help-23

[fiery merlin]

You can also do it a different way.

You have:

c = 16/x
cx = 16
x = 16/c

You multiply both sides by x to get x out of the bottom.

Then you get x by itself.

[radiant depot]

so it woudl be 16 cos (24)?

[fiery merlin]

Almost.

Remember that c is cos(24 degrees).

[radiant depot]

ohh

[fiery merlin]

Also, c is the bottom of the fraction.

So, cos(24 degrees) should be the denominator.

x = 16/cos(24 degrees)

[radiant depot]

this a little confusing, what would the final equaton be

oh jeez

ok

[fiery merlin]

c and cos(24 degrees) are the same number, so you can write either one.

[radiant depot]

17.514

[fiery merlin]

,calc 16/cos(24 * pi/180)

[radiant depot]

ignore the reaction just so i can go over this again when we are done

oh wait what

what did i do wrong

[fiery merlin]

Oh, wait.

[flat frigate]

Result:

17.514180456097

[radiant depot]

oh haha

[fiery merlin]

I did it wrong.

[radiant depot]

no worries

im gonna try this one now

[fiery merlin]

OK.

[radiant depot]

hwo does this look

[fiery merlin]

Well, think of a kite.

You have you standing there holding the string.

Then the string goes up to the kite.

Then there's someone standing under the kite.

So, the length of the kite string would be between you and the kite, right?

So, label you and the kite on the triangle.

With like M and K or something.

[radiant depot]

oh so flip it

[fiery merlin]

It's like that.

[radiant depot]

oh thanks

[fiery merlin]

Always think about how it would look in real life before filling in numbers.

Or variables.

[radiant depot]

i frogot how kites worked LOL

[fiery merlin]

Oh, OK.

[radiant depot]

is this better?

[fiery merlin]

Yes, that's good.

[radiant depot]

ok cool

so would it be SOH

sin

[fiery merlin]

Yes, that's right.

[radiant depot]

ok could i just do sin^-1 (65) ?

[fiery merlin]

Well, always start with what SOH stands for.

Write out that equation first.

Sine equals Opposite over Hypotenuse.

[flat frigate]

Chai T. Rex

[fiery merlin]

So, write that equation for this triangle.

[radiant depot]

x= x/85?

[fiery merlin]

Almost.

[radiant depot]

or t = x/85

or soemthign liek that

😭

[fiery merlin]

Well, you have Sine equals....

So, you'd write sin(65 degrees) = x/85.

Does that make sense?

[radiant depot]

ohh yes

[fiery merlin]

Don't do the one letter for trig function thing at first.

Always write out the whole thing.

Then, you can take the first letter of the trig function, s.

s = x/85.

You're just doing a substitution.

You have s = sin(65 degrees).

s is just an abbreviation.

[radiant depot]

i see

[fiery merlin]

To remember what it stands for later, you need to have it written out.

That's why you should write out the whole thing first so that you can look back and see what s is short for.

So, you'd write:

sin(65 degrees) = x/85
s = x/85

Now after you solve for x, you can look back up and see that s is short for sin(65 degrees).

Does that make sense?

[radiant depot]

yeah it does

but what wuold sin (65) be?

do i solve that first?

[fiery merlin]

No, there are no variables there.

sin(65 degrees) is for your calculator.

But we don't want to do that part just yet.

[radiant depot]

alright so should i multiply both sides? bc of the x/85

[fiery merlin]

Yes, that's right.

[radiant depot]

oh this is confusing kinda

what goes here = x/85

[fiery merlin]

Oh, first, you write out SOH.

sin(65 degrees) = x/85

Does it make sense how I got that?

[radiant depot]

yeah but what would i take away on the left side

like 85sin(65)=x

OHH

that does make sense LOL

[fiery merlin]

Yes, that's right.

[radiant depot]

in my head that seemed so wrong

[fiery merlin]

First, you write out the SOH part, then you use regular algebra.

[radiant depot]

77.036?

[fiery merlin]

,calc 85 * sin(65 * pi/180)

[flat frigate]

Result:

77.036161898115

[radiant depot]

ayeee

[fiery merlin]

Looks good.

[radiant depot]

ok i got ONE more if u dont midn

[fiery merlin]

OK.

[radiant depot]

ignore the drawing

ill draw one out rq

a new one

[fiery merlin]

OK.

[silent arrow]

Hello I'm new can I ask a 2 math equation it's exponential inequality.

[fiery merlin]

You can. Just go to the Math Help (Available) channels section, pick a help channel, and, as the first thing you say in it, say your problem and where you're stuck.

[radiant depot]

how this look

[fiery merlin]

OK, but there's one problem.

Angles of elevation and depression are like you start off flat.

Then, elevation goes up from flat. Depression goes down from flat.

[silent arrow]

Thanks and I still don't know how to fully use discord I only used it as a archive

[fiery merlin]

So, you'd have a flat line that touches the top of the triangle.

[radiant depot]

oh so shouyld imove 15 degrees to the bottom part

bottom intersection

[fiery merlin]

Oh, OK. There are some instructions on the #❓how-to-get-help channel.

No, not exactly.

[radiant depot]

hmm

[fiery merlin]

You should put your pen at the top point of the triangle.

[silent arrow]

Imma try it thanks

[fiery merlin]

Then draw a flat line to the right.

[fiery merlin]

No problem.

[radiant depot]

i cant figure it out

i can imagine it

[radiant depot]

but i dont knwo where the 15 degrees would go

[fiery merlin]

Like that.

That's a flat line parallel to the ground.

[radiant depot]

so it woudl look like this?

[fiery merlin]

Does that make sense so far?

Nope.

Do you see the line I put parallel to the ground?

[radiant depot]

yea

[fiery merlin]

OK, so the angle of depression is the angle between a flat line and the triangle's line.

So, it would be between the hypotenuse and that parallel line I added.

[radiant depot]

?

[fiery merlin]

The angles are always between a line parallel to the ground and another line.

Does that make sense?

What you have is almost right.

You need 15 degrees between two lines, so you have to draw the parallel-to-the-ground line in there.

[radiant depot]

ok so how would i write the equation

[fiery merlin]

OK, so first you need an angle inside the triangle.

The left side of the triangle is straight up from the ground at a right angle.

So, when it meets the parallel-to-the-ground line at the top, it meets it at a right angle.

[radiant depot]

yes

[fiery merlin]

OK, so the angle inside the triangle plus 15 degrees equals a right angle.

So, what would the angle inside the triangle be?

[radiant depot]

75

[fiery merlin]

Right.

So, now we're dealing with one angle inside the triangle and two sides in the triangle, so we can use SOH CAH TOA.

[radiant depot]

ok so

adj and opp

so toa

so tan (75) = 120/x

[fiery merlin]

Almost.

[radiant depot]

darn it

[fiery merlin]

Which side is the opposite of (on the other side of the triangle) the angle?

[radiant depot]

ummmm

my brain is shutting off can u explain that again

[fiery merlin]

Well, adjacent means next to.

Opposite means on the far side of.

So, we have a 75 degree angle at the top.

Which side is it next to (adjacent to) and which side is it on the other side of the triangle of (opposite from)?

If you need to, you can take a break or sleep.

[radiant depot]

nah i gotta figure this out tn i got a quiz tmrw

[fiery merlin]

Are you tired?

[radiant depot]

120?

[radiant depot]

yesss but its the last question im just tryna get it over with yk

[fiery merlin]

Is 120 the side next to the angle or across from the angle?

[radiant depot]

next to

oh so x

[fiery merlin]

OK, so adjacent means next to, so that's the adjacent side.

[radiant depot]

yes

[fiery merlin]

The x is the side across the triangle from the angle.

So, that's the opposite side.

So, we have TOA.

[radiant depot]

so tan (75) = x/120 ?

[fiery merlin]

Yes, that's right.

[radiant depot]

LOL

[fiery merlin]

Now solve for x.

[radiant depot]

that was it 😭

120tan(75)

= x

[fiery merlin]

Right.

So, what's x?

[radiant depot]

447.846

[fiery merlin]

,calc 120 * tan(75 * pi/180)

[flat frigate]

Result:

447.84609690827

[fiery merlin]

Looks good.

[radiant depot]

YESSS

Thanks for the help i aprpeciate it

[fiery merlin]

You're welcome.

[radiant depot]

are you a teacher ?

[fiery merlin]

No, I've just been helping here for a while.

[radiant depot]

Cool

keep this open tho im gonna write all this down to remember it

[fiery merlin]

OK, make sure to get enough sleep for your quiz.

[radiant depot]

I will thank you

[fiery merlin]

No problem.

[radiant depot]

.close

[safe radish]

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[loud tusk]

Find the length of the shortest path from the point (12, 14) to the point (8, 7) that touches both the x- and y-axes.

[loud tusk]

this is how i think itll look like

Im not sure how to proceed though

the shortest path should be equal to this

[safe radish]

@loud tusk Has your question been resolved?

[ebon fiber]

imagine there is a triangle, and use the two side lengths to create an equation for distance

Correction

Then differentiate implicitly maybe? I didnt think this through before responding sorry

[safe radish]

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[pallid hare]

How to get X Value And disappear Some Numbers??

100(x-200) = 99 ( x-98)

[plucky elk]

Use a(b-c) = ab - ac

[pallid hare]

And disappeared ab x ab ?

[plucky elk]

Yea I don't know what that means

,tex .alg lesson

[flat frigate]

riemann

[safe radish]

@pallid hare Has your question been resolved?

[pallid hare]

Wow

Thx

[safe radish]

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[pallid hare]

✅

[safe radish]

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[hollow forge]

I need help for this question please

[hollow forge]

its seems like no matter what i input it returns wrong

<@&286206848099549185>

please help?

anyone?

please?

[safe radish]

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

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

[hollow forge]

3

!3

im on step THREE

3

[safe radish]

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

@hollow forge Has your question been resolved?

[empty gyro]

!show

[safe radish]

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

[hollow forge]

i put it in interval notation

and

it seems correct

but its being returned wrong

[plucky elk]

What is "it"

[hollow forge]

the answer

[plucky elk]

How did you get your "answer"

[hollow forge]

the wierd string of code looking stuff in the text box

[plucky elk]

Yes people can read that

What people can't read is how you got it

[hollow forge]

hold on i wrote it down on a loose leaf lemme rewrite it

is my handwriting clear enough?

[plucky elk]

When you multiplied by x, you assumed x>0

That eliminates x<0 solutions

[hollow forge]

i mean

[plucky elk]

To include them, assume x<0 so you flip the inequality when you divide by x

[hollow forge]

oooooh

soooo hold on

ahhh iseee

[hollow forge]

Wait

I also have to flip the inequality

Wait no ive mucked it up

[plucky elk]

How did 5 become 5x

[hollow forge]

Got confused for a min

Wait i dont divide with x anywhere

Ignore the x by the 5

[hollow forge]

so you mean when i multiply by x?

[plucky elk]

Oh yes I do

[hollow forge]

So then that should be the correct interval notation right?

[plucky elk]

No

[plucky elk]

.

[hollow forge]

Oh wait

I see now

Thats not right

theres no possible way for 25x to be bigger than 16 cuz x is below zero

[hollow forge]

Sooo like this?

[plucky elk]

Correct

[hollow forge]

so then

Would this be the right answer then?

ooooh im starting to get it now

i have to do both scenarios, when x is above and below 0

to get the right domain

[hollow forge]

thanks alot! i owe you one!

now how do i close this

[fleet condor]

.close

[hollow forge]

Thank you!

.close

[safe radish]

Channel closed

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[empty gyro]

.reopen

[safe radish]

✅

[empty gyro]

@hollow forge

[empty gyro]

You are writing 5x, but the problem shows 5-x

[junior smelt]

Looks like $5\cdot x$ as they’ve typeset it, no? \catthink

[flat frigate]

@junior smelt

[empty gyro]

Oh you are right

Stupid tiny fonts and bad vision

.close

[safe radish]

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[empty gyro]

https://tenor.com/view/patrick-star-binoculars-gif-10150805

[safe radish]

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[orchid garnet]

How do I use 2x-2=x-1 in a graph

[hallow shuttle]

well it only has x so the graph will just be a vertical line

you only have 1 dimension

[orchid garnet]

So I put a dot at 1x?

[hallow shuttle]

no solve for x

[orchid garnet]

Because that's the solution for the equation

[orchid garnet]

Ohhhh

[hallow shuttle]

x=1

[orchid garnet]

Ye

[hallow shuttle]

so it will be a vertical line

at 1

for all values of y, x will be 1

[orchid garnet]

Ok thx

.close

[safe radish]

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[twilit torrent]

dumb question but if i want to square root both these quantities

[twilit torrent]

quantity A = |2m+1|

Quantity B = |2(m+1)| = |2m+2|

That isn't right though, is it

Something wrong with quantity B i feel

[hasty falcon]

it is right

perfectly correct with what you did

[twilit torrent]

which quantity is bigger then?

Quantity B?

Answer is the relationship between two quantities can't be determined

[hasty falcon]

yes it depends upon the values of m

[twilit torrent]

how?

m = -1
QA) |-1| = 1
QB) |0| = 0

it doesn't depend on m

[hasty falcon]

try to compare A = |x| and B = |x+1| for simplicity

[twilit torrent]

ah x = -2

[hasty falcon]

put x = 1 above you have A = 1 and B = 2
put x = -1 above you have A = 1 and B = 0

[twilit torrent]

A = |2| and B = |1|

[twilit torrent]

right ughhh

[hasty falcon]

so you can't say for sure unless ranges or values of m are mentioned

[twilit torrent]

honestly what is the cue though that it can't be determined

like yeah sure i see

but on first glance i thought B > A lol after simplification

Is there a generalizing claim? Or just test numbers

[hasty falcon]

do you know the graph of y = |x|?

[twilit torrent]

yes

|x+1| is a shift 1 unit left yes

and then graphically u can imagine an intersection

[hasty falcon]

yes..that's one way..another way is to have a lot of practice and enhancing your knowledge basis that

for now you can think graphically

[twilit torrent]

|x| and |x+1| yeah easier

but the |2x+1| and |2x+2|

dang i'll just remember from now on ig lol

[hasty falcon]

try to draw it graphically

both of them

[safe radish]

@twilit torrent Has your question been resolved?

[twilit torrent]

sure thanks

[safe radish]

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[terse bane]

How do i find the centre of this circle?

[terse bane]

obv its not a full circle, but where is the locus?

[empty gyro]

If w=a+bi, then arg(w)=tan(a/b)

[grave flint]

don't think so

[empty gyro]

Oops. Arctan, not tan

[grave flint]

I still don't think so

[terse bane]

so i can separate it into this right

arg(z-2i) - arg(z+2i) = π/6

[grave flint]

yeah

[terse bane]

if we let z = x + iy

we then get that

[empty gyro]

God I need sleep.
$w=a+bi\to \arg(w)=\atan{\frac{b}{a}}$

[flat frigate]

SWR

[grave flint]

also only for the first and fourth quadrant ^^

[terse bane]

arg(x + (y-2)i) - arg(x + (y+2)i) = π/6

how do you find circle/radius from this tho

[safe radish]

@terse bane Has your question been resolved?

[terse bane]

<@&286206848099549185>

[terse bane]

.close

[safe radish]

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[lean otter]

How do I evaluate $\ds \int \f1{(x^2+y^2)^{\ff32}} \dd x$ without using hyperbolic/trig substitution?

[peak estuary]

you will probably have to add a smart zero or multiply by a smart one. you could cheat by taking the result and differentiating it. you will only need product and chain rule, so to integrate you only need ibp and u sub to undo that. the issue is probably that the functions for ibp arent visible right now

[lean otter]

yeah cant see anything rn

yikes

okay whatever the trig sub isnt too bad eitherway

thanks

.close

[safe radish]

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[reef quartz]

can someone help me with question a?

[hollow pagoda]

hm whats ur question dude 🙂

sub z in |z| ?

[reef quartz]

(1 + cos(theta))^2 + sin^2(theta)?

and then square root that

[hollow pagoda]

|z| = sqrt(1+cos(theta))^2 + (sin(theta))^2)

yh?

whats ur question where did u fail

[reef quartz]

yes

idk what to do after that

[hollow pagoda]

what u mean?

hint:
use this:
(cosx) ^ 2 + (sinx)^2 = 1

try to solve

[reef quartz]

aight

[reef quartz]

I got 2 + 2cos(theta)

square root of all that i mean

.close

[safe radish]

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[silk token]

whats the difference between a row-equivalent matrix and an equivalent matrix?

[lean otter]

equivalent implies that they represent the same linear transformation

row equivalent implies that you can obtain one from the other via elementary row operations

[silk token]

and how do I notice that, with the hermite form?

[safe radish]

@silk token Has your question been resolved?

[safe radish]

@silk token Has your question been resolved?

[safe radish]

@silk token Has your question been resolved?

[charred acorn]

May I get help

[nova gulch]

to get help, go to an empty help channel and ask your question. unfortunately, this room is still open because the person using it hasn’t closed it.

[safe radish]

@silk token Has your question been resolved?

[safe radish]

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[safe radish]

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[tidal axle]

i really need help getting this answer

[tidal axle]

anyone there?

[fathom hull]

do you know about the vertical line test?

[tidal axle]

kinda

[fathom hull]

okay. the vertical line test just states that if you can draw a vertical (up and down) line on the function have it touch at two points, it's not a function

[tidal axle]

so its not a function right?

[fathom hull]

Yep! not a function because a vertical line can be drawn to intersect the graph at more than one point

so A :3

[tidal axle]

thanks

[fathom hull]

np

[tidal axle]

alright im in help-23 how do i exit? someone else might need this

[fathom hull]

do .close

[tidal axle]

.close

[safe radish]

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[thick silo]

I need help understanding how to convert measurements such as m3 to L.

Based on charts, such as the one below, meter and liter are both "base", but is the calculation different for (what I think is called) cubic meter? How do you convert something that is technically the same "base"?

[plucky elk]

1000 cm^3 = 1 L

https://www.unitconverters.net/volume/cubic-centimeter-to-liter.htm

[thick silo]

So, 0,24*1000 = 0.24 cubic meters is 240 liter?

[plucky elk]

yes

[long maple]

Liter is a base for Volume.
Meter is a base for distance.
m³ is used for volume.
0.001 m³ is 1 liter

[plucky elk]

https://www.unitconverters.net/volume-converter.html

[thick silo]

Thanks - That won't help me during a pen and paper only math exam, tho :,)

[thick silo]

Aah, I see!

Thanks to you both

.close

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[latent wedge]

did i solve this correctly

[latent wedge]

or do i need to express it as y = mx + b

[safe radish]

@latent wedge Has your question been resolved?

[latent wedge]

<@&286206848099549185>

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@latent wedge Has your question been resolved?

[latent wedge]

<@&286206848099549185>

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@latent wedge Has your question been resolved?

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[hoary mirage]

Hey guys

[hoary mirage]

I have a statistic question

I dont know how to use cumulative standardized normal distribution table to find the number from the instruction

can someone tell me?

it says z0.005, but there is no such number in the distribution table

[raven heart]

get a better table then

[hoary mirage]

cant

its all I have

it makes no sense, theres no z0.005 in there

[raven heart]

it's not like you can conjure z0.005 if you don't have a good table or a calc

[hoary mirage]

thats why I need your help on how to get z0.005 in another way

[raven heart]

you can't have a calculator then ?

[hoary mirage]

I dont have the t 89

[raven heart]

what do you have

[hoary mirage]

just the t 30xs

I dont think thats a graphing calculator though

[raven heart]

maybe they have a function for the normal distribution anyway

ok doesn't seem like it has that

[hoary mirage]

hmm let me think

[raven heart]

wait actually

you have to use the table in reverse here

[hoary mirage]

what do you mean

[raven heart]

i.e. find the probability closest to 0.995 (=1-0.005) in the table

the row and the column will give you the corresponding z value

[hoary mirage]

theres no 0.995 on this table

wth

[raven heart]

that's why I said closest

[hoary mirage]

hold on, Im going to show you the z table

[raven heart]

yeah

[hoary mirage]

thats what it look like

[raven heart]

pretty much 0.995

which corresponds to Z = 2.57 or 2.58

[hoary mirage]

how would I type it in the calculator? Because I noticed that the numbers are located at z=2.5

[raven heart]

type what in the calc

[hoary mirage]

because you said we should find 0.995 right? we found it but we wouldnt get z=2.57 or 2.58 from that table. Those numbers are in the same row as z=2.5 on the lower left size

[raven heart]

yeah

[hoary mirage]

sorry, Im not good with this

[raven heart]

and the column corresponds to the 2nd decimal

[hoary mirage]

OHH

[raven heart]

0.07 and 0.08

[hoary mirage]

I got it now

thanks, I think I understand it a little

[hoary mirage]

wait but how do we know how to get 2.575

the question is asking us to round to the nearest 3 digit

[raven heart]

well then you're screwed

although averaging the two shouldn't give too bad of a result tbf

since the average of 0.9949 and 0.9951 is 0.995

but with your table you won't be able to get much more than that

@hoary mirage

[hoary mirage]

thanks

[hoary mirage]

I understand now, tyvm

!done

[safe radish]

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[hoary mirage]

.close

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[red moth]

I have a question about finding the range of an inverse image of a set

[red moth]

specifically part c

I already know the inverse image of three is a set that contains 1 and 5

Just not sure what it means by the range of f

Does it mean all of the values that f(1,2,3,4,5) can take?

[neat kiln]

Can you show your arrow diagram ❤️

3

[red moth]

Yeah it might take me a sec though

It's a bit messy

This is the definition my textbook provides. Just want to make sure I am interpreting it correctly

Hello? @neat kiln

.close

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[potent solstice]

Hey everyone! I've been working on a differential equation and came across a step where they raised both sides of the equation to the power of
e. I'm a bit confused about why this is done. Can anyone explain the reasoning behind raising everything to the power of e? I'd really appreciate any insights or resources on this. Thanks!

[potent solstice]

I believe I now understand any e function that is raised to the power of In will be the value contained inside of In()

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[shrewd topaz]

​Next, consider other asymptotes. The type of asymptote depends on comparing the degree of the numerator and denominator of the rational function in lowest terms. If the numerator has lesser degree than the​ denominator, then there is a horizontal asymptote

what does this mean^

like if there's x/x^2 then there's a horizontal asymptote?

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[wanton otter]

hi

[wanton otter]

Can anyone please explain this?

I am confused on what exactly it is asking

please help

is it -10?

Just not used to that box thing

[reef estuary]

yes

[reef estuary]

the box is just a made-up operator for this question

[wanton otter]

ok thanks

I appreciate it

Never seen that before

[reef estuary]

all you have to do in these questions is see what the box means - in this case it means 2x - 3y

[reef estuary]

it's not a real operator so you wouldnt have seen it before

[wanton otter]

Haha good point

One other question if it is ok

?

[lean otter]

1/9 ?

[wanton otter]

okk I was thinking that but wasn't sure

Can I ask how you got that

[reef estuary]

how did you get it?

you said you were thinking that, so what made you think of 1/9

[wanton otter]

lol it was just a guess

It seemed like the most reasonable transition between 1/4 and 1/16th

considering the options

[reef estuary]

do you realise that all the other terms are 1/(perfect square)

[wanton otter]

Not a very good reason

Oh

ohh

[reef estuary]

is there anything you can notice now

[wanton otter]

haha

yes

that makes a lot more sense

thank you

[reef estuary]

np

[wanton otter]

Logic is not always my strong suit

Ok

Just to check

sorry if I am spaming you with pretty basic ones at this point

[reef estuary]

yes it is 80

did you guess this or do you know the reasoning?

[wanton otter]

This one I did know the reasoning

This one I do not

Nor this

Sadly trig identities are not my forte

Ik the second one isn't trig

[reef estuary]

do you know that csc is 1/sin

[wanton otter]

No

[reef estuary]

well

[wanton otter]

Oh

wait

that is dumb

right inverse sin is 1/sin

I wasn't thinking there

I think you can see part of my problem

[reef estuary]

🤣 it's alright

yeah so which other expression means 1/sin

[wanton otter]

hmmm

don't quote me on this

I am going to hazard a guess for A?

wait

hm

[reef estuary]

no guessing

tell me why A

[wanton otter]

Well I think I may be incorrect looking at it now. But because if I remember Tan equals 1

And sin^2+cos^2 equal tan

so it would be 1/sin? which is csc?

That is just my tenative reasoning

[reef estuary]

sin^2 + cos^2 is not tan

sin^2 + cos^2 = 1

[wanton otter]

oops

ah well

that is good to know

[reef estuary]

but you somehow got the right answer with the wrong reasoning

[wanton otter]

yay!

haha

[reef estuary]

sin^2 = 1 -cos^2

[wanton otter]

To wrongs can make a right it appears

[reef estuary]

so 1/sin = 1/sqrt(1-cos^2)

[wanton otter]

ok awesome

[wanton otter]

Any advice for this

Btw thank you so much for your help. I know you are volunteering and busy so I appreciate it

[reef estuary]

what is CG + GD

using the values given

[wanton otter]

I would hazard to say 7?

[reef estuary]

yes, 12 - 5

so what would (CG + GD)^2 be

[wanton otter]

49

[reef estuary]

$(CG)^2 + 2(CG)(GD) + (GD)^2 = 49$

[flat frigate]

nalin

[reef estuary]

what is (CG)^2 + (GD)^2

using pythagoras' theorem

[wanton otter]

Ok I know this is going to sound awful

But I am blanking

would you mind showing me how

[reef estuary]

how I got this?

[wanton otter]

Like to use it in this context

[reef estuary]

oh ok so you have a right angled triangle CGD, with the two short sides being CG and GD, so as per pythogoras' theorem, the sum of squares of the short sides is ... what?

[wanton otter]

The sum should be 49 right?

hmmm

I apologize I am unsure. It has been about a year since I have done this

[reef estuary]

it's alright, just tell me what you would find by finding the sum of squares of the short sides

dont think of it in this context yet

just tell me what we can find using that

would we not find the square of the long side?

$a^2 + b^2 = c^2$

[flat frigate]

nalin

[reef estuary]

a, b are our short sides

[wanton otter]

hmmm

ok

so 3 and 4 then

because if the hypotenuse is 5

5 to the second power is 25

and 3 x 3= 9, 4x4=16

25?

Idk I just kind of pieced that together

[reef estuary]

no

[wanton otter]

darn

lol

[reef estuary]

you're right about the 25 part

but you cant assume it's 3 and 4

let's take the 25 and continue working from here

[wanton otter]

ok

[reef estuary]

so (CG)^2 + (GD)^2 = 25

[reef estuary]

from this,

we can tell now

that

$2(CG)(GD) + 25 = 49 \Rightarrow (CG)(GD) = 12$

[flat frigate]

nalin

[reef estuary]

the area of a triangle is 1/2 * b * h so we want to find 1/2 CF * GD. Since CGD and FGD are congruent, 1/2 CF = CG

so we have to find CG * GD overall

[reef estuary]

which we just did

[wanton otter]

So it is 12

[reef estuary]

yes

[wanton otter]

ok great

last question if it is ok to ask

I guess technically 2

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[unreal kindle]

Hello, x and y are two elements of a group G; the order of xy is finite and we call this order a. I need to show that $(yx)^{a+1} = yx$

[flat frigate]

lilisworld

[warm stirrup]

you can expand out (yx)^(a+1)

as yxyxyx...yx

and then try to find (xy)^a within that

[unreal kindle]

ok

@warm stirrup ok thanks i found it so now they ask what is the order of yx so i said a, is it because it's a cyclic group?

[warm stirrup]

you can just take (yx)^(a+1)=yx and multiply both sides by (yx)^-1

[unreal kindle]

ok

[unreal kindle]

and now it asks that if we assume xy=yx and the order of x is m, the order of y is n; show that a divides $mn$

[flat frigate]

lilisworld

[unreal kindle]

i think we use lagrange theorem?

[safe radish]

@unreal kindle Has your question been resolved?

[unreal kindle]

@warm stirrup

so i tried counting all the possible elements of <xy> and for some reason i found mn elements

which is clearly wrong because a should divide it, not be equal to it

<@&286206848099549185>

i counted the elements like this: 1(for e)+(m-1)(n-1)(for the combinations of all the product of y and x)+(m-1)+(n-1)=mn=a?

[unreal kindle]

.close

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[unborn moss]

can someone help me with understanding this problem with Bayes theorem

[unborn moss]

In the town of Maplewood a certain type of DVD player is sold at just two stores. 27% of the sales are from store A and 73% of the sales are from store B. 2.2% of the DVD players sold at store A are defective while 4.9% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A?

im stuck on this problem

[lean otter]

What can you pick as A and B here?

[unborn moss]

a. 0.858

b. 0.166

c. 0.142

d. 0.022

?

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[tacit cosmos]

So conceptually in this question

We are basically multiplying the area (shaded region in the xy graph) to the height function, which is 2xy.

.close

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[desert iron]

Are there functions that we cannot integrate

[tacit cosmos]

Yes

consider 1/x

Or 1/x^2

[hybrid wedge]

We can integrate 1/x and 1/x²

[tacit cosmos]

Or e^x^x?

[reef estuary]

yes

if you mean find the indefinite integral of

for example, $e^{-x^2}$

[flat frigate]

nalin

[desert iron]

We can't integrate this at all?

[hybrid wedge]

We can

[tacit cosmos]

Gaussian integral

aka normal distribution

[desert iron]

So are all functions integratble?

[hybrid wedge]

Discontinuous functions are not integrable

[crimson field]

Any function which isn't bounded on a closed interval isn't Riemann integrable.

[crimson field]

False.

[hybrid wedge]

Are they integrable?

[reef estuary]

i mentioned indefinite integral

[crimson field]

Sometimes, yeah.

[reef estuary]

it is not indefinitely integrable

[reef estuary]

bruh no

[desert iron]

What about $\frac{1}{x+sin^2(x)}$

[flat frigate]

Hamdy Hisham

[crimson field]

All step-functions are integrable for example.

[desert iron]

Is that integrable

[reef estuary]

i believe it isnt

[desert iron]

There must be a crazy mathsmetician who found out how to do it

[crimson field]

It will be integrable over any interval which doesn't contain 0. For, it is continuous everyone except x = 0.

[reef estuary]

some functions just dont have an antiderivative

when im talking about "is it integrable", i mean does it have an indefinite integral

[desert iron]

So what's the anti derivative of it or how to find it

[reef estuary]

over intervals, most functions are integrable

[desert iron]

I'm talking about the same thing

[crimson field]

Well that's a harder question. The integral can exist even if you can't find it's antiderivative.

[desert iron]

So my question is :
Do all functions have anti derivatives ?

[desert iron]

Ok it exists but can you find it ?

[crimson field]

I'm not sure.

[reef estuary]

no, not all functions have anti-derivatives

[crimson field]

Numerical methods or a more careful analysis.

[reef estuary]

dude can you stop confusing him, he's talking about indefinite integrals

[crimson field]

I'm sorry your brain can't comprehend people can think of two things at the same time.

[desert iron]

So i can find the area under this curve without knowing the anti derivative??

[hybrid wedge]

Can anyone just tell me if we can integrate a particular function over some interval then why it can't be integrated indefinitely

[desert iron]

🤯

[crimson field]

Sometimes, yes. It's just not always easy, sadly.

[desert iron]

Are talking about Riemann sum?

[reef estuary]

?

[crimson field]

If you know the integral exists you can go to the definition of the definite integral to sometimes find it's value. For, if the integral exists then you know the limit exists and is unique to determine it's value.

[crimson field]

Did I confuse you?

[reef estuary]

what did i even do, why are you so mad?

[crimson field]

Just looking through my book and it says that any continuous function has a primitive (antiderivative) so if it's continuous you know it exists.

[reef estuary]

oh, can you help me with one thing then?

how would i find the primitive of

$\frac{\sin x}{x}$

[flat frigate]

nalin

[reef estuary]

Ah I see, I was wrong. @desert iron any continous function does have a primitive, just that in some cases, the antiderivative is not an elementary function

I apologise for the error on my part

[desert iron]

What's elementary functions?

[desert iron]

Np

[reef estuary]

basically what you come across in everyday math, like sinx, x^2, etc

they're defined as functions that take sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, including possibly their inverses

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[safe radish]

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[stiff aurora]

can any1 tell me a gud conic sections and straight line online source which teaches from basic level

[plucky elk]

khan academy

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[versed anchor]

Anyone know how to solve (a)? Im using what my lecture gave, but I kept getting other answer

[dapper venture]

!show

[safe radish]

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

[versed anchor]

Bruh i cant rotate this

[dapper venture]

...

do you know what inf mean

[versed anchor]

Infimum?

[dapper venture]

not the name

the definition

[versed anchor]

Kinda blurred on that, but i think it's monotone decreasing, the sequence is bounded below

|an - inf(an)|>epsilon, for every n is over N

[dapper venture]

intuitively infimum is the greatest lower bound

is 1 a lower bound for the sequence?

[versed anchor]

No?

But 0 is?

[dapper venture]

yep

it have nothing to do with montone decreasing

[versed anchor]

Ahhh

Aight

My mistake there fr, accidentally drew a wrong graph for inf, which is actually for sup

Thx btw

[dapper venture]

no problem

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[timber basin]

Hints please

[peak estuary]

how many people die in each town?

[timber basin]

1258 and 12563

@peak estuary

[peak estuary]

how many people live in both towns combined?

how many people die in both towns combined?

[timber basin]

778214 total people

13821 died

[peak estuary]

no

if in one town already over 12k people died then that cant be true

[timber basin]

Opps sorry

Misspelt 1

What next?

[peak estuary]

now you can calculate the death rate of both towns combined

[timber basin]

How?

I am getting 18 people over 1000 died

[peak estuary]

yeah

uhm

did we make a stupid mistake?

[timber basin]

I don't know

Please check and tell me if I did

[peak estuary]

if yes then I am not seeing it

[timber basin]

So 18 is correct?

As we can see it was 14.3 and 18.2 so between 18

[peak estuary]

18 should be correct

[safe radish]

@timber basin Has your question been resolved?

[timber basin]

Do you know any short method for this question?

I solved it with calculator

[peak estuary]

well in principle you could do all of these by hand. maybe they wanted you to notice that 16 is the only number between 14.3 and 18.2 and therefore take that one?

[safe radish]

@timber basin Has your question been resolved?

[safe radish]

@timber basin Has your question been resolved?

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[twilit torrent]

I can't combinatorics, could someone help me clarify how to do this?

[twilit torrent]

Quantity A: (40C5)/ (40P5)?

Quantity B: (1/11)^5 * 1/4?

[buoyant shadow]

B is correct, what you did for A equals 1/5!

that's wrong

[safe radish]

@twilit torrent Has your question been resolved?

[twilit torrent]

i know the numerator for A is correct (i guess) but not sure what goes for the denom tbh

[buoyant shadow]

hint, B is also 1 / (11^5 × 4)

[twilit torrent]

i'm not sure what to do with that

[buoyant shadow]

the numerator is 1

[twilit torrent]

yeah

[buoyant shadow]

in both cases there's 1 winning combination

[twilit torrent]

right i get it

i just want to calculate A though

rather than get the answer

through comparing denominator

[twilit torrent]

Hmm okay i see what you mean

A = 1/ 40C5

B = 1/(11^5 * 4)?

[buoyant shadow]

yeah

[twilit torrent]

i see interesting, so would i just list out the "total ways" in these kinda questions

and then append a 1 in the numerator

[buoyant shadow]

not always 1

[twilit torrent]

i mean yeah depending on the circumstance

[buoyant shadow]

yes this shouls always work

[twilit torrent]

sure thanks

.close

[safe radish]

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[south harbor]

(x+3) is a factor of 2x⁵ + 4x⁴ +3x³ + kx² -14x + 3

[south harbor]

I really did forget how to do this

And also why is there a k?

I can just divide it

But the k

[thin bridge]

supposedly k is a constant for you to determine

[quiet juniper]

Synthetic division

[thin bridge]

overcomplicating

[south harbor]

Synthetic will work?

[thin bridge]

factor theorem can be applied directly to determine k

[quiet juniper]

yeah ur right

[thin bridge]

synthetic will work, may be more efficient if you're then also asked to factorise fully / determine othe roots

[quiet juniper]

I just read "factor" and thought "oh he wants to factor x+3 out of this" tbh

[south harbor]

Can i do synthetic division and that will be my answer?

[thin bridge]

what's the end goal

just to determine k or do other stuff as well

[south harbor]

Find the other (number)(x+3)+remainder = the dividend

Well, i could find k too

Can i put kx² as 1?

[thin bridge]

doing the initial synthetic division,
you should have a quotient and remainder with k in it

no

k is k

[south harbor]

1k?

[thin bridge]

if you insist

[south harbor]

Or just k

[thin bridge]

k = k = 1k

writing the 1 is unnecessary

[south harbor]

Yeah

[thin bridge]

doing the initial synthetic division,
you should have a quotient and remainder with k in it
and since you are told (x+3) is a factor,
you want to know when the remainder is 0
allowing you to determine the value of k
which can then be used to get your quotient

[south harbor]

X=-3

Okii so now i got -27k

I multiply it by -3

Then i still put k?

81k

[thin bridge]

what?

Okii so now i got -27k
where's that coming from

[thin bridge]

multiplying by -3, you'll get 81k, so that's the value you put

[south harbor]

But there will be more than 1 k

[thin bridge]

yeh, 81 of them

81k is just an expression, the algorithm works the same way

[south harbor]

Like ill get ,x⁴ + kx³ + kx² - kx +x

[thin bridge]

no?

[south harbor]

Or something like that

[thin bridge]

no?

[south harbor]

Like there will be 2 k

Or more

[thin bridge]

no?

[south harbor]

Kk

Kkkk

Wait lemme jus

[thin bridge]

continue the division algorithm

[thin bridge]

no

you fked up the order of operations

-14 + 81k isn't 67k

[south harbor]

Oh

Breh

[thin bridge]

adding the number 5 (just the number 5 not 5 apples)
to 1 apple
doesn't give you 6 apples

[south harbor]

Hauh?

[thin bridge]

that's essentially what you did

forcibly combined stuff that aren't like terms

[south harbor]

Oh

[thin bridge]

i used apples and something that clearly isn't apples to make a ridiculous example

[south harbor]

What's the right procedure??

[thin bridge]

if you can't combine the terms, just leave the expression/sum/difference as is

[south harbor]

81k - 14 or -14 + 81k?

[thin bridge]

yes

[south harbor]

Woah

Ight ight

[thin bridge]

also 1 sec

didn't catch the same mistake you made earlier

k - 27 isn't -27k

so you'll need to fix that first