help-13

[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.
• 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.

[high forge]

i'm confused on how to condense this-

[high forge]

$ln(x)-ln(y)-ln(z)$

[wraith dagger]

BlueCookiez

[high forge]

i get that you first do $ln(x)-ln(y)$

[wraith dagger]

BlueCookiez

[high forge]

$ln(x)/(y)$

[wraith dagger]

BlueCookiez

[high forge]

which is equal to

$ln((x)/(y))$

but how do take that and combine it with -ln(z)

[high forge]

i don't know if this is the right answer but i got this

$ln(xz/y)$

[wraith dagger]

BlueCookiez

[dire geode]

z should be in the denominator

[dire geode]

Because you're subtracting log z

[cedar kiln]

@high forge Has your question been resolved?

Channel closed

Closed by @high forge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crimson sedge]

let’s say i have sqrt 72

[crimson sedge]

and i wanna simplify it

how can i double check that 6 sqrt 2 = sqrt 72

would i just 6^2*whatever is inside the sqrt?

[slate lintel]

yeah
when a number goes from outside to inside it gains a ^2
when a number goes from inside to outside it loses that ^2

[crimson sedge]

alright sick awesome

.close

[cedar kiln]

Channel closed

Closed by @fringe kernel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cedar kiln]

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

[distant pecan]

1

do i do

[void sand]

are you familiar with trig quadrants?

[distant pecan]

-pi/3 times 2pi?

and then check the unit circle

[distant pecan]

uhm

is that the unit circle

[void sand]

sorta

[nova snow]

ASTC

[void sand]

^^

or CAST, depending on where you're from lmao

[distant pecan]

ok

so whats

[distant pecan]

how do i solve this

[nova snow]

You don’t need to do any calculations you can look at it geometrically if you know what the quadrants are

[distant pecan]

uhuh

adym

wdym

[nova snow]

Do you know what the quadrants look like?

[distant pecan]

on the unit circle?

@nova snow

[nova snow]

Not quite what I mean

I’ve drawn it here

Have you seen this before

[distant pecan]

oh

well

yeah

tghats the unit circle

[nova snow]

Well not really it’s only got the angles dividing the circle into 90 degrees

[distant pecan]

ok

[nova snow]

I’ve just converted the degrees to radians

[distant pecan]

ok

well whats the step

[nova snow]

What do you notice about the direction angles are measured here

[distant pecan]

idk

what does that mean

direction angles

[void sand]

-θ = 360 - θ

[nova snow]

Is it clockwise, counter clockwise?

[distant pecan]

uhm

counter

[nova snow]

Yeah

[slate lintel]

this is probably a more useful way to see it as it's normally marked

[nova snow]

So which way do you think negative angles are measured

[distant pecan]

wdym

[nova snow]

If theta > 0 follows counter clockwise

which way does theta < 0 go

[distant pecan]

clockwise

[nova snow]

yes

[distant pecan]

so whats this have to do with the problem i sent

[nova snow]

Well take a look you have -pi/3

What’s that in degrees

[distant pecan]

-60?

[nova snow]

Yeah

[distant pecan]

so first quadrant

[nova snow]

NO

oops

Sorry caps

Lol

Look here

[distant pecan]

ph

ph

oh

[nova snow]

This is how it works for negative angles

[distant pecan]

ok

thats confusing

[nova snow]

Quadrant 4 becomes quadrant 1

It’s just reversed

[distant pecan]

what about 90 in radian

[void sand]

pi/2

[distant pecan]

like in terms of pi

[distant pecan]

how

why

[void sand]

wdym

[distant pecan]

oh

[nova snow]

do you know how to convert degrees into radians

[void sand]

a circle has 2pi radians

which is 360 degrees

so a quarter of a circle is pi/2 = 90 degrees

[nova snow]

In reference to this, which quadrant is -60 in

[distant pecan]

in the 4th

[nova snow]

correct

[distant pecan]

ok?

but how does that matter

ohh

ok

[void sand]

did you not ask me?

[distant pecan]

i get it

sorry yeah

[nova snow]

[distant pecan]

what about -20

[nova snow]

where do you think it is

[distant pecan]

in the fourth quadrant

[nova snow]

Mhm

[distant pecan]

but whats the pi term

[nova snow]

Radians

[distant pecan]

yeah

in terms of pi

[nova snow]

pi/9

[distant pecan]

why

[nova snow]

Did your teacher tell you the formula for converting degrees to radians

[distant pecan]

yeah

oh wait

ohhhh

[nova snow]

then you should know

[distant pecan]

yeah i figured it ot

[nova snow]

Here’s a bonus what quadrant is 5pi/3 in

[cedar kiln]

@distant pecan 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.
• 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.

[runic sage]

Suppose the polynomial $f(x)$ is of degree $3$ and satisfies $f(3)=2$, $f(4)=4$, $f(5)=-3$, and $f(6)=8$.

Determine the value of $f(0)$.

[wraith dagger]

dabbingpotato

[runic sage]

Okay so basically I made a system of equations with this stuff

3rd degree polynomial goes by the form $ax^3 + bx^2 + cx + d$

[wraith dagger]

dabbingpotato

[runic sage]

So I got

$27a + 9b + 3c + d = 2$\
$64a + 16b + 4c + d = 4$\
$125a + 25b +5c + d = -3$\
$216a + 36b + 6c + d = 8$\

[slate lintel]

use \\ for newline

[wraith dagger]

dabbingpotato

[runic sage]

thx

i know its possible to solve now because 4 variables and 4 equations

but i'm lazy is there an easier way

[slate lintel]

lmaoo

[muted bear]

are you familiar with nth order differences?

[runic sage]

mafth

[runic sage]

nope

if you explain i might know what it is

[muted bear]

Heres an image from when i helped somebody else

The top is a quadratic function, a 2nd degree polynomial

So its 2nd order difference, ala the difference of differemces of terms is constant

The bottom is a linear function, a 1st degree polynomial

So its first order difference is constant

Sincw you function is degree 3, what nth order difference is constant

[runic sage]

3rd order difference?

sorry if i'm being stupid i don't really get it

ohhh wait

does that mean if a function is degree 3

that means the difference is 2nd order?

or no

[muted bear]

lemme create a table

[runic sage]

okay

[muted bear]

currently youre table looks something like this

[runic sage]

okay

so the difference it

2, -7, and 11

[muted bear]

be careful with signs

[runic sage]

mb

[muted bear]

so here would be your second order difference

[runic sage]

ohhh ok

[muted bear]

and this is your 3rd order difference

depending on whether you want to solve a boring system of equations or backfill a table with a bunch of differences, this is going to be tedious

[runic sage]

darn

how would i solve it with differences

[muted bear]

keep working backwards

[runic sage]

okay i have a question

does the +27 always stay constant?

[muted bear]

yes

[runic sage]

why is that?

[muted bear]

because you know the polynomial is degree 3, when you check the 3rd order difference, it is always constant

[runic sage]

so then for example if the polynomial is degree 12

the 12th order difference is always constant?

[muted bear]

yes

[runic sage]

oh neat

[muted bear]

but its a lot of work to find

[runic sage]

you'd need 12 values on the graph to find that

right?

[muted bear]

yeah

[runic sage]

consecutive as well

[muted bear]

you need 13 actually

[runic sage]

oh right

[muted bear]

in an arithmetic sequence, not necessarily difference 1

[runic sage]

okay i think this is a less tedious way then solving system of equations

let me work this one out

i got - 328

[muted bear]

yup

i also checked with wolfram alpha

[runic sage]

yoo it was right

thank you so much

[muted bear]

youre welcome

[runic sage]

you saved me from system of equations

🙏

.close

[cedar kiln]

Channel closed

Closed by @runic sage

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.
• 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.

[whole bloom]

just times normally

y-3 times -4 and x-2 times 2

theres a negative

Wait what answer are U looking for

What does it say

X in terms of y?

No what does the question ask for

Ok what?

But why did U circle that

Yeah and what does it say for that specific one

[cedar kiln]

Channel closed

Closed by @turbid thistle

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.
• 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.

[ruby briar]

Show that (p → q) ∧ (q → r) → (p → r) is a tautology.

[exotic furnace]

!status

[cedar kiln]

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

[ruby briar]

2. I have begun but got stuck midway

[exotic furnace]

What have you done so far

[ruby briar]

i have wrote p implies q to negation p or q

the first one

and q implies r also to negation q or r

then stuck

don't know what to do next

[rustic ridge]

Write a truth table for the propsitions

[ruby briar]

can we do it without the truth table the question was to prove without the truth table

[cedar kiln]

@ruby briar Has your question been resolved?

[exotic furnace]

You can try continuing to get rid of all the conditionals

[ruby briar]

how to remove the next conditional

i have removed 2

[exotic furnace]

you can do the same thing

[ruby briar]

can you tell me the next step

[exotic furnace]

What do you end up with

[ruby briar]

<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>∼</mo><mi>p</mi><mo>∨</mo><mi>q</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mo>∼</mo><mi>q</mi><mo>∨</mo><mi>r</mi><mo>)</mo><mo>→</mo><mo>(</mo><mi>p</mi><mo>→</mo><mi>r</mi><mo>)</mo></math>

don't know what to do next

should we take the negation for the whole thing or just the second one when removing the last implication

@exotic furnace what to do next

[exotic furnace]

Continue to remove the implications yeah

[ruby briar]

we have a doubt there

if we remove the implication should we apply the negation for

or just for

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[ruby briar]

.reopen

[cedar kiln]

✅

[exotic furnace]

Whole thing

[ruby briar]

we got this then

any idea what to do

@rustic totem next

any idea

<@&286206848099549185> anyone knows what to do next

[spice kraken]

$(P\land Q)\lor R \Leftrightarrow (P\lor R)\land (Q\lor R)$

[wraith dagger]

WhereWolf

[ruby briar]

how to use distributive law here

there won't be any use it's just expand we cannot use absorption law after that

$(P

$(P\land Q)\lor R $

$(P\land Q)\lor R \Leftrightarrow (P\lor R)\land (Q\lor R)$

[wraith dagger]

BarneyStinson

[ruby briar]

bro can you also tell us how to use this tool to write equations

[exotic furnace]

Yeah distributive plus a bit of commutative

[ruby briar]

thanks a lot got it

fogot commutative law

*forgot

.close

[cedar kiln]

Channel closed

Closed by @ruby briar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[umbral dew]

ive been trying to solve Q75 from the last 2 hours, but , im so confused, its not a AP, not a GP

[umbral dew]

ive no idea howw to solve this

can anyone help

Q75

[vague rapids]

!status

[cedar kiln]

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

[umbral dew]

bro

like i havent started yet

like i tried to

but its not making anything

[vague rapids]

Do you know the sum of an AP formula?

[umbral dew]

like i cant aplly ap sum formula, not gp sum formulka

[umbral dew]

yeah

[upper ruin]

What's the general term of that AP?

[umbral dew]

a+(n-1)d?

[vague rapids]

The difference of consecutive terms are in AP, so the general term of the series is a quadratic one

[upper ruin]

Oh sorry, it's not even an AP

[vague rapids]

define the polynomial p(x)=ax^2+bx+c
you have first term=5
So p(1)=5=a(1)^2+b(1)+c

[umbral dew]

yes

[vague rapids]

similarly 2nd term=11
so p(2)=11=a(2)^2+b(2)+c

Now with one more such equation, you can solve for a,b,c

aka the coeficients

[umbral dew]

i didnt get it

[umbral dew]

i see an ap building

[vague rapids]

The difference is in AP, not the terms

[umbral dew]

yeah

[vague rapids]

and thus you can conclude the general term of that sequence will be a quadratic polynomial

so we define the polynomial to be ax^2+bx+c

[umbral dew]

and what are

a, b and c

here

[vague rapids]

coefficients

a general quadratic

[umbral dew]

yes

[vague rapids]

the goal is to find them

[umbral dew]

but

how are you relating them with the series given abouve

[vague rapids]

do you know what a quadratic polynomial is?

[umbral dew]

yes

polynomial with

highest degree 2

[vague rapids]

Yes

so like

a+(n-1)d is the general term of an AP

[umbral dew]

yes

[vague rapids]

and you find a,n,d

but here

it is not in AP

It is the result of different values of x in the polynomial ax^2+bx+c

like if we put x=2 we should get answer to be 11

[umbral dew]

yes

okay

and after finding

a,b and c

then?

[molten canyon]

Ok

[vague rapids]

First of all let's find them

[umbral dew]

wwait

let me

okay

so

a=1
b=3
c=1

[vague rapids]

Yes

so the polynomial is x^2+3x+1

plugging in 1, we get 5
with 2, we get 11

[umbral dew]

yes

[vague rapids]

so we need the sum from x=1 to x=20

instead of individually calculating 20 sums

[umbral dew]

yes

how

[vague rapids]

see

[umbral dew]

individual it would be so complicated and time takinhg

[vague rapids]

1^2+3(1)+1+2^2+3(2)+3^2+3(3)+1 and so on

so you can group them

(1^2+2^2+3^2...20^2)+(3(1)+3(2)+3(3)...3(20))+(1+2+3...20)

now you can apply formulas

sum of first n numbers is (n)(n+1)/2

sum of first n square numbers is n(n+1)(2n+1)/6

[umbral dew]

yes

oh yes

i get it

okay

thanks beard

man

[vague rapids]

welcome

[umbral dew]

.close

[cedar kiln]

Channel closed

Closed by @umbral dew

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.
• 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.

[opal vale]

How would I find the new position of the turning point after it’s reflected in y=-1?

[cerulean star]

ok, just do one transformation at a time on the vertex.

so where does the vertex end up after the translation

[opal vale]

Idk how a point gets reflected across somewhere other than x axis

4,3 to where?

[cerulean star]

$T_{<4,3>}(0,0)$

[wraith dagger]

Disorganized

[cerulean star]

yes, (0,0) --> (4,3)

[cerulean star]

recall that the motion of reflection is perpendicular to the line of reflection

[opal vale]

So only the x will change?

So it’s now -4,3?

[cerulean star]

and the image and preimage are equidistant to the line of reflection

[cerulean star]

no

wrong coordinate

[opal vale]

Oh I see

[cerulean star]

no

[opal vale]

But the x axis is perpendicular to the line of reflection?

[cerulean star]

no it is not.

is y= -1 a horizontal line or a vertical line?

(just guess if you don't know)

[opal vale]

Vertical

Nvm

I drew it wrong

[cerulean star]

no

[opal vale]

One sec let me draw it

I thought it was like this

[cerulean star]

doesn't look like (4,3) to me

do this

amke a new grid axis

[opal vale]

I got it

Thanks I understand now

[cerulean star]

good job

[opal vale]

Thanks brother

Cya later

[cerulean star]

cya

[opal vale]

.close

[cedar kiln]

Channel closed

Closed by @opal vale

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.
• 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.

[thin hedge]

what formula are they using here

[thin hedge]

in the video

to get those first 5 terms

[tropic oxide]

do you maybe have a link to the video?

[thin hedge]

sure

https://www.youtube.com/watch?v=nciYP0AdiGo&t=62s

here

[tropic oxide]

aha

[thin hedge]

could i just use the formula a1+(n-1)d

[tropic oxide]

you could, but you're losing sight of the basics.

[thin hedge]

or is it simpler

so the difference is 50

and that is constant throughout

are we solely adding in arithmetic?

[tropic oxide]

"when dealing with arithmetic sequences, is addition the only action that we ever do in general?"

no

[thin hedge]

how do i know when to add or subtract

like in the example shown how did they know to add

is it just directions?

[tropic oxide]

$d = a_n - a_{n-1}$

[wraith dagger]

Ann

[tropic oxide]

d is equal to any term minus the term before it

[thin hedge]

should i j use the formula then

for all of it

cuz it's standard

[tropic oxide]

i am not gonna tell you what you should and shouldn't do

but in my opinion, it is a bad idea to blind yourself to the basics

to go from any term in an arithmetic sequence to the next, you add d.

[thin hedge]

thx so much

[cedar kiln]

@thin hedge Has your question been resolved?

Channel closed

Closed by @thin hedge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[nova snow]

$\log_{5}\left(50\right)-\log_{5}\left(2\right) can be simplified to \log_{5}\left(\frac{50}{2}\right) right?$

[wraith dagger]

water beam

[nova snow]

oh my goodness

$\log_{5}\left(\frac{50}{2}\right)$

[wraith dagger]

water beam

[nova snow]

is equivalent to $\log_{5}\left(50\right)-\log_{5}\left(2\right)$

[wraith dagger]

water beam

[nova snow]

?

[spice kraken]

yes

[vague rapids]

Yes

[nova snow]

what happens to the A and B if i have $A\log_{a}\left(x\right)+B\log_{a}\left(y\right)$

[wraith dagger]

water beam

[glass sky]

put it on the power

1 sec

same goes for B log y to base a

then use the property

cool?

[nova snow]

well im trying to evaluate the expression using log laws and i know that $\log_{a}\left(x\right)+\log_{a}\left(y\right)$ can be simplified to $\log_{a}\left(xy\right)$ but when theres a coefficient in front does it get multiplied together?

[wraith dagger]

water beam

[vague rapids]

$$A\log_{a}x=\log_{a}\left(x^{A}\right)$$
$$B\log_{a}x=\log_{a}\left(x^{B}\right)$$

[wraith dagger]

B-eard

[nova snow]

hm

okay so

[vague rapids]

shitty internet

[glass sky]

what do you think it should be after looking at what you just read

[nova snow]

Would $A\log_{a}\left(x\right)+B\log_{a}\left(y\right)$ equal to $\log_{a}\left(xy^{\left(A+B\right)}\right)$

[wraith dagger]

water beam

[glass sky]

sadly no

[nova snow]

rip

[upper ruin]

Show the steps to get it

[upper ruin]

You only need to apply mechanically the log rules, nothing more

[nova snow]

oh so would it be

$\log_{a}\left(x^{A}\cdot y^{B}\right)$

[wraith dagger]

water beam

[vague rapids]

Yes

[upper ruin]

Yes

[glass sky]

w

[nova snow]

nice

[glass sky]

glhf

[nova snow]

ggs

[slate lintel]

ff20

[ocean mural]

nice

[nova snow]

how about dis $A\log_{a}\left(x\right)-\ B\log_{a}\left(y\right)$ , does it become $\log_{a}\left(\frac{x^{A}}{y^{B}}\right)$

[wraith dagger]

water beam

[slate lintel]

yep

[nova snow]

W

[nova snow]

oh by the way if A or B were to be negative then x or y would just have a negative power right

wouldnt change anything?

[slate lintel]

yeah nothing changes, you just did one with B negative

[nova snow]

alright

[tropic oxide]

[nova snow]

good tex

[tropic oxide]

this output is objectively horrendous

[nova snow]

nuhuh

[tropic oxide]

ok so you are choosing to be contrarian today got it

[nova snow]

If $\log_{a}\left(3\right)=x$ and $\log_{a}\left(5\right)=y$ , find an expression in terms of x and y for $\log_{a}\left(15\right)$

[wraith dagger]

water beam

[nova snow]

Does this just means that i should use the log laws

[tropic oxide]

[nova snow]

wait that came out wrong obv i should but

what does it mean in terms of x and y

[tropic oxide]

write out the log law that you think helps you here

in full

[nova snow]

$\log_{a}\left(x\right)+\log_{a}\left(y\right)=\log_{a}\left(15\right)$

[tropic oxide]

maybe without using the letters x and y to help yourself not get confused

[wraith dagger]

water beam

[nova snow]

🤔

[tropic oxide]

log_a(log_a(3)) + log_a(log_a(5)) isn't equal to log_a(15)

[nova snow]

[tropic oxide]

you cannot badtex me when i did not tex at all.

[nova snow]

yeah i just realized that the expression i wrote means the log of a log

so is it just x + y = log base a of 15

[tropic oxide]

sure is,

but i would recommend underscores as plaintext notation for the base of a log or a subscript in general

x + y = log_a(15)

[nova snow]

wb for $\log_{a}\left(75\right)$ this one seems less obvious on what to write

[wraith dagger]

water beam

[glass sky]

yo can you rewrite your question , not able to follow what your actual question is atm

or just reply to your question

[nova snow]

If $\log{a}\left(3\right)=x$ and $\log{a}\left(5\right)=y$ , find an expression in terms of x and y for $\log_{a}\left(15\right)$

[wraith dagger]

water beam

[glass sky]

ah ic

[nova snow]

ooops

ignore the expression for that

[glass sky]

whats the progress

[nova snow]

If $\log{a}\left(3\right)=x$ and $\log{a}\left(5\right)=y$

[wraith dagger]

water beam

[nova snow]

just this part

[glass sky]

you dont know how to start?

[nova snow]

im not sure what to do with a number like 75

[glass sky]

reberse your aproach , quite litterally

questions would be asked accordingly dont you think

[nova snow]

huh

[glass sky]

1 sec , im getting confused, did you do your question?

or are you modifying your question

[nova snow]

no this is a part of the question

[glass sky]

oh?

[nova snow]

im trying to find an expression in terms of x and y for log base a of 75

[glass sky]

75? in terms of x and y

1 sec

hm lets see

in the first part what did you think to get the answer

[tropic oxide]

consider factorizing 75 btw

[glass sky]

prime factorizing 15 right?

.

[nova snow]

what, like 15 and 5?

[glass sky]

5* 5 * 3

[tropic oxide]

that's one of the many possible ways

given you already know what log_a(15) is it is not even that bad

[glass sky]

fair

[tropic oxide]

unless you're allergic to repeated application of the same idea/law/rule

[nova snow]

2y + x = log_a(75)

oh no wait

should be

x + y^2 = log_a(75)

[tropic oxide]

swing and a miss

you had it right the first time around

[glass sky]

yeah

[nova snow]

what

[tropic oxide]

$\log_a(75) = \log_a(5) + \log_a(15) = y + (x+y)$

[wraith dagger]

Ann

[tropic oxide]

= x + 2y, NOT x + y^2...

[glass sky]

first one was actually correct, in the next attempt you basically squared the log term , not the argument of log

[nova snow]

but x + 2y doesnt make sense

[glass sky]

1 sec

[nova snow]

2 x 5 = 10 which is 2y and since x = 3 then 10 x 3 = 30

[tropic oxide]

first off don't use the letter x for multiplication

second, y is not 5

y is log_a(5)

5 is not the same thing as log_a(5)

2y is not log_a(2*5)

[glass sky]

try to find the values of (i) and (ii)

[tropic oxide]

2y is 2y

[glass sky]

hands on

[tropic oxide]

2y is 2log_a(5), which equals log_a(5^2), which is log_a(25).

log_a(25) is not log_a(10), because 25 is not 10.

5 isn't the same thing as log_a(5).

[glass sky]

or that explains it well yeah cool

[nova snow]

how does 2y mean log_a(5^2)

[tropic oxide]

2y is 2log_a(5), which equals log_a(5^2),

[nova snow]

oh yeah

[tropic oxide]

$2 \log_a(5) = \log_a(5) + \log_a(5) = \log_a(5 \cdot 5) = \log_a(5^2)$

[wraith dagger]

Ann

[glass sky]

^

what did you do here forgot?

[nova snow]

idk i just guessed this one lol

[tropic oxide]

why guess

there's nothing to guess

there are only log laws and their applications

[nova snow]

[wraith dagger]

even order group => solvable
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[dreamy sleet]

oops

,tex .log rules

[wraith dagger]

even order group => solvable

[glass sky]

i suggest you to revise your log properties and stuff, practice some more basic questions if neeeded

[dreamy sleet]

does this help?

[glass sky]

power rule yeah in this case

[nova snow]

thats what im doing right now

thats why im doing these questions

[tropic oxide]

do you have the cheat sheet of log rules in front of you

[nova snow]

yeah

[tropic oxide]

if so then you should not let it leave your field of vision for the duration of your review

[glass sky]

whats a cheat sheet

[nova snow]

i have it written in my book

but i have to turn the pages

[tropic oxide]

a quick reference document

[glass sky]

ah refference notes

ok

mb

[tropic oxide]

get a separate piece of paper and write those rules down where you can see them

[nova snow]

so im trying to just remember them

[tropic oxide]

get a separate piece of paper and write those rules down where you can see them

[nova snow]

o k

[nova snow]

juan more $\log_{a}\left(9a\right)$

[wraith dagger]

water beam

[glass sky]

juan?

[nova snow]

theres um scary a right next to the 9 and how do you get 9 using the given x and y values

[glass sky]

product rule

what does it state

seperate 9 and "a" if "a" looks scary

[nova snow]

log(x * y)

[glass sky]

that is equal to...

just type normally texit is not nessasary here

[tropic oxide]

theres um scary a right next to the 9
get over yourself

[nova snow]

[tropic oxide]

you keep stumbling over your own algebraphobia.

[nova snow]

logaphobia*

[glass sky]

..

[tropic oxide]

no, algebraphobia.

[nova snow]

logphobic

[tropic oxide]

you just described the letter a, which did absolutely nothing to you, as "scary",

[glass sky]

omg we are not having this discussion rn

[nova snow]

if a wasnt assigned a log value then it wouldnt be scary

[glass sky]

also tell me whats log a to base a

IF it is scary get rid of it

also just dont tell me the answer , tell me how

like why log a to base a is what you think it is (if you know it)

[nova snow]

its 1

[glass sky]

if you are unable to do the same , try revising log from the very basics , on what exactly it is and its graph

ok phew you took way to long to respond

[nova snow]

i was looking at the question

thinking how i can do it

[glass sky]

hm?

split 9 and a

[nova snow]

wait wait wait wait

i think i know

let me cook hold on

nevermind

[glass sky]

left is 9 right is a

no?

ok bad joke

[nova snow]

how do i get the variable a into my expression

how do i include it in

[tropic oxide]

wdym

it's already in there

[nova snow]

like i have x and y

[glass sky]

no try to get rid of a

[dreamy sleet]

what did you get?

[nova snow]

but i want a

[tropic oxide]

you know that x and y do not have to be raw numbers right

[glass sky]

...

[tropic oxide]

and a is just a number even if it is not a raw number

[nova snow]

so if i multiplied x by a would that change the whole log thing

[glass sky]

..

what.

[nova snow]

?

[tropic oxide]

you're overthinking it SO hard right now.

if you're able to say log(15) = log(3) + log(5),

then why aren't you also able to say log(9a) = log(9) + log(a)?

[glass sky]

try to make sense out of the given things which you already know

[nova snow]

what if

i did 2ax + y^0

[glass sky]

...

[tropic oxide]

???

[glass sky]

afk

[nova snow]

yeah i dont know what to do here

[tropic oxide]

if you're able to say log(15) = log(3) + log(5),
then why aren't you also able to say log(9a) = log(9) + log(a)?

(bases suppressed, but they're all a.)

[nova snow]

i dont know what expression its looking for

i dont know what to do with the x or y

[glass sky]

try to get log a to base a , from log 9a to base a

DONT THINK OF GETTING X AND Y rn

oops caps

mb

try to remove a

top most priority

i think you are just overlooking the answer and overthinking to somehow get log a to base a in x and y terms

write stuff down on paper , it will help

[nova snow]

im trying but nothing has worked for me yet

[glass sky]

first , dont think log is complicated

you are closing your mind , and overshooting on your question

now lemme present you to some simmilar questions lets see

simplify this for me

[nova snow]

1

[glass sky]

hm??

rethink

[nova snow]

how is it not 1?

log_x(x) always = 1

[glass sky]

can you see a there?

where did that "a" go

bro just disapeared?

[nova snow]

idek anymore

[glass sky]

dont you think?

product rule

[nova snow]

still dont understand how you get that from product

log5a = log5 + log(a)

[glass sky]

hmm

what is log x to base a + log y to base a

[nova snow]

its xy

[glass sky]

?

its log xy to base a

so what is log xy to base a now?

[cedar kiln]

@nova snow 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.
• 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.

[strong pivot]

In english

Z1, ..., zn are the roots of X^n +1

Proove that for every complex polynom P,
XP'(X) = n/2 P(X) + 2/n * (sum from 1 to n of [zk P(X zk)/(zk -1)^2]

We can introduce F = X^p / (X^n +1) where p is an integer different from 0

I have no idea how to do this

[cedar kiln]

@strong pivot Has your question been resolved?

[strong pivot]

<@&286206848099549185>

If anyone is good at polynoms

Any idea is welcome

[cedar kiln]

@strong pivot Has your question been resolved?

[strong pivot]

<@&286206848099549185>

[strong pivot]

.close

[cedar kiln]

Channel closed

Closed by @strong pivot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mighty shuttle]

!status

[cedar kiln]

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

[distant pecan]

1

[mighty shuttle]

when is sin(x)=0

[distant pecan]

idk

[mighty shuttle]

when x=nπ where n is an integer

can you try now?

[distant pecan]

try what

[mighty shuttle]

solving the question

for instance, let's solve for n=1 . we can write sin(x +π/2)=sin(π)

we want x+π/2=π, so x=π/2

[distant pecan]

ok

1 67oprx0c =6]bgB

\yg7

[mighty shuttle]

what?

[distant pecan]

.close

[cedar kiln]

Channel closed

Closed by @distant pecan

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[bold sleet]

It says to find missing side length

[mighty shuttle]

!status

[cedar kiln]

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

[bold sleet]

2

[mighty shuttle]

!show

[cedar kiln]

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

[bold sleet]

Ok well

I know that qp is 14

and q r is also 14

thats all I know

i do see that

its 120 degrees and 60 degrees

I can form a triangle as well

I can split it down the middle

i dont know what rs is tho

[mighty shuttle]

yes, so you can find PR, right?

[bold sleet]

no how

wait what

I need to find rs

right

[mighty shuttle]

finding PR is sufficent, after that you can use trig

[bold sleet]

how do I find pr

i split it down the middle now what

[mighty shuttle]

Construct line PR

[bold sleet]

ok

[mighty shuttle]

as QP=QR, angles QPR and QRP must be equal

and their sum is 120

so you can conclude ∆QPR is equilateral

[bold sleet]

qpr is 120

[mighty shuttle]

yes

as is the sum of angle QPR and QRP

[bold sleet]

ok I see

so pr is 14

[mighty shuttle]

yup

[bold sleet]

so square that and find the legs

with pythagoreum theroum

or something

[mighty shuttle]

no. as angle QPR is 60, angle RPS is also 60(as angle QPR +angle SPR is 120)

[bold sleet]

we have the angles but now what..

[mighty shuttle]

you know trig?

trignometry?

[bold sleet]

no

[mighty shuttle]

hm, I'm not sure if there's a way to do this without trig, sorry

[bold sleet]

its an algebra book

.close

[cedar kiln]

Channel closed

Closed by @bold sleet

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[flint heron]

help

@royal loom

[royal loom]

Don't tag people you don't know

[flint heron]

bro what

no i will

help me rn

[upper garnet]

💀

[flint heron]

@upper garnet

bro help

PLEASE

PELASEEEE

[upper garnet]

in your dreams 😉

[flint heron]

im done

yall tryna see me suffer 💀

[wanton sail]

Please stop spam tagging people

!volunteers

[cedar kiln]

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

[wanton sail]

If you can't respect people's time then you're not welcome here

[cedar kiln]

@flint heron 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.
• 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.

[rare sail]

This has to be a mistake right

the -3 doesnt magically become positive

just simple vector addition but Im still doubting this 😐

[void sand]

looks like a mistake to me

[crystal raptor]

dont doubt yourself

[rare sail]

thanks

.close

[cedar kiln]

Channel closed

Closed by @rare sail

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.
• 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.

@tropic burrow Has your question been resolved?

Channel closed

Closed due to the original message being deleted

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.

[lime wasp]

Prove the second identity in De Morgan's Law. That is, suppose A and B are subsets of R (real numbers). Using U as our universal set, (A ∩ B)^c=A^c U B^c.

[lime wasp]

4. I just want to check up on my proof

[frail needle]

$\int_{0}^{1}x^{2}\sin\left(x\right)dx$

[wraith dagger]

a8d_

[lime wasp]

?

[regal oak]

I just have a question, what do you mean by assuming $(A\cap B)^c$?

[wraith dagger]

Math Is Fun

[regal oak]

You can use integration by parts by the way

[lime wasp]

We are assuming that (A ∩ B)^c, which means that there exists an x such that an element x is part of (A ∩ B)^c.

I think

[regal oak]

So it's basically assuming it's non-empty

There's also this part of the proof where it says $x\in(A\cap B)^c$ means that $x\in U$

[wraith dagger]

Math Is Fun

[lime wasp]

Well were just assuming that (A ∩ B)^c is true, so that we can go from there

Yes

[regal oak]

Oh wait

I misunderstood it

$x\notin A\cap B$ doesn't imply $x\notin A$ and $x\notin B$

[wraith dagger]

Math Is Fun

[regal oak]

But instead imply $x\notin A$ \textit{or} $x\notin B$

[wraith dagger]

Math Is Fun

[lime wasp]

Oh

[regal oak]

To avoid these mistakes, I suggest to use set builder notation to prove these types of statement

[modern compass]

(A ∩ B)^c doesn't have a truth value. It's just an object. This is like saying 'assume box'.
You should start with something in the compliment, like you did a few lines later.

[regal oak]

Also, $x\in A\cup B$ implies $x\in A$ or $x\in B$, not and

[wraith dagger]

Math Is Fun

[lime wasp]

What about, Assume $x in (A\capB)^c?

[regal oak]

Yeah that works

[lime wasp]

I see

Alright Ty

[cedar kiln]

@lime wasp 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.
• 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.

[hallow cedar]

i need help

[hallow cedar]

how do we compare fractions

<@&286206848099549185>

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[rain drift]

Do you have a specific example? What do you mean by "compare"?

[wanton sail]

.close

[cedar kiln]

Channel closed

Closed by @wanton sail

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hoary chasm]

Are point a and b points on the ground

[dire geode]

Where even are a and b in the screenshot

Just link the whole video

It's probably given earlier in the video what they are

[hoary chasm]

The end points of line in image

Horizontal line

[hoary chasm]

Or in air

[dire geode]

Unclear from the image alone

[hoary chasm]

Clear From the calculations?

[dire geode]

Which ones do you think make that clear

[hoary chasm]

The question?

[dire geode]

Which calculations

[cedar kiln]

@hoary chasm Has your question been resolved?

[civic depot]

They are in the air

Using common sense, most of the times birds fly in the air

[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.
• 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.

[glossy jewel]

how to solve this

[glossy jewel]

ik this is a gp

what to do after that?

hello anyone here?

[vestal bear]

what is a gp

[glossy jewel]

Geometric progression

nvm then

.close

[cedar kiln]

Channel closed

Closed by @glossy jewel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stray gazelle]

Can someone help with this?

[tropic oxide]

45% percent

45 percent percent? so 0.45%?

[stray gazelle]

Yeeaaa?

45% of the sample is 1043

[tropic oxide]

are we sure it's 45% and not 0.45%

[stray gazelle]

That's what the question states...

[stray gazelle]

So, I'm pretty sure it's 45%

Why? Is that a problem, or something?

[tropic oxide]

it states "45% percent"

the word percent is written twice

is what im concerned about

[stray gazelle]

I don't think that was intentional. My teacher is known for his typos...

I think he meant 45%

[stray gazelle]

But, without debating the typos of my teacher, would you be able to help?

[tropic oxide]

well ok like

uhh

the confidence interval is our sample mean ± 1.96 times the stdev of the sample mean

would like not to elaborate if possible but there is a readymade formula for this shit

[stray gazelle]

What's the formula?

[stray gazelle]

Thanks, anyway. I guess I'll try find this another way

.close

[cedar kiln]

Channel closed

Closed by @stray gazelle

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.
• 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.

[smoky whale]

Hi guys, can someone please check if I got this correct?

[cedar kiln]

@smoky whale Has your question been resolved?

[junior dome]

when you calculated dV/dr, there are two variables r and h

so it needs product rule

or imo, just write h in terms of r by the given data

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[smoky whale]

.reopen

[cedar kiln]

✅

[smoky whale]

Can you please show me how to apply it?

[junior dome]

you wrote the expression of surface area right?

[cedar kiln]

@smoky whale Has your question been resolved?

[smoky whale]

Yea?

[junior dome]

try to write h in terms of r from there

[smoky whale]

What do you mean

[junior dome]

surface area is 100pi?

[smoky whale]

Yes

[smoky whale]

<@&286206848099549185>

How do I use the product rule with pi

[stuck walrus]

pi is just a constant like any other number

[mortal quail]

ofc u can use it

[smoky whale]

Yes but how do I apply it

[stuck walrus]

you had to use product rule on 2πrh because h is a function of r

[smoky whale]

Now here it is

The formula for product rule

How do I apply it

[stuck walrus]

Can you figure out how

Okay well

f and g are two functions

[smoky whale]

Yep

[stuck walrus]

what are your two functions in 2πrh that are multiplied

[smoky whale]

H and r

[stuck walrus]

(actually you don't have to use it? just do h = kr)

yeah

but actually

try putting h = kr in

then you'll have 2πkr²

[smoky whale]

K is constant?

[stuck walrus]

and you can just pull the 2πk out of the derivative

yes it says in the question