give that a go

[fallen heath]

So this: \ $(P \rightarrow Q) \land (Q \rightarrow R)$ is just $$T \land (P \rightarrow Q) \land (Q \rightarrow R)$$ which is $$= [(P \rightarrow R) \lor \neg(P \rightarrow R)] \land [(P \rightarrow Q) \land (Q \rightarrow R)]$$

[visual raptor]

sorry also im in the mid of a game gimme a few minutes

[fallen heath]

okie

[visual raptor]

ok ready

so the tautolgy helps you get to that step have you skipped any steps or is it some rule about if then that im unaware of?

if then and tuatologies

or hang on

is PthenR or not(PthenR) also a tautology?

It is! ah cool thank you so much ansh i think ive got it from here! 🙂

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[shell ice]

What would the shape highlighted in red be? If there is a shape for that entire section that would be cool but I assume I have to add a kite (top part) and a quad (bottom part) together? But since the kite is not flat, I don't know if I can use the normal formula for the area/volume of a kite. Thank you 🙂

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@shell ice Has your question been resolved?

[shell ice]

<@&286206848099549185>

[zenith sail]

It appears to be made of four flat surfaces: Two quadrilaterals (walls) and two triangles (ceiling)

[shell ice]

Ohh yeah

[zenith sail]

I guess I'm not really sure what your question is.

It exists in three dimensions, so no two-dimensional area formula will calculate it accurately

[shell ice]

Ok yea thanks for your help

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[quiet hollow]

but isn't 100/10 and 10/100 technically the same thing?

[ember geode]

no

[quiet hollow]

one is 10% and the other 1/10?

[cedar kiln]

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[quiet hollow]

oh it closed on me, how is 100/10 and 10/100 different?

[slender trench]

one is 10 full cakes and the other is a just one slice of a cake that was cut into ten slices

[cedar kiln]

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[quiet hollow]

oh right, I just think everything only in %

[quiet hollow]

so % wise tho both are the same if we only look at it that way right?

confused now, why and when we would use this "one is 10 full cakes and the other is a just one slice of a cake that was cut into ten slices" kind of context

instead of calculating/doing everything with percentages %?

cus if there was 10 people, either way everyone gets 1 piece of cake

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[crimson sedge]

how do i do question 7?

i did 3x+5=2y

y= 3/2x+5

idk what to do next

[dire geode]

Perpendicular slopes are negative reciprocal of each other

[crimson sedge]

OH wait

[dire geode]

So if one line's slope is m, the perpendicular line's slope is what?

[crimson sedge]

-2/3

thanks 🙏

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[torn kettle]

what did i do wrong ?

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[torn kettle]

sorted it myself

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[crimson sedge]

Just need help with composite functions but stuck on them

Replace the x with the function

F(x)?

Yes

Wait I’m confused

Which function

Square root of x+8?

Yes

This?

Or is it wrong?

Nope

One sec

$f(g(x)) = \sqrt{8x-12+8}$

[wraith dagger]

Galwa

[crimson sedge]

@crimson sedge

Hmm

So then you combine terms

So 8x-4?

Yup

Wait where did the x+8 go

Or is that just +8?

The x became 8x-12

Okay

So

8x-4

Would you divide inside the square root

What do you mean

What would you do now? Isn’t x=2

Since 8/4 is 2?

Or no

That's the function, you can then plug in any x such that the function is positive

So that would be f(g(x))?

Yes

Square root of 8x-4?

Ohhh

If he asks you for a function

You answer with a function

Not with a real number

Got it

Unless the function is constant

Ty I understand it a lil now

Alright you can close this channel

How do you do that

.close

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[marble latch]

Hi could I get help on this^

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[proud tartan]

I'm stuck for 2(b). Any help would be appreciated!

[proud tartan]

$\sqrt{1 + (\frac{x^4}{3} - \frac{3}{4x^4})^2}$

[wraith dagger]

Snoopy

[proud tartan]

I am trying to solve for the integral above and I know that I should manipulate the expression above such that the square root will cancel out with a square within. But I can't seem to do so.

[cedar kiln]

@proud tartan Has your question been resolved?

[faint stump]

Have you tried common denominator for the $\frac{x^4}{3}-\frac{3}{4x^4}$?

[wraith dagger]

Mango

[faint stump]

It's ugly as it is but starting from there would help

[proud tartan]

I tried factorizing 1/12 but then it just exploded in my face

not sure if I did it incorrectly but I'll give it another go

[faint stump]

Hope this helps: $\frac{x^4}{3} \cdot \frac{4x^4}{4x^4} - \frac{3}{4x^4} \cdot \frac{3}{3}$

[wraith dagger]

Mango

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[short forum]

whats the probability of getting a facecard from a manipulated deck of 52 cards such that the black cards are x2 more probable than the red?

[dusky gate]

Changing the color doesn't change the number of faces or am I crazy?

The probability of getting a face card doesn't change if you use the manipulated deck

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[keen rapids]

A grass lawn has a length of (3x+1)m and a width of (2x-3)m. There is a concrete path of uniform width 2 meters around it. Find the area of the grass lawn with the path.

[whole dune]

you wanna try drawing it out

use ms paint or whatever you have

like this pretty much but label the sides with lengths

[keen rapids]

Yeah, I've tried that. What I'm not sure is that is it ok to calculate without the length?

[dusty hazel]

How would you calculate with the length?

[whole dune]

yeah i think you're supposed to express your answer in x

[keen rapids]

I also don't know haha.
Here's what I did though

(3x+1+4)(2x-3+4)
= 6x^2+13x+5

Then that's it?

[whole dune]

i would assume so

[keen rapids]

Thanks!

I just need someone to say my solution is right :))

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[drifting shell]

if i have a graph in which f(x)=2 and g(x)=-2 and i need to make it so y=x, how would that i do that on the graph?

[drifting shell]

oops

i didnt mean to send it yet

there we go

[south tundra]

Can you send how the question is formulated?

Because your explanation of it is confusing

[drifting shell]

Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. "Graph the line y = x on the same graph."

the qoutes are what i need help with

[drifting shell]

do you need the full set of equations for the graph?

[south tundra]

Oh, so you need to graph y = f(x) = 2, y = g(x) = -2 and y = x I guess

[drifting shell]

i think so

[south tundra]

Just draw two horizontal lines

[drifting shell]

i have, but what about the y=x

[south tundra]

One should have height of 2 and the other one should have -2

[drifting shell]

yep

[south tundra]

y = x is just this

Never seen before?

[drifting shell]

i was

right

darn self doubt

thank you vm

[drifting shell]

i have seen almost all types of graphs and even helped some people with them, im just not there with school yet and am in a bit of a downspiral

thank you for breaking it

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[gentle lintel]

$\sqrt{\frac18 + \sqrt{\frac18 + ...}}$

[wraith dagger]

Chromium

[gentle lintel]

in general, if $y = \sqrt{x + \sqrt{x + ...}}$

[wraith dagger]

Chromium

[gentle lintel]

then $y = \frac{1 \pm \sqrt{1 + 4x}}{2}$?

[wraith dagger]

Chromium

[gentle lintel]

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[inner quest]

can someone explain this problem to me. its a passed exam

[gentle lintel]

$\lim_{x \to -1^+} f(x)$

[wraith dagger]

Chromium

[gentle lintel]

do you know what this notation means?

[inner quest]

its a rule representing quantities and operations? or something like that

[gentle lintel]

do you know what $\lim$ is

[wraith dagger]

Chromium

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@inner quest Has your question been resolved?

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[lament sparrow]

Please help

[lament sparrow]

"C:\Users\andre\Downloads\Web capture_24-2-2022_122530_.jpeg"

q # 4

,help

[wraith dagger]

A brief description and guide on how to use me was sent to your DMs!
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[eternal comet]

would you mind writing it out or sending a picture that will be embeded?

[lament sparrow]

ok

the bottom left letter is s

I have to find the value of x

ARGH (╯°□°）╯︵ ┻━┻

[bright prairie]

x/2 is a degree?

[lament sparrow]

no

The letters other that x and y are unimportant

I need to find the value of x and y

<@&286206848099549185>

[bright prairie]

yeah but I can't get why x is for

im kinda dumb sorry

[lament sparrow]

you're fine

[bright prairie]

is it asking |TS|

[lament sparrow]

T, S, and U are unimportant

i'm just trying to find the value of x and y

it's 6th math

[lament sparrow]

it's (1/2*x)

[bright prairie]

it's an equilateral triangle, meaning all sides are equal to one another. It has already given, 22.

make all values equal to 22

[lament sparrow]

right

the worksheet says to write an equation to determine the values of x and y

Oh, wait!

So i have to find out what to multiply by 1/2 to make it 22 mm?

.close

[cedar kiln]

Channel closed

Closed by @lament sparrow

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[desert scroll]

for part b) (ii)

i have (let x = theta) 1/21sinx-20cosx+31 in the form

1/29sin(x-43.6)+31

how would i find the greatest value

<@&286206848099549185>

[eternal comet]

when is a fraction the largest

[desert scroll]

when sin(x-43.6)=-1

so 1/(-29)+31

thanks

forgot bigger denominator means smaller fraction thanks

@eternal comet

.close

[cedar kiln]

Channel closed

Closed by @desert scroll

Use .reopen if this was a mistake.

Available help channel!

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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.

[ember phoenix]

for the surface on the right, why do u need to integrate in 2 seperate areas

rather than just taking it from the smallest point in x to the largest point in x

?

[cedar kiln]

@ember phoenix Has your question been resolved?

[cunning jay]

apparently the function y = x + 1/x is increasing for all values between -1<x<1. This is found by finding the derivative of the function which yields 1-x^-2>0, which is then factorized into (1-x)(1+x)>0 and then you solve for the roots. But i did a different methods and the result made no sense. i had 1 - x^-2 > 0 --> 1 > x^-2 ---> so -1>x and 1> x which doesn't match up with the first solution.

what is going on?

[ember phoenix]

so its basically due the fact that it has a increasing or decreasing function in the vertical direction

hence why it needs to be split up

@cunning jay

[cunning jay]

ok thanks

[cedar kiln]

@ember phoenix Has your question been resolved?

[cedar kiln]

@ember phoenix Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

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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.

[crimson sedge]

how do you do question number 5

this is my working out but it’s extremely wrong

cause the answer is b less than or equal to -7/8

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

still needhelp on working out

[crimson sedge]

<@&286206848099549185>

[dire geode]

You're getting confused in your quadratic formula

Don't move to the right hand side. Your c= b+1

Now calculate the discriminant

[crimson sedge]

@dire geode OH THANKS RIEMANN

thank you so muchhhh

.close

[cedar kiln]

Channel closed

Closed by @jovial reef

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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.

[dawn ermine]

this would be true right? because (A-l)x = 0 needs a nontrivial solution?

im basing it off this example

[cedar kiln]

@dawn ermine Has your question been resolved?

[cedar kiln]

@dawn ermine Has your question been resolved?