help-13

[slender holly]

then move it untill x is -3*

[pastel vault]

no, don't move it

the graph starts from x = -8
okay, so y = (x + 4)^2 and y = (-8 + 4)^2 = 16, so that's out of the graph

draw the curve, but then you stop your pen when x = -3

[slender holly]

curve doesn’t have to be perfect ?

why does it look like this

[pastel vault]

it says to make a table of values

so here's a task for you: write down a table on a blank sheet paper

you have x = -6, 5, -4, -3, -2

[slender holly]

i gotta graph too

[pastel vault]

and you want to sub in these values of x into y = (x + 4)^2

[pastel vault]

this is how you graph

find all the values of y

then plot them on the graph

make a curve that passes through all the points you plotted

[slender holly]

the x values matter or no

[pastel vault]

I've given you these x-values

[slender holly]

ya but if i wanna do a different equation what x values do i use

[pastel vault]

you're going to confuse yourself if you start talking about different equations

but you can use any x values

they just have to be close enough, like say 1 apart

[slender holly]

oh ok so for -6

it would be

4

[pastel vault]

yep, (-6 + 4)^2 =4

[slender holly]

did u forget the negative on 5

[pastel vault]

you need to tell me what x = -5 gives then

[slender holly]

is it like tha

[pastel vault]

yep! that's correct

that was fast

okay so now you need to plot those points

well, y = 9 is outside the graph so you don't need x = -1

[slender holly]

but i thought x can’t go past -3

[pastel vault]

we can worry about that later

[slender holly]

ok

[pastel vault]

if you draw the curve, you can just erase the part to the right of x = -3

that's why you really shouldn't draw graphs in pen btw

pencil is the best

[slender holly]

so like ts

[pastel vault]

right!

minor correction, x = -7 already gives y = 9

[slender holly]

wait huh

[pastel vault]

should be like this

the graph gets very steep there

[slender holly]

oh okay so is that the answer

[pastel vault]

indeed

you remembered the white circle thing, cause x < -1 means that x = -1 is not included

so that's now correct!

[slender holly]

so that’s both ?

[pastel vault]

yes, both functions on the same graph

[pastel vault]

(you need a black circle at x = -3 also)

[slender holly]

uh liek this

[pastel vault]

um, close enough

maybe just draw a line at this point between x = -7 and x = -6

the line does not intersect x = -7 at all, cause it goes out of the graph

[slender holly]

oh

do say anything yet

imma do the first part and tell me if it’s wrong

1 sec

ignore the curve

[pastel vault]

incorrect so far

omg, it's x less or equal to -3, so you were close

a tip is that the functions are usually in order from left to right

[slender holly]

oh i

i read it wrong

is it just the other way then

[pastel vault]

yes, from the left

and you still need that black dot at x = -3

[slender holly]

can u help with the second part i haven’t seen that before

[pastel vault]

ah, okay so -3 < x < 4

draw y = 3, but you start at x = -3 and you finish at x = 4

and you need white dots for both endpoints, cause you have < and <

[slender holly]

oh that’s easy

lemme try the last part with what i told me

[pastel vault]

yes that quadratic is very similar to the one you did in q1

it has that zero at x = 5 though and you start at x = 4

[slender holly]

nevermind i forgot

can u remind me

[pastel vault]

if you think about that quadratic in q1

it's vertically symmetrical

so that means here, x = 4 and x = 6 have the same y-value (1)

if you make a table of values for x = 4, 5, 6, 7

y = .........

plot the points and join the curve as before

you'll see what I mean

[slender holly]

correct

?

so i should make a table before i graph

[pastel vault]

correct so far

now with your table, plot the points and join them using a curve

and then you also have the 'really steep' thing where your graph escapes upwards

so it never hits x = 8 (cause y = 9)

[pastel vault]

close enough

I know it's hard to draw

just want to make sure you know what's actually happening with the graph

oh right, your circle at x = 4 should be filled in

[slender holly]

are u sure because there is no underline

[pastel vault]

oh nvm

I thought I saw one

[slender holly]

ok this one really confused me me

because it’s doing extra stuff with the first part instead of just a number

[pastel vault]

ah, those are just lines like in q2

lines are easy, you just pick two points

say for x + 2, when x = -8, y = -6

and x = -4 gives y = -2

join the two points, think about whether the circle should be white or black, and that's it

[slender holly]

oh okay point doesn’t matter ?

[pastel vault]

yes, which x-values you do isn't too important

you can just use x = -4 and x = 3 for the next one also

[slender holly]

did i completely mess it up

[pastel vault]

your lines are always curved

if you plot (-4, -2)

keep (-8, -6) the same except there's no white circle there

then draw a straight line as best as you can

you should get it

okay I have to go though

no worries, you can just close this one and make a new channel so that it goes to the top

[slender holly]

aw ok

[cedar kiln]

@slender holly Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[gray stirrup]

how does this work?

[worldly chasm]

@gray stirrup which part?

[gray stirrup]

how the r is negative

[worldly chasm]

I'm assuming this is a solution

[gray stirrup]

when x = -r/ sqrt 10

[worldly chasm]

I'm assuming that it's using the fact that cosine is negative in the 2nd quadrant

the cosine corresponds to the x-coordinate of a point on the unit circle with an angle theta from the positive x-axis

[gray stirrup]

when its sin theta r is also negative tho

[worldly chasm]

and so when the angle is in (90, 270) degrees the x coordinate is negative.

[worldly chasm]

it's again, using the fact that the x coordinate is negative in the 2nd quadrant.

just we eventually get a positive answer, because a negative times a negative is positive.

(-3 and -r/sqrt(10))

[gray stirrup]

if the line was in the 3rd quadrant whould r be postive since neg times neg is pos?

[worldly chasm]

if the line was in the 3rd quadrant then the slope would be positive

so the y coordinate would be negative (because neg times pos is neg)

[gray stirrup]

sorry but i still dont get it

[worldly chasm]

no worries.

talk me through what you do understand.

[gray stirrup]

since the slope is negative r is negative?

[worldly chasm]

no

x is negative, r is not negative

and x is negative because we're in quadrant 2.

[gray stirrup]

if we were in qudrant 4 and x is postive while y is negatvie how woudl that affect it?

.close

[cedar kiln]

Channel closed

Closed by @gray stirrup

Use .reopen if this was a mistake.

[gray stirrup]

thnak you for your help @worldly chasm

[worldly chasm]

sorry

[gray stirrup]

its good

[worldly chasm]

If we were in quad 4, then x is positive and y is negative

a line here would have a negative slope

so you would have x be positive, and y be formed from (pos x value time neg slope = neg)

[gray stirrup]

ty

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[tidal turret]

Hello, I need help figuring out whats the next step after trying to solve this inequality

[chrome elk]

Somehow in solving this you have got rid of the inequality

Bring it back and that should help

[tidal turret]

So by going back to the 2nd step before I did the factoring thingy?

[fair peak]

Use wavy curve

Is answer x belongs to (-5, -3) U (-1 , infinity)

[chrome elk]

Essentially

[chrome elk]

!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.

[chrome elk]

Explain to me what you did in the second step

[dry stump]

I believe you separate the 2 by doing 2(x + 5), then remove the 2 giving you x+5

[chrome elk]

You are both ignoring the glaring issue here

[tidal turret]

In the 2nd step, i was following a format of a similar problem by taking some of the terms of the denominator into the numerators equation and plugging it in there, which resulted in the 3rd step

[chrome elk]

Sure but what happened to the >

You moved the fraction from the RHS to the LHS

So what's left on the RHS

[tidal turret]

In that part, i was following along with a classmate's notes and I kinda assumed the > part was not neccessary anymore for the equation...

[dry stump]

He subtracted the right fraction to itself and combined it with the other on the left, so the right is 0

[cedar kiln]

@tidal turret Has your question been resolved?

Channel closed

Closed by @tidal turret

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[balmy prawn]

is sin more appropiate or cos

[buoyant latch]

They both can work

But what does the mnemonic say?

[balmy prawn]

how do u determine if u should us sin cos or tan

btw whats mnemonic?

[neon void]

draw the triangle on a circle

with the angle corner at the center

[balmy prawn]

done

[neon void]

ok great can i see it

[buoyant latch]

Have you heard of sohcahtoa

[balmy prawn]

the quality of my laptop is horror but i did it on my paper

[neon void]

ion really like mnemonics they dont realy teach you anything

[balmy prawn]

yep

[buoyant latch]

That’s a mnemonic

[balmy prawn]

ohh

[buoyant latch]

It’s just some letters or phrase that helps you remember something

In this example it should help you remember which one to use

[balmy prawn]

so all sin cos tan do is show the ratio

of two line

right

[buoyant latch]

Yeah

[balmy prawn]

ohh so it doesnt really show u the length of one line

[buoyant latch]

They do do a bit more than that but you don’t have to worry at the moment

[buoyant latch]

Well but it does tell you how long x would be relative to the hypotenuse

[neon void]

have you gone through the unit circle and all that yet

[balmy prawn]

nope..

i just started

[neon void]

💀 can ppl teach trig right for once

[buoyant latch]

What does the mnemonic mean?

[balmy prawn]

sooo sin cos tan ONLY shows the ratio between the line and the hypotenuse

not the opposite to the adjacent or smth

[neon void]

that's tangent

sin cos is ratio of a leg of the triangle to the hypotenuse

[balmy prawn]

waitt so can u summerise it

[neon void]

no

[balmy prawn]

so i can turn this to notes

[buoyant latch]

Suppose I have a right angles triangle

[neon void]

thats why im asking you to draw circles

[buoyant latch]

Could you tell me what the letters in sohcahtoa stand for

[neon void]

dang why cant i remix on mobile

[balmy prawn]

s= opposite over hypotenuse

c= adjacent over hypotenuse

t=opposite over adjacent

[buoyant latch]

sin(θ) = …

Yeah

Okay so which is opposite which is adjacent which is hypotenuse in the picture

[balmy prawn]

the line on the left vertical side is opposite, the line on the up side is hypotenuse, the last one is adjacent

[buoyant latch]

Good

So sine says sin(θ) = vertical line / hypotenuse

If I know what the vertical line is, say 3, and the angle θ is given, could you tell me what the hypotenuse is?

[balmy prawn]

uhm

so its 3 over hypotenuse

or smth

its ok gng

imma go eat dinner and come back later

.close

[cedar kiln]

Channel closed

Closed by @balmy prawn

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[limber bone]

ello @here, could some1 help me w this, idk how to solve for z

[slender ginkgo]

try

simplifying

${\frac{z+4}{z+4i}}$ and ${z = x + iy}$

[wraith dagger]

k

[slender ginkgo]

then compare the im and re parts

@limber bone

[limber bone]

there'd be z^2?

@slender ginkgo then what to do from here?

[slender ginkgo]

can u show what u get

[ \frac{(x+4) + iy}{x + (y+4)i}]

[wraith dagger]

k

[slender ginkgo]

cool

${z^2 = x^2 + 2xyi - y^2}$

[wraith dagger]

k

[limber bone]

@slender ginkgo

@here, help ;>

[slender ginkgo]

u kinda need to summarize more

[slender ginkgo]

my idea is to simplify using this

[ \frac{(x+4 + iy)(x - i - 4y)}{x^2 + (y+4)^2}]

[wraith dagger]

k

[slender ginkgo]

,w expand (x+4 + iy)(x - 4i - yi)

[ = \frac{(x^2 + 4x + y^2 + 4y) + (-4x -4y - 16)i}{x^2 + (y+4)^2}]

[wraith dagger]

Results provided by WolframAlpha

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

Requested by nuclearinteraction

k

[slender ginkgo]

now notice

${\frac{z+4}{z+4i}}$ is real

[wraith dagger]

k

[slender ginkgo]

@limber bone

[fair peak]

Bruhh, i was verifying the answer before moving up to the explanation

[cedar kiln]

@limber bone Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[upper ruin]

Personally, I would have started by multiplying top and bottom by the conjugate of the denominator, hence by $\overline{z + 4i}$

In doing this, your new denominator becomes instantly real, and you can just work on making the numerator real without worrying about the denominator

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[wraith dagger]

Alberto Z.

[cedar kiln]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[languid crystal]

anyonne know how to do 7c

[urban coral]

you're probably supposed to find the height of the pole using the angle of elevation of V from A, then use that in a trigonometric function to find the angle stated in c.

[languid crystal]

i got that part i js have no idea how to find the height of the pole

[urban coral]

consider drawing the triangle formed by C, V and A

after filling in the given information, you should be able to see which function you'll need for the job

[languid crystal]

for the triangle i only have one angle and one side tho

[urban coral]

that's good enough

[languid crystal]

i dont think ive learnt any formulas with only those variables

[urban coral]

have you learnt about inverse trigonometric functions?

[languid crystal]

like cosec, cot, and sec

[urban coral]

not those

as in arcsin, arccos, arctan (or sin^-1, cos^-1, tan^-1)

[languid crystal]

yes

[urban coral]

you'll have to use one of those

[languid crystal]

but the triangle isnt right angled

[urban coral]

actually no come to think of it, you don't need to use one of those

[urban coral]

why is it not?

the pole is vertical

[languid crystal]

yes but isnt v o nan elevation from a of 30 degrees

so one of the angles is 30 degrees

[urban coral]

does that forbid CVA from being a right triangle?

[languid crystal]

it doesnt look like a right angle

are we assuming its just a right angle

[urban coral]

we don't need to assume

the plane containing A, B, and C is horizontal

and the pole is vertical

assuming no funny shenanigans (which I doubt there is), you have a clear right angle between the pole and the plane

imagine looking at CVA from the side

[languid crystal]

ah ok i do not understand the meaning of vertical and horizontal plane

[urban coral]

do you understand the concept of vertical and horizontal then?

[languid crystal]

yeah i do now

i thought it meant like a vertical down from c

[urban coral]

so now can you draw the triangle CVA?

[languid crystal]

yes let me see

33.42 degrees?

[urban coral]

what?

[languid crystal]

for the elevation of V from P

the answer

[urban coral]

well I haven't calculated it myself, but if you want to show your working leading up to it, I can check that for you

[languid crystal]

$30\cdot tan(30)=\sqrt{3}a$

[wraith dagger]

blud

[languid crystal]

$tan^-1(\frac{\sqrt{3}a}{\frac{21a}{8}})=33.42 degrees$

[wraith dagger]

blud

[urban coral]

wait wait, where did this come from?

[languid crystal]

oh i mean 3a times by tan

PC is from part b

[urban coral]

and sqrt(3)a came from...?

oh you didn't use a variable for the height of the pole, I see

[languid crystal]

tan(30) is sqrt3/3

yh i js solved it

[urban coral]

hm, usually recommended to state what you're solving for

[languid crystal]

yeah probably a good idea

[urban coral]

,w arctan(8sqrt(3) / 21) in degrees

eh why am I doing an arctan

[languid crystal]

isnt arctan right

[urban coral]

hold up I'm confusing myself

[wraith dagger]

Results provided by WolframAlpha

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

Requested by mikya_hkr

[languid crystal]

isnt it in degrees

[urban coral]

ah ok

earlier it was in radians

then yeah, works

[languid crystal]

hooray it is right

wait can u help me with one more question

its js clarifying somethig

[urban coral]

do send it

[languid crystal]

ok its js the part b of that question

to prove PC = that do you use the bisector method thing

[urban coral]

I'm not too sure about this particular one, sorry

but I suppose I can check any working for you to see if it's logical

[languid crystal]

ok so bisector theorem states that uh

$\frac{AB}{AC}=\frac{PB}{CP}$

[wraith dagger]

blud

[languid crystal]

$\frac{5a}{3a}=\frac{5}{3}=\frac{AB}{AC}$

[wraith dagger]

blud

[languid crystal]

then $\frac{PC}{PB}=\frac{AC}{AB}=\frac{3}{5}$

[wraith dagger]

blud

[urban coral]

looks right then

[languid crystal]

yeah uhhh

$PC=\frac{3}{3+5}BC=\frac{3}{8}(7a)=\frac{21a}{8}$

[wraith dagger]

blud

[languid crystal]

problem is i have no idea how does that 3/(3+5) show up

[urban coral]

well, you split BC into BP and PC in the ratio 5 : 3

so there are a total of 8 parts

3 of which belongs to PC

that's how you get it

[languid crystal]

oh 😭

fair enough

thanks for ur help

ppreciat eit

[urban coral]

nps. anything else?

[languid crystal]

nah thats all

how do i close the thing

[urban coral]

type .close

[languid crystal]

.close

[cedar kiln]

Channel closed

Closed by @languid crystal

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[silent stratus]

Pls help me memorize the table of 14 I am in 9th class tho 🥲🥲

[tropic oxide]

"table of 14"?

what does that mean?

[silent stratus]

Yea I mean , how do I learn from 14×1 to 14×10

[tropic oxide]

i would imagine in the same way as you learned the rest of your times tables

but also tbh i don't see the point

[silent stratus]

We should know tables from 1 to 20 for fast calculation but ik till 13 only 😭

[tropic oxide]

if you need to multiply something by 14 in your head, why not do it as ×7×2

[tropic oxide]

your teacher expects instant recall / memorization of all products up to 20×20?

that's a lot.

[silent stratus]

Not expects but its in general required for maths , as while doing various questions (like surface area and vol etc.) We need to calculate a lot a lot of , and in exam in order to keep pace with time we should learn them in reflex memory

[tropic oxide]

but even then, i don't think 14 is magical. you learn it the same way as any others.

[silent stratus]

Others were easy +( I already learnt till 13 so it is hard to learn more as more information

Is there any trick?

[tropic oxide]

no

[silent stratus]

How many do you know?

How you learnt them?

[tropic oxide]

i don't remember a lot about how i learned the times tables cause it was really long ago

but one thing that i think helped me was skip-counting

[silent stratus]

Not 20×20 , all till 10 , say x × 1 to x×10 (x is 1 to 20)

[last apex]

Learning to do long multiplication fast will be more beneficial

[silent stratus]

How ?

How can I do fast

[last apex]

Practice

[silent stratus]

Not working for me , long multiplications are very messy

[silent stratus]

Skip counting? What's that

[tropic oxide]

reciting one row of the table in order

such as: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

or:
13, 26, 39, 52, 65, 78, 91, 104, 117, 130

and then just do that a whole bunch of times until it sticks in memory

[last apex]

Just add 13/7 over and over

[tropic oxide]

phrasing

13 or 7 or whatever other number you're learning the row for

[silent stratus]

If I wanted to do this I would multiply by writing , both are time consuming, I just want them in reflex memory like 1-13 are in

[urban coral]

what kind of pace are you expected to keep up with in exams that you can't afford to take 30 seconds off to do some 2-digit by 2-digit multiplication though

[silent stratus]

Always my exam gets completed in last sec , I am not able to check even which results in mistake , if you say 30 sec are nothing then , see :-
Time taken for one 2/2 multiplication = 30 sec
Time taken for 80(approx) multiplication= 80×30= 2400 sec = 2400/60min

This time would be utilised for checking

40min are alot

[urban coral]

I never said 30 seconds is nothing.
I'm asking what kind of pace are you expected to keep up with that a 30-second calculation (frankly speaking, 30 seconds is overestimating and kind of a worse case scenario anyway) is too much.

but if that's the case, I suppose other than raw memorizing the multiplication tables, you could use some tricks like x5, x9, x11, etc.

[silent stratus]

Pls tell me this trick?

[urban coral]

x5 = x10 / 2
x9 = x10 - original
x11 = x10 + original

amongst some others

[silent stratus]

I think only these are the tricks

Not other

[urban coral]

I mean, x15 = x10 + x5

[silent stratus]

I searched a lot on yt

[silent stratus]

That's splitting, that takes same time like multipleing , I want in reflex memory

[urban coral]

then gotta practice, I suppose?

[silent stratus]

By the way yk , any trick to memorize squares from 21 to 30

[silent stratus]

That's what everybody says

[urban coral]

...is there another method though? even if you find another method, you still have to practice with it to make use of it efficiently and correctly

[silent stratus]

Yea that's why I have stopped finding methods and tricks and stick to basics , memorizing basic things

[deep token]

Well yeah because it's true. There isn't exactly a shortcut to remembering/learning itself; but I do suggest that on the weekends, maybe try to do some exercises for you to decrease the general time you take in solving.

[silent stratus]

🙁

[urban coral]

maybe get someone to toss you question after question

[silent stratus]

.

[urban coral]

but there is no shortcut to success unfortunately, not even for that new question you asked

well, 30^2 is kinda shortcut-friendly

since it's just 3^2 with two zeroes after it

[silent stratus]

Yea but 21-29

I tried making any funny mnemonic but not able to

[deep token]

And even if you memorize the product down to the T it'd do nothing against needing full solution for the computation

[urban coral]

but other than that, either you'll have to memorize or calculate, or if you're a madlad, remember that consecutive squares differ by consecutive odd numbers

still, you'd need to do some calculation.

[silent stratus]

Madlad?

[urban coral]

ignore that word if you don't know what it means

not important for the context

[deep token]

Also a trick my classmates use is writing something over and over again until they manage to get it; again, time consuming, because everything takes time whether you like it or not.

[silent stratus]

You're from?

[urban coral]

wait wait wait. are you thinking you can get good without effort?

[silent stratus]

I want to make effort but for making that effort easy I wanted to learn

[deep token]

Which is basically impossible LOL

[urban coral]

there's a limit on how easy effort can get

unless you're some mental math god that sees answers as quickly as they come, you're gonna have to put some effort into making it work for you first, then you can focus on going faster

[silent stratus]

Yea I want to become a math god

Fast as calculators

[deep token]

You're not going to be able to do that without any practice

[urban coral]

well for that

either you are super talented (I know of one of my teachers who can), or super hardworking

[silent stratus]

How much calculation practice should I do and how

[silent stratus]

🙁

[urban coral]

maybe every weekend, take half an hour to an hour out and do arithmetic questions

focus on accuracy first, then build speed without sacrificing accuracy

[deep token]

Math isn't necessarily just about memorization, it's about application and understanding of the topic; there's a reason why in most tests you need to show your solution to prove that you are able to apply and comprehend the subject.

[silent stratus]

I sent this 🙁 , because yous said I need to be super talented

But am normal

[deep token]

So, having said that, just like Mikya (and I from a few minutes ago?) said, you're gonna have to sacrifice some of your time for building your skills in mathematics. Start simple, and build onto the difficulty.

[urban coral]

well clearly you didn't read the second half of the statement?

either you are super talented (I know of one of my teachers who can), or super hardworking

[silent stratus]

Hard working

[deep token]

Well yeah if you want to be as "fast as a calculator" you'd basically have to defy all human logic

[silent stratus]

But I can't give all time to maths that's the problem, with hard working, I am just in 9th

[silent stratus]

Yea I want to break the limits 🔥

[urban coral]

the world doesn't bow to you, I'm afraid. if you can't put in the yards, you're not gonna see results

[deep token]

That's why we told you that it'd take time, no? You can't just be doing math all day, and even then it depends on how you're able to comprehend and understand the topic, and then practice your accuracy and speed.

[urban coral]

besides, I said, half an hour to an hour per weekend

surely you can dedicate just that much time...?

[silent stratus]

Hm

[silent stratus]

Yea

[urban coral]

I'm not asking you to sell your soul by doing 10 hours of practice every day

[silent stratus]

Thanks for guidance everyone

[urban coral]

!done, if nothing else

[cedar kiln]

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

@silent stratus Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[limber bone]

hi @here, could some1 tell me where have i made a mistake, i checked markscheme and c should have been (11/18) instead of (11/6)

[vestal bluff]

its the same thing

you moved the 3 to the sin2y

so your c is 3 times more

[limber bone]

lol, 3c = (11/6) ig

thzz,

.solved

[cedar kiln]

Channel closed

Closed by @limber bone

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[topaz hinge]

Given triangle SAE. Let D be the midpoint of AE, I be the midpoint of SD, and K be the intersection point of AI and SE. Find the ratio IK/AI.

I've tried calculated SK/KE = 1/2 but stucking there. How can I calculate the ratio?

[cedar kiln]

@topaz hinge Has your question been resolved?

[topaz hinge]

<@&286206848099549185>

[honest field]

hmm how did you calculate SK/KE = 1/2

[topaz hinge]

using the manelaus theorem $\frac{SK}{KE}\times\frac{EA}{DA}\times\frac{DI}{IS}=1$

[wraith dagger]

wuird

[honest field]

alright nice

now apply the Melenaus theorem to ∆AEK with line SID intersecting it

[topaz hinge]

woah, let me try it

[honest field]

Alternatively you can apply Melenaus theorem to ∆AID and line SKE right from the start

[topaz hinge]

omg thank you so much!!! I didn't see these at the first place

it's kinda hard to see

.close

[cedar kiln]

Channel closed

Closed by @topaz hinge

Use .reopen if this was a mistake.

[honest field]

me nhật 💀

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[cedar kiln]

Please don't occupy multiple help channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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 sentinel]

My question is what are some good resources to study for AMC10 and AIME?

[grave sentinel]

Can someone please help

idk

ig no one

.close

[cedar kiln]

Channel closed

Closed by @grave sentinel

Use .reopen if this was a mistake.

[grave sentinel]

.reopen

[cedar kiln]

✅ Original question: #help-13 message

[grave sentinel]

Guys please help

Like I am using these boooks

and AoPS Math JAMS, AoPS Math Wikis, AoPS Math Classes...

.close

[cedar kiln]

Channel closed

Closed by @grave sentinel

Use .reopen if this was a mistake.

[grave sentinel]

.reopen

[cedar kiln]

✅ Original question: #help-13 message

[grave sentinel]

Gng pls help

[cedar kiln]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

@grave sentinel Has your question been resolved?

[hexed parrot]

what do u need help with broo

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[obtuse coral]

This is the graph of the first derivative. Knowing that, where is the original function concave up/down?

[severe cipher]

can y'all help me with something

[worldly chasm]

!help

[cedar kiln]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[worldly chasm]

so do you recall the criteria for concave up/down?

[obtuse coral]

.close

[cedar kiln]

Channel closed

Closed by @obtuse coral

Use .reopen if this was a mistake.

[obtuse coral]

I got it

Thank you, tho

.close

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[inner sandal]

guys can someone help me with this it’s actually pissing me off I been at it for like 3 hours

[neon void]

well you should break it up into two inequalities first because of the absolute value

[inner sandal]

yes I get that I make it once with > and once with <

but after I solve it my answer is different than the model answer

like they want me to do all of this and it’s so confusing

[dreamy void]

you also have to keep in mind that multiplying by x+2 might change signs

[inner sandal]

like how did we find out -2 is part of the X value just because it’s in the denominator while in the second inequality the X value is root 13 but in the first inequality when we solved it we got 1 excluded from the set

[inner sandal]

like part of the domain

someone helpppp

pls

I been at this for 3 hours lowkey

[dreamy void]

Can you rephrase your question a bit more clearly?

[inner sandal]

ok so in the first step of solving the denominator can’t be 0 so x≠2 but then at the end of the first part of solving the domain is -2 but then for the second inequality we also establish that x≠2 but when we get the domain it’s -infinity and -root13

[dreamy void]

So your question is, how we get ]-oo, -sqrt(13)[ in the last part?

It helps to draw this on a number line

,calc sqrt(13)

[wraith dagger]

Result:

3.605551275464

[dreamy void]

So you would notice that -sqrt(13) which is -3.605.. is smaller than -2, so their intersection would result to starting at -sqrt(13), not -2. For example, say we had x=-3 which satisfies x<-2 but you'd get a wrong answer for x<-sqrt(13) since -3 is greater than -sqrt(13).

[inner sandal]

OHHH

SO BECAUSE root 13 is less than -2 so we used root 13 for the domain

but 1 is bigger than -2 so when we got it we excluded it from the set in the final answer

[dreamy void]

yes

[dreamy void]

1 was excluded because in the first inequality case, if you set x=1 you get 0>0 which is wrong

in other words the strict inequality makes us exclude x=1

[inner sandal]

so if I had gotten a different number from the calculations I wouldn’t have excluded it?

[dreamy void]

questions like that are hard to answer, you have to think logically

like

If you drew y=(x-1)^2

and you wanted to see when it's positive you would realize it's if x is not 1, because at 1 it has a root

all you gotta do is think about your simplified result in the end, and what it means

[inner sandal]

okay I kind of get you

[dreamy void]

sometimes it helps to draw a picture instead of doing everything algebraically

[inner sandal]

could you explain this part too

I’m a bit confused why we need to reverse the inequality symbol and do it twice

for each inequality so four times total

[dreamy void]

After resolving the abs value you have two inequalites

If you consider one of them, you get again two cases

because when you multiply by x+2 both sides, the < sign might flip, depending whether x+2 was positive/negative

[inner sandal]

ohh

OHH ALRIGHT

I got itt

[dreamy void]

you are basically slicing a big hard problem into 4 smaller ones

[inner sandal]

thanks a lot

[dreamy void]

because they are easier to work with

[inner sandal]

yes I was trying to understand why

[dreamy void]

and in the end you combine the solutions

[inner sandal]

like why we’re even doing all that

[inner sandal]

yes

okay thanks a lot

how do I end the

help

[dreamy void]

type .close

[inner sandal]

okay thanks

.close

[cedar kiln]

Channel closed

Closed by @inner sandal

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[modest sky]

how do i answer number 27 ?

[neat dune]

What have you tried?

[modest sky]

so like ik the formula is area for sector
theta / 360 x pi x r^2

but how do i like get the value of theta

[neat dune]

Well, you don't need theta here. It tells you it's divided into 20 congruent sectors. So each sector is 1/20th the total area.

[modest sky]

ohh

[neat dune]

yup 😄

[modest sky]

OK THANKYOU

.close

[cedar kiln]

Channel closed

Closed by @modest sky

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[slender prism]

How do I divide polynomials using synthetic division and two known factors
I don’t know if this is against server rules or anything it’s not a test but it’s my homework and I wasn’t here for it

I looked everywhere online to try and find how to answer this question and I think I know how to use synthetic division now but I’m not really sure what to do

The actual problem is this: The polynomial function
f(X)=2x^4 - 7x^3 - 2x^2+13x+6 has
known factors (x + 1) and (x - 2). Using synthetic division or diagrams, write the polynomial function as a product of linear functions. Show ALL your work and upload the paper.

I also don’t know what “write the polynomial function as a product of linear functions” means either

I also just joined this server so if im not following a rule or something sorry

[carmine bronze]

Linear functions likely means linear factors as in (x - a).

[cedar kiln]

@slender prism Has your question been resolved?

[slender prism]

Oh ok

.close

[cedar kiln]

Channel closed

Closed by @slender prism

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[obtuse coral]

Not sure whether my q was answered in a different channel

I lost it

[obtuse coral]

Anyway, I need help graphing this out

My teacher drew smth like this, but I’m not sure how it’s right

[cedar kiln]

@obtuse coral Has your question been resolved?

[cedar kiln]

@obtuse coral Has your question been resolved?

[cedar kiln]

@obtuse coral Has your question been resolved?

[compact jay]

derivative is positive on all those intervals so the function is increasing on all those intervals

second derivative is showing concavity

[obtuse coral]

Is there any way u could sketch it out for me?

[compact jay]

the thing u attached looks correct

[obtuse coral]

Doesn’t it need to be concave up before x=1, though?

That looks like concave down to me

[compact jay]

it’s concave up just the other half isn’t in the graph

for reference

that’s how I understand it

[obtuse coral]

I don’t really understand this part of what you drew

@compact jay

That part’s drawn as concave down when in reality it should be concave up

Right?

Nvm

.close

[cedar kiln]

Channel closed

Closed by @obtuse coral

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[lost aurora]

A geometry student wants to draw a rectangle inscribed in a semicircle of radius 8. If one side
must be on the semicircle's diameter, what is the area of the largest rectangle that the student
can draw?

[lost aurora]

u have to use optimization

[hallow pelican]

so like, calculus

[lost aurora]

yeah basically

[hallow pelican]

dumb question. tell the teacher that solution methods dont matter

[lost aurora]

its an optimizaiton unit, so u kinda have to use that

i got a horrible teacher

but yk how to do it?

[hallow pelican]

mhm

[lost aurora]

can u teach me

[hallow pelican]

is this you?

https://tenor.com/view/v2-ultra-kill-dead-chat-gif-27002020

so, what relation does x and y have?

[lost aurora]

but it says one side must be the semicircles full diameter

so doesnt it have to cover the whole semi circle's diameter

[hallow pelican]

that doesnt make sense at all

[upper ruin]

Read more carefully

[hallow pelican]

it says "on"

[lost aurora]

okay i see

so then how do i approach it from there

[hallow pelican]

.

[lost aurora]

oh

mb

x is the radius?

i mean xy=A

[hallow pelican]

x is a side length...

[lost aurora]

yeah

[hallow pelican]

think about x and y for a moment

[lost aurora]

they both are side lengths of the rectangle

?

[hallow pelican]

exactly

so

[lost aurora]

if u multiply them u get the area

?

[hallow pelican]

am i going to drop a huge tip? tick for yeah cross for no

they are related by the pythagorean theorem

[lost aurora]

ohhh

[upper ruin]

Hint: draw a suitable radius

[lost aurora]

wait give me a second to try it now

[upper ruin]

And you'll see why/how

[lost aurora]

is it x=4 and y= root 48

[upper ruin]

,rccw

[upper ruin]

Awful mistake!

[hallow pelican]

why did you simplfy the square root like that😭

[lost aurora]

oh shit can I not

[upper ruin]

Of course not!!

$$\sqrt{A + B} \neq \sqrt{A} + \sqrt{B}$$

[wraith dagger]

Alberto Z.

[lost aurora]

Sorry give me a sec I’m solving it

[upper ruin]

Otherwise $\sqrt{3^2 + 4^2} = 3 + 4 = 7$, when instead it is 5

[wraith dagger]

Alberto Z.

[upper ruin]

Yeah no hurry

[lost aurora]

ohhh yeah ur right

but do I use product rule

for some reason I feel like I made it so complicated

[upper ruin]

You'll need it, yes

[upper ruin]

No no your reasoning was good,the problem was that bad simplification

[lost aurora]

Wait nvm

Sorry I’m stupidly

[upper ruin]

,rccw

[lost aurora]

I brought it to the other side

[upper ruin]

Wait, is x half or the whole side length?

[lost aurora]

Half

[upper ruin]

Alright, then the area is 2x•y

[lost aurora]

oh shoot okay

Why is thst tho?

Is it not x/2 * y

Bc half the side length

[upper ruin]

Because if x is half of the side, then the whole side is 2x 😅

[lost aurora]

Oh wait ur right oops

[upper ruin]

You could do it the other way round (hence x being the whole base), but then inside the root you'd have an x²/4 which is unpleasant for the calculations

[lost aurora]

I’m stuck

[upper ruin]

,rccw

[upper ruin]

You forgot the chain rule 😬

[lost aurora]

oh shoot UR ROGHT

[cedar kiln]

@lost aurora Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[torn marsh]

for the phase shift, can we have h units shifted to the left?

[torn marsh]

as well

and how would it be written

[dusk goblet]

f(x + h)

[long swan]

f(x+h)

Haha

[torn marsh]

ohh ok thanks

.close

[cedar kiln]

Channel closed

Closed by @torn marsh

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[vernal kite]

how do i do this

[vernal kite]

i expanded the thing inside the bracket

then x = 0 so i got (iy - 6) / iy

now idk what to do

[sonic thicket]

Why x = 0 ?

[vernal kite]

bc the real part of that = 0

[hollow trail]

the real part of (z - 6)/z is 0, not the real part of z

[sonic thicket]

How?

[vernal kite]

let z = x + iy

and then expand

[sonic thicket]

What did you get after expanding? Without setting x = 0

[vernal kite]

so what do i do then

[hollow trail]

so take the real part of the entire expression (z - 6)/z

[vernal kite]

(x + iy - 6) / (x +iy)

[sonic thicket]

Remove the complex number from the denominator

[vernal kite]

so (x - 6)/(x) = 0

therefore x = 6

?

[tacit girder]

Yes x=6

Because denominator can not be x=0

[vernal kite]

yea

but then how do i find y

[tacit girder]

Clearly y=0

[vernal kite]

so x = 6

[tacit girder]

x(x-6)+y^2/(x^2-y^2)=0

[vernal kite]

it’s a vertical line?

oh

real-ise the denominator?

[tacit girder]

You don't need to find the values

Just look at the numberator

x^2+y^2-6x=0

[vernal kite]

so if x = 6, y = 0

[vernal kite]

how did u get this

[tacit girder]

as I said by simplifying the given equation

z=x+iy

[vernal kite]

.close

[cedar kiln]

Channel closed

Closed by @vernal kite

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[magic solar]

Could anyone help with proving Wilson’s theorem and converse

[magic solar]

If (p-1)!+1 is divisible by p, p is prime & the converse too pls

[hot cipher]

Theres such a neat way of proving this one

Wilsons at least

Well, I hope you know what a Field is, and that you can agree with me that Z/pZ is a field.

[magic solar]

Idk what that is

Is there any algebraic way

[hot cipher]

Do you know about mod n?

[magic solar]

Idk about modular arithemetic either

[hot cipher]

🥀

[magic solar]

But like I get what it is

Sorta

Just don’t know notation

[hot cipher]

If you dont really know what it is, then it will just be a big "believe me" tbh

i think it can be done with residue anyways

[magic solar]

Surely there is an algebraic method

[last apex]

Fields are very algebraic objects if you ask me

[hot cipher]

not that im aware of

[last apex]

But ikwym

[hot cipher]

Z/pZ is a field way of proving it is so clean tbh

[magic solar]

I’m guessing z/pz is some integer prime field or some shit

Idk allat though

[hot cipher]

I can give you the basic rundown of it

[magic solar]

Umm sure

[hot cipher]

Basics of modular arithmetic:
Z is the set of integers
nZ is the set of all the integers multiples of n.
Z/nZ is what we call a partition / quotient modulo n

I think you know what a remainder is

Well, it divides integers based on remainder when dividing by n

for example:
any number divided by 2, can only have either remainder 0 or 1 (aka its even or odd)

therefore, Z/2Z only has two elements
${[0]_2,[1]_2}$

[wraith dagger]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[magic solar]

Sure

[hot cipher]

Where [0] and [1] are sets themselves, and we call them modulo classes. For the general idea, just know that classes share a lot of properties within themselves

Well, any Z/pZ is what we call a field

Which, apart from a few basic properties of arithmetic, have the added benefit that all elements have an inverse under multiplication

Z/pZ has p elements, ${[0]_p,[1]_p...[p-1]_p}$

[wraith dagger]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[hot cipher]

Since we know its a field, all elements (except 0) have an inverse.
sooo, if we do

$[1]_p\cdot [2]_p...\cdot [p-1]_p$

[wraith dagger]

∫ᴄ 𝐅·𝑑𝑟 = ∬ʀ ∇⨯𝐅 𝑑𝐴

[hot cipher]

Then there must be a way to arrange all elements (except 1 and p-1) such that its paired to its inverse.

mb, missed the actual -1, the idea is the same, just that you pair all elements minus the first and last (1 and p-1)

The others become 1, so you are left with p-1

which has remainder congruent* to -1
had a brainfart for a sec

[magic solar]

Tbh this is a bit much

[hot cipher]

the closest youll get to "algebraic" is using division with remainder

But tbh, its arguably messier than this

[cedar kiln]

@magic solar Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[split cave]

hi is this an example of if A then B? x<5 -> x< or equal to 5

[split cave]

if A is true and B is false then its false

but how do I know which one is A or B?

[maiden dune]

I mean if A is True and B is False.

Then...

$A \implies \neg B$

[wraith dagger]

Reborn

[maiden dune]

If you're saying...

$x < 5 \implies x \le 5$

[wraith dagger]

Reborn

[maiden dune]

it is right.

Because...

$x \le 5$ means $x < 5$ (OR) $x = 5$

[wraith dagger]

Reborn

[maiden dune]

Or, in more logical terms,...

$x \le 5 \implies (x < 5) \lor (x = 5)$

[wraith dagger]

Reborn

[maiden dune]

Notice that $x < 5 \implies x \le 5$ because $x < 5$ could mean $x < 5$ (True) [or] $x < 5$ could mean $x = 5$ (False)

[wraith dagger]

Reborn

[cedar kiln]

@split cave Has your question been resolved?

[split cave]

so in implication A is always the first statement the if part and B is the last statement the conclusion correct?

No matter how u turn it

x<5 then x< or equal to 5

here x<5 is A

and x< or equal to 5 is B

x or equal to 5 then x<5

x or equal to 5 is A

and x<5 is B

correct?

[cedar kiln]

@split cave Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• Do not immediately ping people or roles. After 15 minutes, feel free to ping <@&286206848099549185> once.
• 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.

[lament vector]

Looking for help on this question

[tropic oxide]

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[vital jay]

Well can you show c is a zero?

[tropic oxide]

bad time to use the numeral zero

[vital jay]

Yeah fair enough

[lament vector]

well it says I need to prove that -4 is a zero of c

[vestal bluff]

how would you prove that

[vital jay]

Yup, do you know how to do that?

[lament vector]

long division

[vital jay]

Well maybe, but there's a much much simpler way

[lament vector]

Ik u can do synthetic but my teacher said she only wants long for our tests and homework

[vital jay]

Well what does it mean for c to be a zero of P(x)?

[lament vector]

That when we do long division with x-4 the remainder will be 0?

[vital jay]

That's one interpretation, but it also means that P(c)=0

[lament vector]

ok

[vital jay]

Which is the same thing right? Because if P(x) is a multiple of (x-c), then since (c-c)=0 we must have P(c)=0

[lament vector]

yea

[vital jay]

So can you show c is a zero like that?

[lament vector]

so do i do long division?

cuz i also have to find the other zeros through factoring

[vital jay]

Sure why not, I guess that'll be useful for the second part

Yeah

[lament vector]

ok ill try to set it up

ok, now this is where i dont know where to start

[vital jay]

Hmm I haven't tried explaining this topic before

But you need to start by aligning with the largest term, right?

[lament vector]

I believe I need a multiple to make x=x^3

so x^2?

[vital jay]

Yep

Don't forget to apply x^2 to both terms btw, x^3 - 4x^2

[lament vector]

so then

[vital jay]

And what would be the remainder after subtracting x^3 - 4x^2?

[lament vector]

-3x

[vital jay]

Let me rephrase

What would be the remainder of (x^3-3x^2-18x+40) - x^2(x-4) ?

Because x^2 isn't what's left after factoring right? There's more steps to go

Does that make sense at all?

[lament vector]

Its not just the remainder of x^3-4x^2 and then we bring down the second term?

[vital jay]

Not really, also x^3 - 4x^2 does not equal -3x

[lament vector]

Oh

[vital jay]

The exponents of x don't cancel with subtraction

Here I'll just show you what I mean, gimme a second

[lament vector]

Ok

[vital jay]

So the "long" part of long division is that you need to repeat the previous steps until you're left with something smaller than x-4

To find the next term you repeat the process with the result at the bottom there

[lament vector]

So why do u bring down the 40 too, not just the 18x, repeat and then the 40?

[upper ruin]

What kind of method have you been taught? 🤔

[vital jay]

Well if you remember to bring down the 40 when you need to I guess you don't need it in the middle?

But I like to keep things together whenever possible, since it's less likely for me to make a mistake by forgetting a term

[lament vector]

She taught us to bring the terms down one by one

[upper ruin]

Mmhh weird

Have you a screenshot of that?

[vital jay]

Also..........

I just realized since c = -4 we should be using x+4, not x-4

[lament vector]

Oh dam

Perhaps I should ask my teacher what's going on then

With her method

[vital jay]

It shouldn't make much of a difference really

Just different ways of presenting the same process

[lament vector]

Oh ok

[vital jay]

The term thing I mean

x-4 and x+4 are very different and that needs to be corrected in our work

[lament vector]

Ok

[vital jay]

So can you show me the result of the first step with x+4?

[lament vector]

Kk one sec

Now I'm not sure where to go

[lone slate]

Just subtract it first

[vital jay]

Yeah, you've essentially got x^3 - x^3 and -3x^2 - 4x^2, how do those two things resolve?

[lament vector]

Im not sure

So the x^3 cancels out

[vital jay]

Yep!

For the -3x^2 - 4x^2, you can pull out the x^2 part like this -3x^2 - 4x^2 = (-3 - 4)x^2

[lament vector]

So then it's-7x^2?

[vital jay]

Yep!

So can you use that to set up the next step?

[lament vector]

Is this the set up

[vital jay]

Close, you don't need that extra minus sign out front

Or

[lament vector]

So this

[vital jay]

Yup!

Now I see you've already put 7x up at the top

[lament vector]

Yea 7x^2

[vital jay]

Actually it would just be 7x, no square

Because just like we had x^2 to make the x match x^3, we need -7x to make x match -7x^2

Like we did x^2(x+4) = x^3 + 4x^2

So now we do -7x(x+4) = -7x^2 + ...

Does that make sense at all?

[lament vector]

Ohhhhhh

Cuz we have to make x = 7x^2

[vital jay]

Yep!

[lament vector]

Ok so I brought 18x down now what

[vital jay]

Well can you finish my incomplete equation here?

What is -7x(x+4)?

[lament vector]

-7x^2+27x

[vital jay]

Hmm, two things. The second term there should be negative right? And 27 is close but not quite right

[lament vector]

-28

[vital jay]

Ye

So now you do (-7x^2-18x) - (-7x^2-28x)

[lament vector]

10x?

[vital jay]

Yup!

[lament vector]

Here's where I am at

[vital jay]

Looks good!

I see in your answer you've put 10x, which is the right idea but you actually just want 10

Because 10 times (x+4) will give you a 10x term, right?

[lament vector]

Yesyesyes

[vital jay]

Just like how we put 7x instead of 7x^2

[lament vector]

Yea

[vital jay]

Can you finish this off then? All that remains is to show that there's no remainder

[vital jay]

Yup!

So can you tell me what the result of the division would be? For the sake of finding the other zeros

[lament vector]

Now I gotta factor further