help-0

[vagrant falcon]

oh

ok

[median oar]

n = 2, write your 2 x values

Keep going until you get a value >= 2pi

[median oar]

Just list them

[vagrant falcon]

0,1

[median oar]

We pretty much never write pi in decimal in math

We just write it as pi

[vagrant falcon]

ok

when I plugin 0, i get

0, pi/4

when I plugin 1, i get

pi, 5pi/4

[median oar]

What we are doing is this btw

Graphically

This is the 2 triangles here

[vagrant falcon]

ok

[median oar]

Soz bad pic

Then we unrestrict our sin to that + any 2pi

[vagrant falcon]

ok

[median oar]

That’s this step

[vagrant falcon]

ok

[median oar]

Then we solved for x

[vagrant falcon]

ok

[median oar]

Now it looks like this

Then we restrict the domain back to 0 to 2pi

[vagrant falcon]

ok

[median oar]

We get this

The intersections are our solutions

All we’ve done earlier is doing these steps

But with the triangles and some algebra

[vagrant falcon]

ah ok

[median oar]

(Just to give you an idea what our steps mean graphically)

[vagrant falcon]

yes

it can help to double check the solutions

cuz i do have a graphing calc

[median oar]

Yea if you need to

Yep you should get as many solutions as there are intersections

[vagrant falcon]

ok

[median oar]

Also you know how we were trying to draw that triangle

[vagrant falcon]

yea

[median oar]

You see the green intersect

[vagrant falcon]

ye

[median oar]

That’s what we call the principle angle

[vagrant falcon]

ok

[median oar]

Before we do all the 2x + pi/4 scaling

[vagrant falcon]

so just to make sure

[median oar]

There’s always a solution between 0 to pi/2

(For positive values)

So that’s why we wanted to find the triangle with the angle on the origin, and a base on the x axis

[vagrant falcon]

0,pi,pi/4,5pi/4 are all solutions

given the interval [0,2pi)

[median oar]

You’re missing one aren’t you

Oh wait

You should put them in order

pi > pi/4

[vagrant falcon]

0
pi/4
pi
5pi/4

[median oar]

Right

Next one is at 2pi

That’s not in the domain

[vagrant falcon]

yes

[median oar]

Fantastic

[vagrant falcon]

if it was]

[median oar]

That’s it!

[vagrant falcon]

then 2pi would

but yea

thanks

for

helping me view this multiple ways

[median oar]

👍

It’s a bit tricky if you don’t really get to know it

[vagrant falcon]

i appreciate your patience (im just learning this stuff)

[median oar]

(Ps try some questions with other trig functions!)

[vagrant falcon]

yea i will

[median oar]

You just have to make sure you label the triangle appropriately and find the other pair of the triangle

With the correct signs

[vagrant falcon]

ok

[median oar]

(It turns out the signs do match whatever mnemonic people use to remember)

SATC or something idk

[vagrant falcon]

yea lol

[median oar]

But it just really has to do with hypotenuse is always positive

Then you check the sign of the quadrants

[vagrant falcon]

yea

unfortnately

my teacher wants this to be done algebraically

as the primary way of solving it

not just plugin into graphing calculator and solve

[median oar]

You can draw the triangle just fine, all the diagrams do is tell you what the angle should be

[vagrant falcon]

yea

that will help alot

thank you

[median oar]

👍

[vagrant falcon]

.close

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[unique forge]

what would this be because i dont understand

[tacit arch]

what's GNP

[lone heart]

@unique forge Has your question been resolved?

[unique forge]

gross national product

[lone heart]

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[alpine sable]

help

[alpine sable]

thats mad

help

[tardy stag]

what have you tried? what are your thoughts?

[alpine sable]

idk tbh

[tardy stag]

well
here's a thought: the drawing is very symmetric, so if you just focus on one area of the drawing then anything you learn can be applied to all of it

see if you can label some edges or angles

[alpine sable]

k

i need help for this one too

[tardy stag]

same problem?

[alpine sable]

yes

[tardy stag]

perhaps you two could work on it together

[fallen verge]

consider focusing on this triangle

[alpine sable]

k

oh ye

cuz

2:1

[fallen verge]

law of cosines

[alpine sable]

i have 0 idea

[somber eagle]

i have a much easier idea i feel like

[alpine sable]

pls provide

[tardy stag]

i usually slap a coordinate system on this sort of thing

[fallen verge]

coordinate systems are kinda annoying for hexagons

you oculd do vectors, but i really think law of cosines is easier

[somber eagle]

you can find that length

and then find the height of the inner hexagon

you could think of the hexagon as 6 equilateral triangles

[fallen verge]

what

[somber eagle]

to find the height

[fallen verge]

oh i guess, theres some pythag shenanigans

[alpine sable]

thats what i thought but didnt get around to figuring it

[fallen verge]

find this angle

[alpine sable]

wouldnt that be

120

[fallen verge]

indeed

[alpine sable]

then what 😭

[fallen verge]

and you know two of the sides

[alpine sable]

1 and 2

[fallen verge]

so you can use law of cosines

[alpine sable]

i dont know law of cosines

fuck

[fallen verge]

$c^2=a^2+b^2-2ab\cos C$

[alpine sable]

help pls

[ocean seal]

GarlicBredFries

[fallen verge]

C being the angle

[somber eagle]

unfortunately i cant post enitre solution at fear of being told off

[alpine sable]

ur gunna get told off if u tell the solution?

[somber eagle]

yep because helpers have to "teach" not give answers

[tardy stag]

if you haven't covered law of cosines you might look for other techniques

[west girder]

If you don’t know LOC just draw an altitude and solve

Same thing assuming Yk 30-60-90 ratios

[fallen verge]

oh right

[somber eagle]

did everyone just give up?

[alpine sable]

ye

ik its 7:1 now

[somber eagle]

did someone help? or did you figure it out

[alpine sable]

i figured it out

[somber eagle]

nice

[alpine sable]

no i told him

[somber eagle]

oh

[tardy stag]

i would look at this triangle

[alpine sable]

wtf u saying

[somber eagle]

sussy right angle triangle

[alpine sable]

im sad now

[somber eagle]

this figures out that side length way in like 3 less steps lol

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[midnight girder]

i need help with this sum

[somber eagle]

do you know the formula for the area of a trapezium?

[midnight girder]

1/2(a+b)*h

[somber eagle]

yeah

you know a

and you know b

therefore you have some number multiplied by h = 39.2

[midnight girder]

so

wait i didnt get it

[somber eagle]

??? that wouldnt even be correct

[midnight girder]

no i meant times h not equal to h

[somber eagle]

it clearly says times, how is it confusing

[midnight girder]

ohh so is it 16?

[somber eagle]

yep

[midnight girder]

the lenght

omg thank you so much

[somber eagle]

np

[wary stream]

I wasn't paying close attention because I saw a + b and my mind went to it being a 2D anwer

[midnight girder]

your a life saver

[lone heart]

@midnight girder Has your question been resolved?

[limber crescent]

Yes

.close

[wary stream]

This isn't your channel

You can't do that

[lone heart]

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[shell dove]

am i doing this correctly?

[shell dove]

i’m really confused on how to graph these and writing the equations

[lone heart]

@shell dove Has your question been resolved?

[shell dove]

<@&286206848099549185>

[shell dove]

<@&286206848099549185>

[frozen tiger]

you are

[shell dove]

i’m confused on #2

i’m just confused overall

[frozen tiger]

hm

[shell dove]

i don’t understand how to graph at all

i was lucky to even get that

[frozen tiger]

try it first with 0(or something that has an obvious value)

for example something like cos(x+pi/3) make it start with -pi/3 to make it equal to 1

[frozen tiger]

Then you can move on to something like -pi/3+pi/2

[frozen tiger]

or pi/6

And then just connect the dots(doesn't have to be perfect if you're drawing it)

[shell dove]

mmm alright i’ll try it

yeah no i just don’t understand it overall

it makes absolutely 0 sense to me

[frozen tiger]

yk how sin0 and cos0, sinpi/2, cospi/2, sinpi, cospi, etc etc have definitive easy values right?

You just have to make what is in the sin equivalent to those values to make it easier to graph

[lone heart]

@shell dove Has your question been resolved?

[lone heart]

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[grand hornet]

would the first step be to factor?

[slender gull]

Factorisation would be useful, yes.

Then LCM/simplification.

[grand hornet]

then after make them equal by yeah

but after they are equal do i just minus them?

the problem is that when they are equal they have a cubic as the denominator and that is not an option

am i missing a step?

[tardy tapir]

thats not an equal sign

[grand hornet]

yeah but they both have to be equal in order to minus right?

[tardy tapir]

um how?

[white crater]

factorise it first then simplify

oh he alr said that mb

[grand hornet]

but when i simplify, it goes back to the original problem

[white crater]

hmm

factorise the denominator what u get

[grand hornet]

(x+1)(x+2)(x+3)

[white crater]

both denominators*

what

[grand hornet]

like thats when they are equal

[tardy tapir]

how are they equal?

[grand hornet]

the right side denominator is (x+3)(x+2) when factored

[tardy tapir]

yes

[slender gull]

The denominator*

[grand hornet]

the left side denominator is (x+2)(x+1)

[tardy tapir]

right

[grand hornet]

what do i do from there

[tardy tapir]

now you could take one common factor that is?

[grand hornet]

(x+1)(x+2)(x+3)

they both can equal this

[white crater]

no dont do that

[grand hornet]

what should i do

[white crater]

u have (x+3)(x+2) and (x+2)(x+1)

[grand hornet]

yes

[white crater]

whats common in both

[grand hornet]

(x+2)

[white crater]

so therefore we can??

[grand hornet]

umm

i dont know

[white crater]

if theres a common factor

we can cancel it out

[grand hornet]

yes but the problem is that they are both denominators?

you cant cancel out two denominators unless ur multiplying right

[raven scroll]

im pretty sure you were on the right track here lol

[grand hornet]

oh okay so what do i do after

[white crater]

oh wait yeah

mb

[tardy tapir]

that is correct but that would make it a bit long ig

[grand hornet]

its fine

its how im learning

[tardy tapir]

then its fine

[grand hornet]

but i dont know what to do

after that

[tardy tapir]

just take the lcm and form a cubic in the numerator

[grand hornet]

the cubic is in the numerator?

what

wait but do i minus them when they are equal

so

then it would just be a trinomial over a cubic

thats not right

[raven scroll]

at this step you can apply the fraction rule

[grand hornet]

hold on

yes i know

i think i might have figured it out

gimme a second

[raven scroll]

then simplify

[grand hornet]

oh wait

oh okay ill simplyify then

gimme a sec

@raven scroll thank you

solved

.close

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[paper sage]

One way to control the altitude of aircraft when they land is by means of interference between
a direct beam and a ground reflection from a radio transmitter emitting the wavelength 90 cm.
At what height h should you place the transmitter antenna to create a signal maximum in a
direction that has a slope of 3.0° above the horizontal? Keep in mind that the radio signal is phase-shifted
180° when reflected to the earth's surface.

[paper sage]

This is the sketch I drew

But I don’t know how to proceed

[fathom harness]

Have to find h?

[fathom harness]

Oh, this is the text

[paper sage]

yeah indeed

but the problem I have I don't know if my sketch is good? or right in this case

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@paper sage Has your question been resolved?

[left isle]

i'm not sure about where 90cm plays in, but if you just put the small triangle inside the first one, you would have some kind of similar triangles situation

they're proportional

maybe that could help?

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[lone heart]

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[round sphinx]

Help with this

[lethal belfry]

!status

[lone heart]

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

[round sphinx]

4

I got an answer and would like my work checked

[lethal belfry]

what's your answer?

[round sphinx]

A

[lethal belfry]

That looks more like sin(x) to me ( The sin curve reaches 1 at ~1.7 instead of ~3.4)

[round sphinx]

Ohh

[lethal belfry]

sorry, bot 1.7, 0.85, the first graph is sin2x

[round sphinx]

I am guessing its B or D?

[lethal belfry]

B isn't a positive sin curve imo

[round sphinx]

C?

Ok wait

Hmm

Idk

I am confused

[lethal belfry]

I suggest you try graphing it yourself. Have you tried that?

[round sphinx]

Ill do that

@lethal belfryIts D

[lethal belfry]

yup

[crimson carbon]

You should recall your graph transformations if let's say the argument x is scaled by a scalar k we have a horizontal stretch by a factor of 1/k if 0<k<1 or a horizontal shrink if k>1 by a factor of 1/k

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[random heart]

What would be the bounds for this?

[random heart]

I integrated from -pi/2 to pi but it was wrong

[wheat obsidian]

This looks like a line integral problem. Do you have the formula for the length of a line? It should have a "ds" or similar in it.

Your bounds look good! Now we need to make sure the rest of the integral is okay.

[random heart]

shouldnt the answer for this be (9pi+8)/2?

[random heart]

no, i dont

[random heart]

oh wait thats area

[wheat obsidian]

I literally have no idea what the answer is. It's more important to get the process right. What was the set-up for your integral?

[random heart]

i think my set up was wrong

[random heart]

is this the formula?

[wheat obsidian]

Yep, that looks like the one!

[lone heart]

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[lone heart]

@modest jolt Has your question been resolved?

[winter light]

Let's start from the last which is the easiest, what is its value?

Whatever⁰ = 1 right?

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[graceful pawn]

i uh

think that

Line DC and BE are the bisectors of angle BDA and AEC respectively?

[subtle birch]

why do you think so?

[graceful pawn]

because im bad at geometry

[upbeat gorge]

What can you observe from the problem statement

[graceful pawn]

triangle DAB and AEC are similar triangles

[upbeat gorge]

Well yeah, they’re equilateral

But what are some relevant things that come from equilateral triangles

[graceful pawn]

i don't really know

[upbeat gorge]

What properties of equilateral triangles do you know

[graceful pawn]

60 degrees

equal sides

[upbeat gorge]

Yes

60 degrees is the more relevant one

All angles are 60°

Now let’s move to the other two similar triangles

[graceful pawn]

wait ther'es more similar ones???

[upbeat gorge]

Actually mb congruent

Well, congruent triangles are similar, but anyway

[graceful pawn]

is it the two small segments on the left and right of triangle ABC?

[upbeat gorge]

Read the problem — there were two triangles stated to be congruent

[graceful pawn]

shi

i thought they meant angle

is the answer 120

wait

yeah is it 120?

@upbeat gorge ??

[upbeat gorge]

Yes!

[upbeat gorge]

What did you do, for the record?

[graceful pawn]

more geometry sigh

[upbeat gorge]

I used cyclic quads lol

[graceful pawn]

When you rotate line DC to align it with line BE, it moves 60 degrees

so angle EIC and DIB are both 60 degrees

.close

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[restive chasm]

Open.

[restive chasm]

Given f(x) is upward concave in (a,b) then prove that,

(b-a) f((a+b)/2) < integral [a,b] f(x) dx < (b-a) (f(a) + f(b) )/2

The one in black.

I need analytical approach.

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[somber spoke]

I’m slightly lost on part 4

And 5

I’ve done all the previous parts but no clue how to approach this here

[karmic grove]

f_2-k (x) has 2-k as one of the root

[zealous lichen]

for q4 write $f_{2-k}(x)$ in terms of $f_k(x)$

[ocean seal]

WhereWolf

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[fickle laurel]

How to prove this

[finite flax]

1. What class is this for?
2. What section of the book is this?
3. What do 4.1, 4.2, 4.3, and 4.18 say?

[fickle laurel]

I'll go find out now and send it to you

This is the derivation in a paper, and I can't understand it a bit

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@fickle laurel Has your question been resolved?

[lone heart]

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[upbeat eagle]

Something easy

[upbeat eagle]

x^2 = 6

x= +_ root6

If x^3 = 6

Would it also be

x= +_ Cube6

No right?

[upbeat hornet]

Consider (-1)^3

[upbeat eagle]

Makes positive

So no

?

[upbeat hornet]

-1 * -1 * -1 = ?

[upbeat eagle]

-1

lol i meant negative

[upbeat hornet]

so can you solve x^3 = 1

[upbeat eagle]

Just 1

[upbeat hornet]

How about x^3 = 6?

[upbeat eagle]

Cuberoot 6

?

————
Another question

The middle one, let’s say it’s -81/8

Would it be -81/8 -8(ect)

And not combined -81/8 -8 =-145/8(ect)

[upbeat hornet]

Yes, it is the only solution in the reals

,rotate

[upbeat eagle]

Just the middle

[upbeat hornet]

can you send this one again

[upbeat eagle]

As A-B(X+C)^2

SOlving cubes

Usually they ask p(x+q)^2 + r

so if that +81/8 was minus

It would just be -81/8 -8

If they wanted as A-B(X+C)^2

[upbeat hornet]

What is the question?

[upbeat eagle]

It just move -81/8 to A

[upbeat hornet]

,tex .original

[ocean seal]

even order group => solvable

[upbeat eagle]

No original it’s just questions combined

My question is is the first line correct

--

Does that help?

[upbeat hornet]

the first expression on the first line is equal to the expression on the second line

[upbeat eagle]

ok

Yep

Thats all

: ))))

.close

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[turbid root]

no idea on part b.

I don't know where I went wrong.

I tried to find the area of the 3rd triangle. Which is 500. Then using that information tried to do some algebra and got the answer. However it is wrong. The answer is 43

[tardy tapir]

try to find the area of the triangle again

500 is incorrect

[turbid root]

like the values of the rectangle and first triangle are incorrect?

[tardy tapir]

idk about the value of rectangle which u calculated

the triangle is not 500

[turbid root]

Ok

Let me re-try.

[wary stream]

The area of the first triangle, you did 0.5 * 25 * 30, where's 30 from?

[turbid root]

thank you very much. I checked it.

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[sharp tendon]

So what did I do wrong here🗿

[sharp tendon]

It should be 1/16 not 1/8

[tardy tapir]

see the 4th line

cos40 - 1/2

2cos40 - 1

it should be (2cos40 - 1)/2

[sharp tendon]

So the 1/2 gets factored out and we get 1/8 right

[tardy tapir]

yep

[sharp tendon]

Then finally in last line it should be 1/8 * (0+1/2) right?

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[spark quartz]

can someone help me understand what the point of having a transformation matrix from basis A to basis A is? isn't the whole point of a transformation matrix to change a vector from one basis to another?

[mortal trellis]

no

we just want to be able to write down the function f in some basis

[spark quartz]

so what exactly does that matrix tell me?

[mortal trellis]

lets say A={a1, a2, a3}

the first column tells you that f(a1) = 1*a1 - 1*a2 + 1*a3

the second column tells you f(a2) = -18*a1 -22*a2 -25*a3

and third tells you f(a3) = 15*a1 + 15*a2 + 22*a3

[spark quartz]

hmm

[echo socket]

It basically tells you what happens to A in terms of the vectors that make up A

[spark quartz]

what do you mean what happens to A?

[echo socket]

What happens to the vectors of A during the transformation

[spark quartz]

but the transformation will always be from A to A right

[mortal trellis]

that doesnt really make sense to say

the transformation is from V to V

or however your space is called

you just fix the basis A to write everything in

for example in most cases you write everything in terms of the standard basis

aka A={e1, e2, e3}

[spark quartz]

ok so if A = {e1, e2, e3} then f(e1) = 1 * (1, 0, 0) - 1 * (0, 1, 0) + 1 * (0, 0, 1) = (1, -1, 1)

which means that the first vector of A doesn't change when transforming under the standard basis?

or something like that

[mortal trellis]

huh

what should that even mean

the point I wanted to make is that most of the matrices you are see are of this form _A M(f)_A for the same basis A. namely the standard basis

so its nothing unusual

or weird

[spark quartz]

oh

so you could say that a random 3x3 has an implied (E_3) on both sides?

${}{E_3} M(f) {E_3}$

[ocean seal]

severed_toast

[mortal trellis]

basically

[spark quartz]

okay great thanks

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[alpine sable]

Hello

[alpine sable]

I have 0 clue on how to do this

[pliant kestrel]

You should have a formula for binomial expansion

[alpine sable]

yes

[pliant kestrel]

Then you only have to look at one of the terms

And youll be good

[alpine sable]

okay i wont close this

i will ping u

[pliant kestrel]

Take your time

[alpine sable]

if i need help

okay

[lone heart]

@alpine sable Has your question been resolved?

[pliant kestrel]

Have you done it ?

[tacit arch]

why? what questions do you have?

[lone heart]

@alpine sable Has your question been resolved?

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[trail stirrup]

This is a project im working on but i cant figure out the process to make a function

I want to make a function that uses a standard bingo board with a free space in the middle and estimates the chances of winning based on the amount of numbers called
example: b(75)=1
b(3)=0
etc

[tacit arch]

there are a lot of functions that satisfy b(75) = 1 and b(3) = 0

[trail stirrup]

but i mean for bingo

[tacit arch]

what do you mean "estimates chances of winning"

[trail stirrup]

like if 40 numbers are called

how likely was it for you to have gotten a bingo

[lone heart]

@trail stirrup Has your question been resolved?

[trail stirrup]

<@&286206848099549185>

[old moat]

show your work my guy

[trail stirrup]

I dont have any because i dot know how to approach this

dont*

brb

[old moat]

http://www.durangobill.com/BingoHowTo.html

@trail stirrup

[trail stirrup]

ok ty

my only problem is that i cant use programmng langs

someone already sent me python

this is c+=

sorry c++

[lone heart]

@trail stirrup Has your question been resolved?

[lone heart]

@trail stirrup Has your question been resolved?

[trail stirrup]

So how do i do this in math

[lone heart]

@trail stirrup Has your question been resolved?

[lone heart]

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[alpine sable]

Is there an easier way to do this instead of substituting each a value?

After solving for the integral

[weak field]

Integrate it and find the minima

[trail stirrup]

BRO MY QUESTION HASNT BEEN RESLVED

[wispy ibex]

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

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[rotund shoal]

Bit confused on what exactly it is asking for here?

sin(180-0.2)?

[simple tapir]

Not quite

The problem doesn't say $\alpha=0.2$, it says $\sin(\alpha)=0.2$

[ocean seal]

Eve

[rotund shoal]

Ohh right

I see what you mean

Thank you

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[grand hornet]

i dont know how to solve this

i need help

[sour dove]

so we know that it can't be the two tables right? These are outputs of a sequence, and a sequence is in sequential order (n = 1, 2, 3, 4, etc).

It' can't be Table 2 because those n inputs have to be integers. And it can't be Table 1 because the values are out of order from the list above

so how can we test a or b?

Also, did you go through the sample solution link in the description?

[grand hornet]

yes i did it doesnt explain it

but i now know why its not table 1 and 2

but how would i generate the formulas A % B

A & B

lets say it didnt give me choices

[sour dove]

you can do a plug and chug. Put in n = 1, 2, 3, 4 and then see which one lines up. But one is more obvious than the other

[sour dove]

ah okay

[grand hornet]

yeah

[sour dove]

okay so the general formula for a geometric sequence is $a_n = a_1 (r^{n-1})$, where $r$ is the ratio between terms

[ocean seal]

MellowDramaLlama

[grand hornet]

why is the formula include n - 1

why not just n

where does the -1 come from

[sour dove]

because we need to account for the first value. Remember that anything to the 0th power is 1, and n=1 is the start

[grand hornet]

that doesnt make sense to me

[sour dove]

what's 1-1?

[grand hornet]

0

[sour dove]

and what is, say 20^0 ?

[grand hornet]

1

[sour dove]

there you go

that becomes a_1

the first term

a_1(r^0) = a_1

[grand hornet]

so minus one makes it where y can equal 0?

[sour dove]

there's no y here. Look at my given formula above

[grand hornet]

without the minus you couldnt get x = 0

my bad

wrong variable

[grand hornet]

right?

is that correct

[sour dove]

yeah pretty much. We're multiply a_1's value by r to some power each time. That'll make our formula increase or decrease respectively. when n = 1, we get r^0 = 1. So then our formula a_1 = a_1(r^0) --> a_1 = a_1. It's redundant but our geometric formula depends on knowing the first term at least

[grand hornet]

so you cant have the formula without the n - 1?

the table doesnt start at 0 so whats the point of having n - 1?

i thought an exponential function was y = ab^x

why is it different now

[sour dove]

it's a matter of flavor. You could start at n = 0, but most start at n = 1

[grand hornet]

oh okay

i looked in the sample solution here it is

could you explain it

hold on let me send it

[sour dove]

it's the same thing. Swap out a_1 for a, b for r, and n for x

[grand hornet]

how is it finding the 10%?

[sour dove]

$a_n = a_1(r^{n-1})$ and $y = ab^x$

[ocean seal]

MellowDramaLlama

[grand hornet]

i see

but how did the sample solution find 10%

where did that come from

[sour dove]

take the 2nd term, and divide it by the first term: $\frac{3.3}{3} = 1.1$

[ocean seal]

MellowDramaLlama

[grand hornet]

ohhh

[sour dove]

and just to verify, do the same with the 3rd term and 2nd term

[grand hornet]

yes

[sour dove]

,w 3.63/3.3

[ocean seal]

Results provided by WolframAlpha

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

Requested by mellowdramallama

[grand hornet]

yes

but another quesiton

how do i get the 3?

is it by

idk

how do i get it

like in the answer'

[sour dove]

the first value? It's given to you most of the time

[grand hornet]

G(n) = 3(1.1)n–1

so it gives me 3?

what if it doesnt?

how can i find it

[sour dove]

for a geometric sequence, you either get just the formula, or the first few terms

[grand hornet]

oh wait

i found out how

this is another problem

but

it explains how to derive the formula from just dividing two numbers

in the table

so if we apply it to this problem

heres the process then:

we divide two numbers: 3.3/3 = 1.1

b = 1.1

b = 1 + .1

Growth Rate:

.1(100) = 10

bruh

what did i do wrong

wait

OMG

THATS CORRECT

i got the 10%

[sour dove]

lol yep. Nice work.

if you want another way to look at it (what makes sense to me)

[grand hornet]

easier way is to just divide two numbers, look at the decimal, multiply it by 100 and get the percentage

in ur head

right

[sour dove]

If you want a shortcut just omit the 1. in it

for example 1.25 represents a 25% growth rate 😉

[grand hornet]

oh yeah

thats easy

lol

[sour dove]

say if for example we well a product for $68 dollars. We want to increase the product's cost by 13%.

So then we would need to multiply the 68 by .13 to get the percentage and then add it to the original cost

[grand hornet]

G(n) = 3(1.1)^n–1

[sour dove]

y = 68 + 68(.13)

we can then factor out a 68: y = 68(1 + .13)

then we have our formula: y = 68(1.13)

[grand hornet]

wait

how did you factor out a 68?

what happened

[sour dove]

68(1.13) = 68(1 + .13) = 68 + 68(.13)

[grand hornet]

wait what

ummm

there are two 68's

how did one dissapear

[sour dove]

lol yes

it didn't

it was just factored out

[grand hornet]

where

[sour dove]

like take something like this

y = a + a*b
you can factor out an a term to get y = a(1 + b)

that's all I did

[grand hornet]

ohhh

makes sense now lol

okay thank you

really much

that took a while

buy you stayed

thank you

[sour dove]

no worries at all! I'm glad that you understood it 🙂

[grand hornet]

W

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[keen pewter]

How can I write the explicit formula for a geometric function, the first value is -4, the ratio is 2

[wind cloak]

Geometric function or geometric sequence?

[keen pewter]

Sequence

Sorry

[wind cloak]

do you know how to write the general term of a geometric sequence?

[keen pewter]

Yea

I was already able to get 8th term

I just don’t understand how to turn that into explicit

My teacher never taught me lol

[wind cloak]

$T_n = ar^{n-1}$

[ocean seal]

NEON

[wind cloak]

Where a is the first term and r is the common ratio

[keen pewter]

Ratio

[wind cloak]

mb haha

[keen pewter]

Yea but I can’t turn that into explicit I just don’t understand idk why

[wind cloak]

Plug in a = -4 and r = 2

[keen pewter]

Got it

And then?

I did $a_n = (-4)(2)^{n-1}$

[ocean seal]

lxve

[wind cloak]

yup

Now that's your nth term

Keep putting in value for n from 1 to how many ever terms

That gives you the sequence

[keen pewter]

But doing $a_n = -8^{1-1}$ gives -1

[ocean seal]

lxve

[keen pewter]

Instead of -4

Oh wait

You don’t multiply them together

Ohh

Got it

Thanks man

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[gilded magnet]

Show work

The angle between the vectors are always 90

Pi/2

Since z axis is always perpendicular to x-y plane

[scenic wedge]

what is the vector xy being 2

what does that mean

ahh got it

using mag a * mag b *sin theta = mag a x b

thanks for help

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[vital nest]

This ain't a limit problem. First i gotta prove that the sequence is indeed convergent

Idk how do i

[tacit arch]

Well did you use the hint

[vital nest]

I can't carry with the hint cuz i dunno what to do with it

[tacit arch]

That's where you should start

[vital nest]

Yea i understand but i can't tell how to proceed with it

[royal socket]

Hint 2: ||harmonic series||

[vital nest]

(n+1)u_n = 2(1 + 1/2 + ... + 1/n)
or, (n+1)u_n < (1 + 1/2 + ... + 1/n)
or, u_n < [1 + 1/2 + ... + 1/n + 1/(n+1)]/(n+1) - 1/(n+1)²

Limit of the whole right side thing is 0, so by squeeze theorem 0 < u_n < v_n, we have lim v_n = 0, so u_n is 0 as well? Or is there any fault

[lone heart]

@vital nest Has your question been resolved?

[vital nest]

K it's indeed is wrong sign of inequality, silly mistake

[lone heart]

@vital nest Has your question been resolved?

[lone heart]

@vital nest Has your question been resolved?

[upbeat hornet]

the step between the first line and the second line is wrong

[vital nest]

I've realised it long ago

[upbeat hornet]

What is the proof once corrected?

[vital nest]

Idk guess i am stuck again

[lone heart]

@vital nest Has your question been resolved?

[obsidian nest]

who can teach me some 5th grade things so i can get ahead in school

pls

[lone heart]

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[pliant cedar]

hello, im trying to prove that a continuous function on a closed interval is bounded...can anybody help me do this? i have seen proofs based on sequences and stuff but i havent studied sequences yet...can somebody direct me in the right direction to write a proof without the use of sequences

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[alpine sable]

Use product rule to diff

Heres my current work:

Is that correct?

Answer should be :

[wanton pebble]

i think last step is wrong

[alpine sable]

okay tbf i was just guessing at that point because it looked nothing like the answer

[wanton pebble]

1/2 z^(-1/2)

write that again

in simple form

[alpine sable]

i did

i simplified it

[alpine sable]

im confused

im pretty sure someone else told me the literal exact opposite

hold on let me check my notes

[wanton pebble]

you are using 1/2 wrong

[alpine sable]

wait so im cofnused

because what doies the -1 do then?

because you have the 1/2 making it into a surd

but its -1/2 so its also inverse

[wanton pebble]

-1/2 is just power of z

[alpine sable]

so it would be for example if the quiestion was z^-1/2 it would be 1/ root Z no?

[wanton pebble]

yes

so why did you write 1/2 in denominator

[alpine sable]

i thought you would have to multiply the denominator by 1/2 no?

[wanton pebble]

tell me what is diff of x^(-4)

[alpine sable]

1/x^4

[wanton pebble]

no

[alpine sable]

what

[wanton pebble]

i am asking differential of that

[alpine sable]

oh shit sorry

-4x^-5

[wanton pebble]

okie

so what us differential of x^-1/2

[alpine sable]

-1/2x^-3/2

[wanton pebble]

wait sorry differential of x^1/2

[alpine sable]

1/2x^-1/2

[wanton pebble]

and what will be 1 X 1/2 x^-1/2

[alpine sable]

im confused. you mean multiplying by 1?

[wanton pebble]

yes

[alpine sable]

1/2x^-1/2

doesnt change

[wanton pebble]

so why do you change it in last step

[alpine sable]

i just wrote it in a different format

[wanton pebble]

1 /(1/2)= 2 ≠ 1/2

you can't write 1/2 as 1/(1/2)

[alpine sable]

see this is what is confusing let me show you what i did last time

[wanton pebble]

okie

[alpine sable]

i got told i couldnt do that

[wanton pebble]

yes u cant

[alpine sable]

thats this tho isnt it?

[wanton pebble]

cause u^-1/2 ≠ 1/u^-1/2

the problem was with your u

[thick lynx]

$u^{-\frac 1 2} = \frac{1}{u^{\frac 1 2}}$

[wheat isle]

1/sqrt(u)

[thick lynx]

Yes, I wrote it like this to make it clearer

[alpine sable]

could you write it with a 1/2 in front of the u and tell me what thatgives you?

so it would be 1/2u^-1/2

and what does that simplify to

[thick lynx]

$\frac 1 2 \cdot u^{-\frac 1 2} = \frac 1 2 \cdot \frac{1}{u^{\frac 1 2}} = \frac{1}{2u^{\frac 1 2}}$

[alpine sable]

ohhhhhhhhhhhhhhhhh

i see now that its been broken up

[wanton pebble]

yp

[alpine sable]

alright imma print that and also retry with that new infromation and brb

[wanton pebble]

sure

[alpine sable]

Okay I’ve done it but I still have a slight issue. Bear in mind I had another slight issue with the previous question that the answers got slightly wrong. Here’s my new working:

Lemme know if you see anything wrong with it

[wanton pebble]

yeah

it is wrong

[thick lynx]

It should be a $(x + 1) \frac{1}{2 \sqrt{x - 1}}$.

Not x - 1

[alpine sable]

oh i see

thanks i think that clears it up

.close

[lone heart]

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[strange fractal]

in trig can u use a 90 degree angle?

[snow hazel]

trigonometry usually defines only non-right angle triangle

I think u can use it for only in trig ratios

[strange fractal]

Ohhh ok

Thank u

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[copper aspen]

hello there

[somber eagle]

how did you go from the first integral from the second

[copper aspen]

i used the Half angle formula

[somber eagle]

why not just turn the sin^2x into cos2x

[pulsar aspen]

That's not even correct

[somber eagle]

yes it is

[copper aspen]

sry i dont get it

[zealous lichen]

I think it's just sin^3x = (3sinx - sin 3x)/4

[pulsar aspen]

cos 2x = 1-2sin^2 x

[zealous lichen]

so your answer looks different

[somber eagle]

i meant turn it into something with cos2x

did you have to take it literal

[copper aspen]

oh i guess thats what im missing

[copper aspen]

but is it possibly to have this answer directly

like without using integration by parts

[royal socket]

it's better to be clear with what ur saying..

[somber eagle]

bruh

[somber eagle]

thats the way you start

[copper aspen]

thx!!

i'll try that now

that works!!

thx

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[flat roost]

how do i add 3 partial derivatives up on wolfram alpha, theyre really massive and i simply cannot afford to add them up myself, thanks

[flat roost]

the derivatives in question are

https://www.wolframalpha.com/input?i=double+partial+derivative&assumption={"F"%2C+"SecondDerivativeCalculator"%2C+"derivativefunction"}+->"B*z%2Fa_0+*+e^(-sqrt(x^2+%2B+y^2+%2B+z^2)+%2F+(2*a_0))"&assumption={"F"%2C+"SecondDerivativeCalculator"%2C+"derivativevariable"}+->"x"

https://www.wolframalpha.com/input?i=double+partial+derivative&assumption={"F"%2C+"SecondDerivativeCalculator"%2C+"derivativefunction"}+->"B*z%2Fa_0+*+e^(-sqrt(x^2+%2B+y^2+%2B+z^2)+%2F+(2*a_0))"&assumption={"F"%2C+"SecondDerivativeCalculator"%2C+"derivativevariable"}+->"y"

https://www.wolframalpha.com/input?i=double+partial+derivative&assumption={"F"%2C+"SecondDerivativeCalculator"%2C+"derivativefunction"}+->"B*z%2Fa_0+*+e^(-sqrt(x^2+%2B+y^2+%2B+z^2)+%2F+(2*a_0))"&assumption={"F"%2C+"SecondDerivativeCalculator"%2C+"derivativevariable"}+->"z"

[lone heart]

@flat roost Has your question been resolved?

[ancient saddle]

mmm you mean

,w d2/dx2(Bz/a_0 * e^(-sqrt(x^2 + y^2 + z^2) / (2a_0))) + d2/dy2(Bz/a_0 * e^(-sqrt(x^2 + y^2 + z^2) / (2a_0))) + d2/dz2(Bz/a_0 * e^(-sqrt(x^2 + y^2 + z^2) / (2a_0)))

[flat roost]

uhh

[ocean seal]

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Requested by eleonardo

[flat roost]

i dont even know anymore

the formatting is very strange

[ancient saddle]

Do you want the sum of all partial second derivatives? 🤔

That alternate form looks nice

In case that's what you want

[flat roost]

yeah of x y and z

[ancient saddle]

Well that's it then

See Alternate forms

[flat roost]

alright