help-27

[winter patrol]

yes, and now it has your name on it

[main gull]

Yes, it's your channel now

Post your question

[restive river]

Ohhhh I see

Thanks bro

[wooden wraith]

Do you know how to find the circumference?

[restive river]

Nah💀

[wooden wraith]

C = 2*pi*r

The arc length of one slice is just one sixth of the circumference

[restive river]

I see

[devout snow]

@restive river Has your question been resolved?

[restive river]

Eh, not rlly, but I'll figure it out

Thanks everyone

Um

How do I leave the space

💀

[devout snow]

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[restive river]

Oop

There we go

[devout snow]

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[heady canyon]

A student saved 25 on Monday and doubled his saving each day, respectively. How much did he save this coming Sunday?

[heady canyon]

wait so like 2nd day is 50 and 3rd day is 100?

[modern stump]

Based on the question I think so

So prob 1600 by Sunday?

[heady canyon]

ohh

thank u sm 💓 have a nice day

.close

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[broken mason]

for b my answer was 24 or 8+8+8, can anyone verify my answer?

[devout snow]

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[restive river]

yo

given that you have this shape

find the shaded region

if the chord is 12 cm and is a tangent to the smaller circle

Honestly I have no clue how to find it

I'd start off by creating a triangle, with side 6, and the other 2 sides being radiuses

[tall stirrup]

is the area variable or you'll need a number

[restive river]

answer is 36cm^2

so i'll need a number

[tall stirrup]

is there anything else given

[restive river]

yeah you see the chord

it's 12 cm

and it's tangent to the smaller circle

[green river]

if there's nothing else given then you can set free variables to whatever you want lol. set the radius of the smaller circle to 0

[tall stirrup]

radius of big/small sphere, etc

[tall stirrup]

exactly

[green river]

they cancel

[restive river]

i'm little confused

if we set r^2 to 0

then your diagram shows R^2 = 144

so R = 12?

[green river]

how come R^2 = 144?

[restive river]

in your diagram r = radius of smaller circle and you set that to 0

so in your equation if we substitute for r = 0 we get R^2 = 144

[green river]

the chord is 12 cm

half the chord is 6 cm

do i understand your question correctly?

[devout snow]

@restive river Has your question been resolved?

[restive river]

yep got it ty

[devout snow]

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[devout snow]

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[bold onyx]

<@&286206848099549185>

[chrome girder]

!15min

[devout snow]

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.

[chrome girder]

use trig functions

sohcahtoa

[bold onyx]

im using tan ?

[chrome girder]

for which one

[restive river]

for which one

[chrome girder]

ha

[restive river]

lmfao

[bold onyx]

A

[chrome girder]

A is opposite and hypotenuse

[lyric hornet]

$\sin\theta=\frac{opp}{hyp}$, $\cos\theta=\frac{adj}{hyp}$, and $\tan\theta=\frac{opp}{adj}$

[woven radish]

XxMrFancyu2xX

[lyric hornet]

I assume you know the ratios but I just wrote them, use these to compute x

You have the angle

find the sides, and one of these sides is x

set up the ratio and solve

[bold onyx]

9 over 48

[lyric hornet]

48º is the angle, theta

9 and x are both sides

also take a look at what sides you have

x is the hypotenuse

and 9 is the opposites side

so which trigonometric ratio should you use?

@bold onyx (sorry for ping)

[bold onyx]

it’s okay

[lyric hornet]

so what trig ratio would you use?

[slender wolf]

if you have all of the sides

then you can use any of the trig functions

but in this case

you can only use a specific one for each question

[devout snow]

@bold onyx Has your question been resolved?

[devout snow]

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[zenith jacinth]

expand the first one

[rich valley]

So… sin^2(t) - 2sin(t)cos(t) + cos^2(t) =1 - sin(2t)

[zenith jacinth]

yes

you forgot something

no

(a-b)² = a² - 2ab + b²

[rich valley]

Can I simplify the 2ab part to sin2t?

[zenith jacinth]

2sin(t)cos(t) = sin(2t)

[rich valley]

Got it

[magic thicket]

use simple identites to prove complicated ones

[rich valley]

What about the second one, do I simplify cot(t) to 1/tan(t)

Or do I multiple by tan top & bottom

[magic thicket]

I'd start by rewriting cot(2t) because I have no clue what that is otherwise

and then see

[zenith jacinth]

$\frac{\cos(t)}{\sin(t)} - \frac{\sin(t)}{\cos(t)} = \frac{\cos²(t) - \sin²(t)}{\sin(t)\cos(t)} = \frac{2\cos(2t)}{\sin(2t)}$

[woven radish]

Ｈｅｒｅｌｓ

[rich valley]

.close

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[ashen vault]

What is this sign, and what does it mean?
Entire theorem I took it from:
Let phi: G -> F be homomorphism of groups. If `K <| F, then phi^(-1)(K) <| G

[ashen vault]

it's from abstract algebra

[restive river]

normal subgroup

[ashen vault]

Thanks a lot

.close

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[formal berry]

Hello, I need help understanding how to compute the SVD of a rectangular matrix. Specifically, how to deal with U and V when the eigenvalues of S are repeated. The case is this matrix: https://www.wolframalpha.com/input?i2d=true&i=svd+decomposition+of+{{0%2C1%2C0%2C0}%2C{1%2C0%2C0%2C0}%2C{0%2C0%2C1%2C0}}
I'm using a math library in PHP that doesn't quite deal with it properly. and so I'm getting a identity matrices for U and V and a non-diagonal S that is identical to the original matrix. Full question is here (hope linking to stackexchange is ok): https://math.stackexchange.com/questions/4686323/svd-picking-u-and-v-when-singular-values-are-repeated

[devout snow]

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@formal berry Has your question been resolved?

[formal berry]

<@&286206848099549185> sorry to ping :/

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@formal berry Has your question been resolved?

[formal berry]

Just realized this is not the proper place for this question :(

.close

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[fathom hare]

help pls

[devout snow]

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

[fathom hare]

1

i know its 6200 days

but idk where to go from there

[prime lily]

Well they sleep 20 hours in one day

So in 6200 days they sleep 20x6200 hours

[fathom hare]

oh im dumb

[prime lily]

But it asks for it in scientific notation

[fathom hare]

would it be 1.24 x 10^5

[prime lily]

Yes

Good

[fathom hare]

tyyy!

[devout snow]

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[restive river]

yo

[restive river]

Assume you have no calculator

and 6 minutes

And very limited mathematical ability

How would you solve this:

What is the number that is 300 places to the right of the decimal point in the decimal expansion of 1/13

[pseudo basin]

the expansion of 1/13 is periodic, so find its period by long division of 1.000... by 13.

[restive river]

forgot how to do long division

[pseudo basin]

or rather, find both the repeating part itself and its length, since both are relevant

[pseudo basin]

... then p sure you're screwed

[restive river]

alright got it i'll check out some video on long division

and try it out

ty

[devout snow]

@restive river Has your question been resolved?

[restive river]

ya I got it

thank you for your advice

[devout snow]

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[devout snow]

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[wintry walrus]

claim

[wintry walrus]

a water tank can hold 180k liters of water. the tank recieves 5000 liters an hour, and outputs 5000 liters an hour.

after a day, 1% of the water is dirty. how many liters of dirt is in the tank after 22 hours?

i have gotten the differential equation

y´ = 50 - y/36

then idk what to do, and in the explaination it just says "solving with geogebra give ---"

does anyone know how to use this feature? 💀

i think it has something to do with this

[devout snow]

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[wintry walrus]

.close

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[coral wraith]

@lusty sapphire this is from yesterdays from. i got that y < 3/4. not sure how to use that

[lusty sapphire]

You'll have to remind me of the convo

[coral wraith]

#help-34 message

[lusty sapphire]

How'd you get y<3/4?

!show

[devout snow]

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

[coral wraith]

Hm that’s a mistake

I get
(0.25*0.25/z-1)/(0.25/z-1) < y

@lusty sapphire

[devout snow]

@coral wraith Has your question been resolved?

[coral wraith]

You there?

@lusty sapphire i get (z-0.0625)/(z-0.25)<y

not sure how it helps

[lusty sapphire]

I'm not seeing how you got that

[coral wraith]

i get
-(1-3z)/(4z-1)<y

[coral wraith]

i had a mistake when expanding

[lusty sapphire]

That looks more right

[coral wraith]

How does it help?

[lusty sapphire]

You're assuming y(1-z)>0.25

[lusty sapphire]

But you showed y is greater than this whole thing. So if you show that this expression times (1-z) leads to a contraindication, you are done

[coral wraith]

Oh

I See

Thanks!

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[proud perch]

ok so i solved the equation:

A^T A x = A^T b

and found the solution set to be x = (3,-5,-2,0) + t(0,1,0,1)

i don't understand how to find the best approximation though

<@&286206848099549185>

[devout snow]

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[fallow echo]

I need to complete the proof for this trig function: $cos(x+pi/4) + cos(x-pi/4) = sqrt2 cosx$

[fallow echo]

$cos(x+pi/4) + cos(x-pi/4) = sqrt2 cosx$

[woven radish]

zesty&festyII

zesty&festyII

[fallow echo]

1. I started by applying the sum to product formula

where I got to $2cosx * cospi/4$

[woven radish]

Stephen

zesty&festyII

[fallow echo]

I don't know why I can't do these things right.

[quaint citrus]

Put a backslash before trig functions, sqrt, and pi

[fallow echo]

Thank you

So, I used (x+pi/4) as "a" and (x-pi/4) as "b"

$\2cos(x+\pi/4/2)+(x-\pi/4/2) cos(x+\pi/4/2)-(x-\pi/4/2)$

[woven radish]

zesty&festyII
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fallow echo]

dammit

$\2cos(x/2+\pi/4/2)+(x/2-\pi/4/2) cos(x/2+\pi/4/2)-(x/2-\pi/4/2)$

[woven radish]

zesty&festyII
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fallow echo]

I don't know what I'm doing. agh.

ANYWAY. basically, I got down to 2cosxcospi/4

.close

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[restive river]

I'm not quite sure where to go when x is on top or if I'm doing this right for the shark one.
I tried setting it up and a few different ways and I really thought I got the shark one but the number ended up larger than the hyp which I don't think is right

[rain hornet]

cos(76) = x/38

x= 38*cos(76)

remeber its adjacent over hypotenuse for cosine

you messed it up by flipping the fraction

[restive river]

Ohh, that makes a lot more sense

I'm not quite sure how to start these, I've tried a few different things but it doesn't provide an angle so I don't really know

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[heavy cliff]

i think its js sinA = 7/hypotenuse to find hypotenuse, u have to use tan to find the angle of B which is tanB = 24/7
once u find the angle u can find the side of hyptonise by doing cos(angle of B) = 7/hypotenuse
then when u find hypotenuse u js sub it back into sinA = 7/hypotenuse

does that make sense sorry if i didnt explain it clear enough 😭😭

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[agile narwhal]

is there anybody familiar with linear programming?

[orchid glade]

ofc

[agile narwhal]

my main concern is how to deal with undirected edges, im given an undirected graph

how to determine which are inocming and which are outgoing when they are undirected

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[forest hound]

trying to see if this is correct?😭

[restive river]

Look at the first line

[forest hound]

soo 1,6,-7

it just goes in order?

[restive river]

Yep

Well technically not necessarily

[orchid glade]

i think no

[restive river]

The first index corresponds to your first variable, second index to second variable, etc...

And in this case the variables are x, y, z

[orchid glade]

just know that the first row r x s then y z then constant

[forest hound]

right

[restive river]

How the question is arranged you have x and y and z in order but they could pull a pranksy and give you ...x+...z+...y

[forest hound]

?

[restive river]

Hmmm no

Again, the first number corresponds to x, second number to y, etc

So the 1 means 1x, not 1y

Last time the -7 was missing, now the 4 is missing, don't you think that implies something went wrong?

[forest hound]

sooo 6y

-7z

[restive river]

Mhm, yep

And constant is...?

[forest hound]

4

[restive river]

You got it

Unless you have more questions you can now close this channel by typing .close

[forest hound]

thanks!

[restive river]

Wait a second

No

You changed the other lines

They were correct already

[restive river]

Don't forget to change them back now that you know how it works

[forest hound]

i think i fixed it

[restive river]

Yep

All good

[forest hound]

thanks!

.close

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[magic turret]

I had a couple questions about independent graphs

[magic turret]

is an independent set is a subset of the vertices of a graph, which contains vertices which are isolated from the others?

in that case for complete graphs Kn, should the value of the independent set always be 1, since every vertex is connected to all others except itself?

additionally, why should the product of the chromatic number and independent set value be greater than or equal to the number of vertices n?

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[restive river]

Hey

[restive river]

What would you do if you cannot using the special triangles for an evaluate question

For example 3pi/13, but you cannot use the special triangle as you don’t get an reference angle of 30,60,90, or 45,45,90

I know what to do when the special triangle is in effect, but I have almost no clue on what to do when it’s not in effect

use a calculator

[arctic field]

memorise sin(1 degree)

[restive river]

13 doesnt divide 360

I think

,calc 360 mod 13

[woven radish]

Result:

9

[restive river]

,w sin(pi/13)

[woven radish]

Results provided by WolframAlpha

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

Requested by Toby#2275

[polar chasm]

already checked that. No closed form

[arctic field]

yikes

[polar chasm]

6th degree

[restive river]

ah yes, let's use the sextic formula

[arctic field]

S_720

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[twilit field]

hey, i don't know how to procede/do this problem, any help's appreciated!

[restive river]

what have you tried

note that (f')^{-1} does not necessarily equal (f^{-1})'

[wooden zodiac]

does the notation say inverse derivative?

[magic thicket]

Derivative of the inverse function

[twilit field]

that's just (inverse of f)' right

[twilit field]

i don't know how to procede

this's a bit new to me really

[magic thicket]

There's a formula for (f^-1)'

It doesn't require knowing the formula for f^-1, only the value at the desired point

[twilit field]

oh

i do have the solution, but i couldn't quite understand it

inverse if strictly incresing?

[magic thicket]

Yes

Because injective

As the solution implies, (f^-1)' = 1/(f' o f^-1)
Or in physics notation, dx/dy = 1 / dy/dx

[twilit field]

oh, didn't realise all injective funcs were inverse, didn't hit me

[magic thicket]

They're invertible when corestricted to their image

[twilit field]

makes sense yeah, just realised

[magic thicket]

By continuity, the image is a segment (R in this case) so it works well

[twilit field]

why'd they take f'(0)?

[magic thicket]

f'(f^-1(-8))

[twilit field]

i get that f(0)'s a point that f' has but

[magic thicket]

__

[twilit field]

ohh icic

thanks!

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[little escarp]

Let $X$ be a vector space and let $T : X \to X$ be a bounded linear operator. Is it true that if $x \in X$ is the only eigenvector of $T$, then $ker(T - z) = \mathbb{C}x$ where $z \in \mathbb{C}$? Why?

[woven radish]

Joy!

[devout snow]

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

[stone stump]

well for starters there can't be only one eigenvector

in fact the second part of your statement says that

somewhere in there should be the actual eigenvalue you want to talk about

[devout snow]

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[undone bone]

help pls

it touches around 1.4

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[lofty monolith]

for part c

[lofty monolith]

have they used c dash because we already used c in part a ?

[restive river]

that would make sense

[lofty monolith]

ok thanks

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[restive river]

Can someone please explain the parts I circled in green?

[devout snow]

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[umbral abyss]

A question in my book reads: Calculate sin a without calculating a if cos a = -√8/3 and a E III. the answer is sin a = -1/3 but i dont understand why because sin-1(-1/3) isn’t in the 3rd quadrant

[devout snow]

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[real patrol]

Help

[main gull]

...... This isn't a spanish server

[real patrol]

oh

..

[main gull]

.close

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[modern stump]

More than 0 or less than 0?

And why

Don't think that's the way

But I just wanna know if it's more than 0 or less than 0 and why

[timber pebble]

i dont get what the problem is saying

are they asking you to find a p such that if p<m then the function has no x intercepts?

wish other poster didnt delete their stuff since i might say the same thing

[devout snow]

@modern stump Has your question been resolved?

[modern stump]

Ye they want to find P

P cna be found through M

My question whether the equation I wrote should be less than zero or mors than zero

And why

[timber pebble]

you wrote the discriminant?

youd want it to be 0, i think

this value is the most extreme youd want to exclude

[devout snow]

@modern stump Has your question been resolved?

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[obtuse berry]

I have tried my best to answer this but the solution makes no sense and I am confused

[obtuse berry]

given solution

how does the drawing make sense??

[balmy quest]

∠DFB = 90°

[obtuse berry]

but why is it 3d?

[balmy quest]

DF ⊥ planeABEF, BF is on the plane, so DF ⊥ BF

[obtuse berry]

huh?

[devout snow]

@obtuse berry Has your question been resolved?

[obtuse berry]

why is the plane 3d?

my brother is helping me now

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[median sigil]

(2+1/2+1/8+1/32….)

[median sigil]

this geometric sequence is divergent right

[kindred basalt]

idk try using geometric series sum

[stuck field]

No.

[devout snow]

@median sigil Has your question been resolved?

[median sigil]

nvm got it

thanks

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[fallow echo]

Hi, another Trig question. Does anyone know how I would double check my answer for the problem $\cos(2sin^-1 \frac{4}{5})$

[woven radish]

zesty&festyII

[fallow echo]

uh, the -1 is intended to mean inverse, not sin -1

[vital patrol]

yeah draw a triangle out with an angle $\theta=\arcsin{\frac{4}{5}}$

[woven radish]

metalbubble

[fallow echo]

Ok, thank you. Haven't learned that yet, but my answer was -7/25 so that checks out. You are quick! Thank you very, very much!

[vital patrol]

anytime g

[fallow echo]

🙂

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[lavish oar]

Explain why polynomial don't have negative power?

[magic thicket]

By definition

[lavish oar]

uhh so ratio aren't polynomial?

suppose is sqrt(2) polynomial?

[magic thicket]

They're rational fractions then

[magic thicket]

All constants are constant polynomials

[lavish oar]

what do you mean by that?

[magic thicket]

√2 is a polynomial of degree 0

[lavish oar]

@magic thicket

[magic thicket]

Does chatgpt have a math degree ?

[lavish oar]

nope also what about this question

[magic thicket]

Has it successfully graduated high school ?

[lavish oar]

I get it : P

[lavish oar]

is this polynomial?

[magic thicket]

What separates the human mind from the machine is the ability to recognize patterns, and derive properties that allows them to simplify their future work

[lavish oar]

so:
if the power is negative not polynomial
expect for above condion all are polynomial

[magic thicket]

So is -π a polynomial?

[lavish oar]

it's a constant polynomial even if pi is the ratio of = c/d the variable x is not negative it is just raised to the power zero

[magic thicket]

π is a constant

It being rational or not is irrelevant

Constants can be viewed as polynomials

[lavish oar]

okay thank you also why according to definition polynomial degree cannot be negative bascially "why ratio of variable x is not polynomial"

this is a dumb question but my mind just telling me to know

[magic thicket]

by definition, a polynomial in the variable $X$ is of the form
$\sum_{k=0}^n a_k X^k$, where the $(a_k)$ are real numbers (if you consider real polynomials)

[woven radish]

mateo713

[magic thicket]

And n >= 0

[lavish oar]

oh okay k just start from zero
I get it it's essentialy sum of term now thank you I understood now

[magic thicket]

Rational fractions however, allow for negative degrees

As by definition, they're fractions of 2 polynomials

[lavish oar]

i see

also accept friend request

@magic thicket

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[fierce pelican]

I don't understand how parity influences the domain of the function

as for context ,

[rose otter]

Can someone help with this question?

[fierce pelican]

already occupied

[blissful delta]

bc even roots are not defined for negative numbers

,tex .exp rules

,tex .exp rules

[fierce pelican]

oh silly me

thanks for reminding this

@blissful delta do you need to say something or should i close this

[blissful delta]

if your question has been answered, you may use .close

[fierce pelican]

oh thanks

.close

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[stuck ether]

hallo guys

[stuck ether]

i have a question

if the standard deviation is 2.89 and the mean is 5

is it higher or lower deviation?

just asking

is it higher deviation? or lower deviation?

[hazy totem]

higher or lower than what ?

[stuck ether]

the mean

[hazy totem]

it doesn't really make sense to compare the standard deviation and the mean directly, is there more context to this ?

[stuck ether]

so if the standard deviation is 2.89

does the data more spread out or closer?

[hazy totem]

again, more spread out or closer compared to what ?

you can't just say "higher or lower" without saying what you're comparing to

and the mean doesn't work as a point of reference, it's apples and oranges

[stuck ether]

to the mean

[hazy totem]

higher or lower deviation than what ??

if the deviation is small then the samples are closer to the mean, if it's large then the samples are more spread out from the mean

is that what you're asking ?

[stuck ether]

yes thats what im asking

[hazy totem]

oh ok, that was unclear

but yes, higher deviation means more spread out

[stuck ether]

so if the standard deviation is lower than the mean it means the data are clustered to the mean?

[hazy totem]

the standard deviation and the mean have no relation to one another directly

they're independent

[stuck ether]

so how do I interpret the standard deviation?

[hazy totem]

You can see it as the average distance to the mean

A standard deviation of 1 means that, on average, samples have a distance of 1 from the mean.

Hence there it's rather likely to be a distance ≤1 and less likely to be very far out from the mean

[stuck ether]

so that means if the data is higher than 0 then it has a higher deviation?

right?

[hazy totem]

"the data is higher than 0" ?

do you mean if the standard deviation is higher than 0 ?

[stuck ether]

yes

[hazy totem]

a standard deviation of 0 means the variable is almost surely equal to its mean

so if there's any spread whatsoever, the standard deviation is strictly greater than 0

[stuck ether]

this is the thing im working

how do I interpret this?

[hazy totem]

Oh, I see

you should have mentioned that in the start

in the first example, the mean is 3.85 so on average people answer "sometimes" (averaging discrete things like this on such a small sample is a bit awkward, but that's the idea)

wait, these numbers don't look right

let me check

As I thought, the standard deviation is wrong

Calculating it myself gave 0.85

[devout snow]

@stuck ether Has your question been resolved?

[stuck ether]

how?

[hazy totem]

the stddev is the square root of the variance

and the variance is the expected value of the squared difference between the samples and the mean

[stuck ether]

this is my solution

[hazy totem]

Computing it, you get V = (5×(3.85-5)²+8×(3.85-4)²+6×(3.85-3)²+1×(3.85-2)²)/20

[frosty cradle]

is this homework? or research? because this is called "Likert scale" data. you can treat them as interval data and take regular means/stdevs/etc., but this is not always justified

[hazy totem]

the average you computed is the average number of people per answered question

that's not what you want

you want the average of the answers

[stuck ether]

its research

[hazy totem]

your data is actually [5,5,5,5,5,4,4,4,4,4,4,4,4,3,3,3,3,3,3,2]

[stuck ether]

this is the table for this

[frosty cradle]

I recommend you read the answers here to better understand what makes this kind of data different. It is "OK" to do what you're trying, but just think carefully about it: https://stats.stackexchange.com/questions/97/what-are-good-basic-statistics-to-use-for-ordinal-data

also, IMO "usually" should be "higher" than "sometimes"

[devout snow]

@stuck ether Has your question been resolved?

[devout snow]

@stuck ether Has your question been resolved?

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[devout snow]

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[mossy gale]

!status

[devout snow]

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

[mossy gale]

@grand valley

[grand valley]

2

[mossy gale]

Show your steps

Please

[grand valley]

i tried to factorize it

[mossy gale]

And?

[grand valley]

3x^2 - 11x + 5

1 1
3 5

[solar solar]

what do you plan on doing with the -11

[mossy gale]

Check for it's discriminator then

[grand valley]

89

is the discriminator

[mossy gale]

I think it doesn't have rational factors

You should solve with quadratic equation

[grand valley]

i will try

[mossy gale]

Do let me know when you're done

[devout snow]

@grand valley Has your question been resolved?

[devout snow]

@grand valley Has your question been resolved?

[devout snow]

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[lusty moth]

How would I type this into a TI89? Also would I use sin, cos, or tan?

[mossy gale]

First do me a favour

Draw the diagram please

A rough sketch would do

[lusty moth]

One sec

It's sending

Not sure why it's sideways

[mossy gale]

That'll work

[grand siren]

,rcw

[mossy gale]

Or you could draw the second boat on the other side

[mossy gale]

For simplicity

If you don't mind, do that

[mossy gale]

Mind marking the triangles with some points?

Like A B C D

[mossy gale]

Let's start with ∆abc

The angle of inclination would be angle(ABC)

Correct?

[lusty moth]

No idea

[mossy gale]

Yes it would be

[lusty moth]

This is trigonometry

[mossy gale]

So we know the side OPPOSITE to angle ABC
And side ADJACENT to angle ABC

[lusty moth]

So we'd use tan?

[mossy gale]

What do you think?

[lusty moth]

Tan

[mossy gale]

Yep

[lusty moth]

I thought I had to use sin for angles?

[mossy gale]

Why?

[lusty moth]

Not sure

[mossy gale]

Sin is when you get opposite and hypotenuse

Anyways

You know how to proceed now, yes?

[lusty moth]

Typing it into the calculator maybe

Let me try it and I'll ask if the answer is correct

[mossy gale]

Please make sure the calculator is on degrees

Not radians

[lusty moth]

Yeah it is

[mossy gale]

Also boat A is 100 metres away

[lusty moth]

Yeah

[mossy gale]

From your diagram it seems like 150 metres

[lusty moth]

I don't think I'm right

Boat a is 100ft away and boat b is 150ft away. I'll switch the numbers

[mossy gale]

Yes

[lusty moth]

I got -96?

Am I supposed to do tan^-1

Or just the regular tan

I'm not sure

How to type it in correctly

[mossy gale]

Tan inverse.

That gives you the angle

[lusty moth]

Is there a specific order that the numbers go in?

48?

[mossy gale]

That's boat B

[lusty moth]

Yeah I did that one first

It is right?

[mossy gale]

Yessir

[lusty moth]

Boat A would be 59?

[mossy gale]

Yessir

[lusty moth]

Okay cool thank you

[lusty moth]

I get confused on how the numbers are organized

In the calculator

[mossy gale]

I don't understand what you're trying to say

They follow bodmas

[lusty moth]

Like why is it tan^-1 (167/100) instead of tan^-1 (100/167)

Or tan^-1 (167)/100

[mossy gale]

Tan inverse is a function

[lusty moth]

Yeah but I meant the numbers after

[mossy gale]

Yes treat it like the square function

[lusty moth]

Cause in trigonometry don't you sometimes have a question where you're doing something like this 50*sin(39)

[mossy gale]

Appropriate use of parentheses should get you going

[mossy gale]

They're all equal type it so I can see where you're wrong

[mossy gale]

Ohhhh

You're confused into where the numbers should go

[lusty moth]

Yeah

[mossy gale]

Tan theta = opposite/adjacent

So the opposite part must always be on top because it's tan theta

Here in this case, 167

Whereas, the adjacent part changes

So you input 100 and 150 accordingly

Let me know if there's any more confusion

[lusty moth]

Tan theta?

Is that just a name for the function?

[mossy gale]

It's a trigonometric function

Here we used the tan inverse function

Functions are bounded by parentheses (usually)

Like tan-¹(x)

Or tan(x)

Sin(x)

Sin-¹(x)

[lusty moth]

I'm still confused on why the numbers are organized in that way

[mossy gale]

Could you hop on VC and tell me what's wrong?

[lusty moth]

Sorry I'm in school at the moment but I think I just figured it out

[mossy gale]

Cool

Have a good day

[lusty moth]

You too and thanks for the help

[devout snow]

@lusty moth Has your question been resolved?

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[pallid oasis]

A plane is flying at an altitude of 12,000 m. From the pilot, the angle of depression to the airport tower is 32°. How far is the tower from a point directly beneath the plane?

[pallid oasis]

Im just wondering what this last part is asking

Is it wanting the hypotenuse or the opposite side length

[winter patrol]

diagram is wrong

[vivid pasture]

damn

[winter patrol]

it makes it worse

[pallid oasis]

So wouldnt it be 7498.43

[winter patrol]

how are you getting that

[pallid oasis]

Or 14150.1

[winter patrol]

did you draw your own hopefully correct diagram

[pallid oasis]

I did 12000*tan(32)? But i originally thought it was 12000/cos(32)

But i did both and entered the answer and it said its wrong

[winter patrol]

lets take a step back

did you draw a diagram

[pallid oasis]

Yea

[winter patrol]

can you show your diagram

[pallid oasis]

Sure

Wait

[winter patrol]

your diagram is wrong

[pallid oasis]

Is 12000 on the hypotenuse

[winter patrol]

no

[pallid oasis]

Whats wrong about it then

[winter patrol]

angles of elevation/depression are angles made with the horizontal

your 32° angle is made with the vertical

[pallid oasis]

But thats where the plane is

And its facing towards the tower

[pallid oasis]

Ohhh

[winter patrol]

made with the horizontal

[pallid oasis]

19204?

Im still confused on what im finding

The hypotenuse

Or adjacent

[winter patrol]

well mark the point directly below the plane

and it should be clear what they mean when they say between that and the tower

[pallid oasis]

Soo

The adjacent

[winter patrol]

yes

[pallid oasis]

Ok

Thank you

[winter patrol]

19204
sounds about right

[pallid oasis]

.close

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[devout snow]

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[rigid slate]

I need some help with undefined integrals, i need a pdf or sum with rules on how to solve them, or even a yt video/ website?

[rigid slate]

i have an exam saturday, ik i could have studied but i was occupied all month with other stuff lol

[supple knot]

what's undefined integrals? improper?

[rigid slate]

improper yeah the one without a fixed interval

idk how to call them in english

[small raptor]

indefinite?

[rigid slate]

yeah

[small raptor]

no bounds right?

[rigid slate]

yeah no bounds

with +c

[supple knot]

this is a start

https://tutorial.math.lamar.edu/classes/calcii/improperintegrals.aspx

oh sorry no

[small raptor]

I think he means indefinite

[supple knot]

https://tutorial.math.lamar.edu/classes/calci/indefiniteintegrals.aspx

yes ty mortta

[small raptor]

https://www.youtube.com/watch?v=6WUjbJEeJwM

[rigid slate]

thaanks

[small raptor]

https://www.youtube.com/watch?v=6WUjbJEeJwM

using U sub

https://www.youtube.com/watch?v=sdYdnpYn-1o

https://www.youtube.com/watch?v=sWSLLO3DS1I

than by parts

[rigid slate]

oh pefect yeah i remember prof explaining these

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[neon bone]

i dont understand any of it and i just need an answer as im kind of in a rush

[neon bone]

please someone help

[winter patrol]

we don't do that here

[patent marsh]

https://tenor.com/view/we-dont-do-that-here-chadwick-boseman-avengers-infinity-war-gif-21347105

[neon bone]

😭

[patent marsh]

we can help you understand and go through the problem but we don't just flat out give an answer

[lusty sapphire]

mean just means average. Do you know how to find average?

[neon bone]

ok

[neon bone]

yeah

add all of it and divide by how many there are

[lusty sapphire]

yup

By "all of it", do you know what that is?

[neon bone]

nvm i figured it out

.close

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[pale dome]

I'm having issues with trigonometric functions to the power of something, specifically, I always thought:
sin⁴(x) = sin(x)⁴

But then I'm trying to take the derivative of both, my calculator says:
[(sin⁴(x)]'= 4cos(4x)
[(sin(x)⁴)]'=4cos(x)sin(x)³
What is going on? Both derivative functions are not the same

[crystal summit]

Notation-wise those are the same

You're not wrong at all, but you've probably entered one of those incorrectly on your calculator

Either that or you're calculator's WACK!

[winter patrol]

can you show what exactly you put into your calc for the former?

[pale dome]

and the latter

oh wait that's what's happening, it's taking it as sin4(x)

[winter patrol]

yeh, your calc didn't understand the notation

,W differentiate sin^4(x)

[woven radish]

Results provided by WolframAlpha

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

Requested by ramonov#0921

[winter patrol]

a more reliable calculator

[pale dome]

yeah that now makes more sense

I was about to wonder if my entire understanding of trig functions to the power of something was wrong

[winter patrol]

sin(x)^n is horrid notation btw and you should NEVER use it, unless you make the point that it's horrid as I'm doing right now

[pale dome]

why so?

[winter patrol]

hard to read, could potentially get mixed up with
sin x^n

if you don't want to wedge the power in between,
use additional parentheses
$${(\sin(x))}^n$$

[woven radish]

ℝamonov

[forest bay]

is the cumulative frequency on a cumulative frequency graph on the x or y axis

[pale dome]

ohhh I see, thanks for the tip

[crystal summit]

Y axis, if you have any other questions pls use an availale channel like #help-2

[forest bay]

k thanks

[pale dome]

I think I just finished now that the mystery is solved

[forest bay]

but it was on available

[pale dome]

thanks ramonov and raonicalias

[forest bay]

.close

[pale dome]

.close

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[whole delta]

Someone please help me with simplifying radicals. I don’t understand.

[earnest kite]

good luck

[wispy geyser]

.close

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@whole delta Has your question been resolved?

[supple knot]

do problems and post and ask here when you get stuck on a problem

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[eager crystal]

Why isn’t 1 a vertical asymptote,

?

1 also makes the denominator 0(divide by 0)

[frosty mantle]

because it can be cancelled out

[eager crystal]

No but if you input in the original equation

It makes it divide by 0

I mean this by “original equation”

1-6+5 is 0

So diving by 0 is not possible

So wouldn’t 1 be a vertical A?

Or

[frosty mantle]

there exists a solution for 1 if you simplify the function which is where we get our f(1)

[eager crystal]

Oh i see

So its kinda extraneous?

1 is extraneous therefore is not an asymptote?

[frosty mantle]

the first step to finding vertical asymptotes is always to simplify

im not entirely sure why

[eager crystal]

Ok i understood that thanks

But i have another question

Where is that y=2 coming from

I can see where those V Asymptotes are coming from

But i can’t see where y=2 is coming from

I still can’t figure out after looking for minutes

The VA are from setting up factors equal to 0

But where is the HA from

?

[frosty mantle]

since the top and bottom are the same degree you just divide the leading coefficients

2x^2/x^2 = 2

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@eager crystal Has your question been resolved?

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[worn maple]

really quick, if a problem said "i jumped x meters and my friend jumped 10 times more than me", would my friend jump 10x or 10+x? and so why?

[magic thicket]

10x
"times"

[worn maple]

ye, that's what i thought, but the answer to the question is 10+x idk why

oh nvm

ye that's it

10x

thank you

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[tulip latch]

why are we inputting 1 when the condition is "as h is approaching 0?"

shouldn't we input 0 instead?

[graceful cosmos]

They're skipping a step.

Notice the a's on the numerator subtract out

and the h in the numerator/denominator divide

[tulip latch]

oooooooh

dang i missed that

[graceful cosmos]

With that algebraic manipulation, you get:
lim 1 / (√[a + h] + √[a])

Apply h -> 0

[tulip latch]

yeah i get it now thanks

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[tulip latch]

so given the information by 12., i could not figrure out how you can draw those parts

these red parts

those parts are not given by the question

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[restive river]

I know this problem is using parts of integrations but i would appreciate for a step by step on this problem. For some reason, my number doesn't align with the answer.

[frosty mantle]

can you show the work you've done so far

[restive river]

one sec

I thought u sub would work originally then did by parts, but even simpling it out doesn’t match the answer

[supple knot]

Parts twice should work

Maybe three times

[restive river]

ok let me check on that

I definitely did something wrong here since it’s not even close to the answer

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@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

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[drifting frigate]

"overall percentage increase" does that means that the 2.5% is increased by 6.6%?

[analog trellis]

If x is the initial capital invested then it means after two years the investment yields (106.6%)x ≡ 1.066x.

[drifting frigate]

oh okay so 2.5 became 6.6

how'd u come up to know that? it says overall percentage increase which means that it increased by 6.6% no?

[analog trellis]

No. "The rate of interest for the first year is 2.5%.".

[drifting frigate]

we know the rate of interest in the first year

and how much it increased with right?

[analog trellis]

To help you, let's set up the question in a way which might help you understand what you need to do.
The yield of the investment is made up of two yearly payments.
Let the first year payment be 2.5% and the second year payment be the unknown percentage b.
If the starting capital invested is x then the amount at the end of the first year would be
1.025x; and after the second year the amount would be (1.025x)b. And we are told this is 1.066x.
This reduces to a algebraic problem.

I'm not sure how to help without giving you most of it without getting into a massive back and forth about every detail.

[analog trellis]

This is basically how you would approach the problem if you was told to find the overall investment given the two yearly interest rate payments. We just used variables where there's a unknown and inserted the known answer in place of your usual final answer.

[jaunty gazelle]

Apparently my work for this is wrong. Can someone explain what I did wrong?

[analog trellis]

I really don't understand how someone can need to be told to get a new unused room. It actually boggles my mind these people survive in society.

[supple knot]

!help

[devout snow]

Please read #❓how-to-get-help

[jaunty gazelle]

Sorry

[drifting frigate]

i think i got it but it's fine, can u go ahead and give most of it?

[jaunty gazelle]

I didn’t notice it was used my internet must of temporarily lagged.

[drifting frigate]

my 7th grade mind is about to explode what is this 💀

[analog trellis]

I think I've given everything you need to be able to solve it. Have you obtained a answer?

[analog trellis]

At least it makes sense. 16 minutes of lag though.

[drifting frigate]

"And we are told this is 1.066x" what exactly do u mean by this?

[analog trellis]

"If x is the initial capital invested then it means after two years the investment yields (106.6%)x ≡ 1.066x."

Just try and read everything I have done over and over and pick through the details as I think you should be able to figure it out on your own with this as a guide.

[drifting frigate]

this is what i'm doing rn. i'm gonna take a small break because my brain can't process anything rn and come back to solve it later.

thank u smmm dude

bless u 🙏

u do math in uni?

[analog trellis]

Just try again later with that as a guide. 🙂

I do maths at my desk at home lol.

[drifting frigate]

will do so 👍

[drifting frigate]

hahhaha, as a hobby?

[analog trellis]

As a hobby. 🙂

[drifting frigate]

woah respectttttt. i have mad respect for those who do math as a hobby 🫡

thanks dude and i wish u a great night/day!!

[analog trellis]

You too.

I got 4% for you to check against later.

[drifting frigate]

hehehe will do so!!!