help-0

[next elbow]

You just put in the respective value for the terms

Once again a1=4

So since a_n = 7 * a_n+1

a2 = 7* a1

And so on

[jade steppe]

what if it's not a1

like a_3-1

[next elbow]

a2 is a1 multiplied by 7

And every term is the previous one multiplied by 7

[jade steppe]

so I always resort to a1=4

[next elbow]

That would be a2 which is a1 multiplied by 7

[next elbow]

Yeah, in this question

[jade steppe]

what is a2

what

whats a3

😭

[next elbow]

7 * a1

[jade steppe]

is there only a1 and a2

[next elbow]

a3 is 7 * a2

[jade steppe]

which is still apart of this question right

[next elbow]

Yes

For the general formula a_n = 7 * a_n-1
My advice is to not view n as a variable, but something that you have to plug in a value to work out for the value

[jade steppe]

aaa okeei

[next elbow]

I hope that’s less confusing

[jade steppe]

yeah it helped a bitt

[next elbow]

Great to hear that

[jade steppe]

thanks

.close

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[frank crow]

so this is what I'm dealing with

at this point I dont really know where to start other than maybe make the 3-x be -(x-3)

[final hatch]

basically g'(3)

[frank crow]

how so?

[final hatch]

hold up let me find formula

[frank crow]

the definition of derivative?

if so I have it here

[final hatch]

in a point yes

[frank crow]

ok ok got it

[thick lynx]

It's not exactly g'(3)

[final hatch]

it is not

cause it's inverse

[frank crow]

oh I get it I get it

[frank crow]

I gotta work like towards it tho

[thick lynx]

Negative inverse

[thick lynx]

[\lim_{x \to 3} \frac{3 - x}{g(x) - 2} = \lim_{x \to 3} \frac{3 - x}{g(x) - g(3)} = \lim_{x \to 3} -\frac{x - 3}{g(x) - g(3)}]

[frank crow]

so I gotta send the top part to the bottom and bottom to the top

[unkempt sundial]

negative reciprocal

[thick lynx]

[= \lim_{x \to 3} -\frac{1}{\frac{g(x) - g(3)}{x - 3}}]

[final hatch]

exactly thanks for pointing it out

[frank crow]

got it

perfect

thanks a lot

[thick lynx]

And now limit laws

[frank crow]

ye ye

[thick lynx]

You can get the limit to the denominator

[frank crow]

ye that part is easy I just have trouble getting there usually

but thanks!!

[thick lynx]

Well inverse should also be fine, since the reciprocal is always the inverse of a number over R

[frank crow]

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[lone heart]

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[blissful palm]

Hello

[blissful palm]

I need help with something

I am trying to calculate the bayesian probability of the universe being finite

But idk how Ik the formula but not sure what I am supposed to do with it

Its believed to be a high number like 98

While it is true that theorists are working on models for a past eternal universe, a Bayesian probability can be assigned to this premise of 98%.

I saw this and just wanted to calculate it for myself but Idk what to do

Thanks guys

👍🙏

1. I dont know where to begin

[lone heart]

@blissful palm Has your question been resolved?

[blissful palm]

<@&286206848099549185>

[lone heart]

@blissful palm Has your question been resolved?

[lone heart]

@blissful palm Has your question been resolved?

[balmy grail]

If this is a homework problem type question, you need to employ Bayesian learning that will look something like, pr[universe is finite given evidence] = pr[seeing evidence given the universe is finite] * pr[ prior ] / pr[ seeing evidence ]
Where the prior is typically 50-50, and you come up with some sort of evidence that the universe is finite
https://en.wikipedia.org/wiki/Bayesian_inference

[balmy grail]

If it’s more of a philosophical argument you might be interested in https://en.wikipedia.org/wiki/Pascal's_wager

[lone heart]

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[balmy canopy]

This homework question has given me a function in standard form. It told me to graph it and the inverse. The next part of the question says "restrict its domain so f^-1(x) is a function." I know f^-1(x) means the inverse and I know what makes a function count as a function, but how would I restrict the domain?

[limpid turret]

Restricting the domain is saying which specific x values you want to keep. Usually expressed as an interval

[balmy canopy]

so would I say something like "y is equal to and cannot be higher than -2"

-2 being the y value of the inverse's parabola

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sour dove]

it might be helpful to show the whole problem and what it's asking

like a screenshot of the problem

[balmy canopy]

2. Consider the following function: f (x) = 2x^2 + 8x + 13
   a. Determine the inverse of f (x)
   b. Restrict it's domain so that f^-1 (x) is a function

[sour dove]

ok so yeah

[sour dove]

do you remember the fact that inverse functions have to be one to one?

[balmy canopy]

What do you mean one to one?

[sour dove]

an x is directly mapped to a unique y

so for example: y = 2x, there's no 2 x values that share the same y value

but on a parabola, say y = x^2, there's lots that share the same y value. x = 2 and x = -4 both equal 4

so they're not one to one

in order to be an inverse function, a function has to be one to one and has to be onto.

I reccommend giving this a quick watch to understand why inverse functions are defined this way

https://www.youtube.com/watch?v=xKNX8BUWR0g

[balmy canopy]

isnt the inverse function just the same as the normal function but with the x values and y values switched?

sorry for the late responses by the way

[sour dove]

yes, to an extent. But that doesnt' work if you have a y values that maps to 2 x values, right?

[balmy canopy]

yes

[sour dove]

like the procedure to find the inverse function is to swap x and y and solve for y

but the function you get is only the inverse if your original function is one to one and onto

[balmy canopy]

but how would i restrict the domain so the inverse is a function?

like would I just cut half of the graph off?

[sour dove]

it's the right idea 🙂

but do you know why we're "cutting it in half"?

[balmy canopy]

Like how the inverse function is opening to the right

Looking like a long C

I'm thinking like would I have to cut the top or bottom half off

So like "y is equal or less than -2"

[sour dove]

yeah you got the right idea

so for a parabola's sake, you'll need to find the vertex and then start there as your domain

you can go either direction, left or right, depending on your needs

[balmy canopy]

I have the vertex, like I have the inverse plotted out already

I just restrict it so it looks like a radical?

(it not actually being a radical)

[sour dove]

one fancy thing about inverses is that if you have f(x) and f^-1(x), then f(f^-1(x)) = f^-1(f(x)) = x

in other words, they're reflective across the line y = x

for example

notice how they're symmetrical across the line y=x?

[balmy canopy]

That's what I'm trying to do

The original function ended up in the top left quadrant, so the inverse is in the bottom right

Lines on graph cannot be a function if a vertical line passes through more than once

So I was wondering if I turn the inverse into one of the bottom two things I drew

[sour dove]

yeah you can. You just need to restrict the domain like we've been talking about.

as an example

we have to restrict the domain of the green on to x values greater than 0 here

otherwise it'll fail the vertical line test

[lone heart]

@balmy canopy Has your question been resolved?

[balmy canopy]

Oh so I really do just cut it in half and state the domain with a restriction

Just seemed weird to me

Should I state one possible restriction or both

I'll do both to be sure

[sour dove]

so when you are finding the inverse, you're doing a square root. Recall that in a square root you actually get a +/- sqrt value

so whichever one you pick you'll need to pick the domain appropriate that reflects on the line y = x

[balmy canopy]

What do you mean

[sour dove]

one second let me show by example

ok so this is an example

we have a parabola

[balmy canopy]

But why are you using the original function instead of the inverse

[sour dove]

to prove a point

actually

hold on, let me find a video. They can probably do a better job explaining this than I can

[lone heart]

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[sour dove]

here, give Eddie Woo a quick watch. He's a wonderful explainer

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

[lone heart]

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[zenith flax]

Unsure of how to go about this

[tacit arch]

do you know power rule for integrals

[zenith flax]

Let me go look at my notes

my power rule in my book is

(x^a)^b = x^a*b

[coral thorn]

no

integral power rule

[zenith flax]

No we werent taught that

We also werent taught with arbitrary constants

I tried this as

its F(b)-F(a)

[tacit arch]

missing /4

int x^n dx = x^(n+1) / (n+1)

[zenith flax]

my discord went down but yes

got it

thank you

it’s lagging on pc

but one more question

this is as simple as fooling out and taking anti right?

.close

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[zenith flax]

and im back

[zenith flax]

Confused

[last ether]

The distance between nπ and (n+2)π is exactly 2π, correct?

What's the periodicity of cos(x)

[zenith flax]

hmm

my god pc disxord sucks

anyways

[zenith flax]

how would i denote this

[last ether]

Subtraction.

[zenith flax]

how would i know that

[last ether]

It's legit just the difference between the two numbers

Well the bounds gotta cover some ground

That's just how integrals work

[buoyant saddle]

(n+2)pi=npi+2pi

[zenith flax]

I’m confused on how subtraction would give me that, as I’m not seeing the vision

[buoyant saddle]

the two differ by 2pi

[zenith flax]

okay gotcha

oh!

[last ether]

Anyways use the periodicity of cosine to get your answer

[zenith flax]

then what?

the*

[buoyant saddle]

sin(x)=sin(x+2pi)

sine repeats

because one rotation around the circle is 2pi radians

so it’ll just end up at the same value

[zenith flax]

Im a bit confused on how you made this equation as its npi?

but i understand how 2pi goes aroudn once

[buoyant saddle]

i’m just saying in general

[zenith flax]

okay gotcha

[buoyant saddle]

so if we had sin(npi+2pi)=sin(npi)

[buoyant saddle]

npi is x really^

[zenith flax]

gotcha

oh this would be 0

because we're landing in the same spot

since 2pi

and then its 9sin(npi)-9sin(npi)

success!

.close

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[limpid turret]

!show

[lone heart]

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

[limpid turret]

I can't tell you why it's wrong without seeing how you got it

[lone heart]

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[lone magnet]

I thought that the answer would just be the derivative at t=14, is there something I’m missing here?

[solemn juniper]

The graph is a velocity/time graph; the derivative would give its acceleration

[lone magnet]

so the answer is the slope at t = 14?

[solemn juniper]

No

That would, again, give the acceleration

[lone magnet]

Is it just -2?

[solemn juniper]

What is your class's definition of "speed"?

[lone magnet]

here are the relevant lecture notes

[lone heart]

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

[solemn juniper]

Velocity and speed aren't the same thing

Do you have a "key concepts" bit on speed?

[lone magnet]

looks like it was the absolute value of the y value at x = 14

[lone magnet]

it says that speed is distance traveled over time elapsed

[solemn juniper]

And instantaneous speed?

Perhaps I should've been more specific

[lone magnet]

absolute value of the speed at t = 14 I think

[solemn juniper]

You think?

[lone magnet]

yeah

[solemn juniper]

While you're correct, I was asking if there was a notes section on it

[solemn juniper]

Absolute value of the velocity

[lone magnet]

the only thing I could find was the notes I put above

[solemn juniper]

Oh I just saw speed in there

Very small text

[lone magnet]

just to be clear, the difference between instantaneous speed and instantaneous velocity is that speed is always positive right

[solemn juniper]

That's one interpretation of it, sure

[lone magnet]

okay, that resolves this question

thanks for the help

.close

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[heady finch]

How is F1 = F2sin(theta) if F1 - F2sin(theta)i = 0?

[lone heart]

@heady finch Has your question been resolved?

[lone heart]

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[tacit vale]

does anyone know why this isn't working?? the thing on the computer screen is the answer key

[tacit vale]

sorry for the blurry photo, hard to take with one hand

all of my answers for this part are coming out wrong and I guess I must have written the equation into the calculator wrong but I'm not sure how to fix it

this is for sinusoidal graphs

[fallen verge]

check for rad vs deg

yeah youre in deg mode

[tacit vale]

man and they just told us to switch it a few weeks ago

thanks, perfect

[fallen verge]

oh yeah physics sucks for that

you need deg for most vector stuff

then in angular, you switch back

[tacit vale]

ahh okay, we were doing stuff with degrees before so it makes sense

we had a sub so she probably forgot to tell us to switch back or I just should have known and didn't

thanks!! I'll close this now

[fallen verge]

youre welcome

[tacit vale]

.close

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[sweet ether]

Hi, ive done up to step 3 but i dont get how they ‘invert and multiply’ to get to the last step. Is it a rule or just something you can do? Thanks

[summer dirge]

a/(b/c) = ac/b

why?

because a/(b/c) = a ÷ b/c = a*(c/b) = ac/b

[chilly crag]

1 / (1/x) = x

[sweet ether]

so 1/(1/x^8) = 1 divided by (1/x^8) = 1 * (x^8/1) = 1*(x^8)/1

hmm ok so whats something i can use to remember that like move the numerator outside the bracket and invert the denominator?

Seems like i overcomplicted i think

[remote pecan]

Because 1/1/x^2=1÷(1/x^2)=1*x^2=x^2

And (x^2)^4=x^(4*2)

=x^8

[sweet ether]

so do the 1s cancel out?

leaving it with 1*x^2

[remote pecan]

If you divide something with a fraction, then it is basically equivalent to multiplying it by the reciprical of tghat fraction

For reference

[sweet ether]

Ahh right yeah forgot all ab that my brain has gotten dumber during the holidays haha

thanks all of u guys!

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[remote pecan]

Haha me too!

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[wheat sparrow]

i got the magnitude of 13

I wrote out 3(12/13 i - 5/13 k)

then got (36/13) i + (-15/13) k

I dont understand how -15/13 is wrong

[ocean whale]

What does it say the answer is?

[wheat sparrow]

nvm im stupid

the answer is shown above, apparently I wrote 15/13 instead.

.close

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[wet frigate]

trying to prove this property for dfs

for this can you just use induction, like suppose we want to prove
dfs(r) visits every node on a path beginning with r.
Base case is trivial,
IH assume r,v1,...,vk is visited, now we want to prove vk+1 is visited
since vk+1 is in adj[vk], from def of dfs algorithm, dfs will be called on vk+1 so it will be visited

is that all u need^?

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@wet frigate Has your question been resolved?

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@wet frigate Has your question been resolved?

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[vapid shuttle]

Computing this directly is sort of a mess, but after all of my work (which I can show if it behooves anyone) I get that the integrand simplifies to -r^5 sin(phi) which I'm just sort of sus of the negative

does anyone know if I may be mistakenly picking it up somehow ( like some orientation thing? ) or know if that looks good

.close

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[astral holly]

Kind of a followup question since the person that helped me had to leave :(.

If I Manage to substitute a improper function to the point where i get a sum of fractions with linear denominators, is that partial Fraction decomposition?
I technically didnt use the normal process to arrive here, and from what I can tell online it wouldnt classify as that.

[serene junco]

Partial fraction decomposition doesn't really involve a substitution

although the two methods might be used together sometimes

[astral holly]

to give quick context ig

https://cdn.discordapp.com/attachments/903481105888452609/1198774646091288698/image.png?ex=65c020e3&is=65adabe3&hm=5a2b774e6cf16a7faa01083c5b5b7569073d2e1daa9d31045b383b077652befb&

substituted for sqroot(x) to this:

https://cdn.discordapp.com/attachments/488104216678760469/1198773982237818992/217447525643190272.png?ex=65c02045&is=65adab45&hm=fedc176d027fba43e06d95e99bbf23898e0edd4c8f47e9a17135301b892fe840&

which then substituted again for m=u+1

to (m-2)(m-1)/m

and at the end, u get m^2/m + 2/m - 3m/m

so now I have 3 fractions with linear denominators

but I didnt really go through the process of partial fraction decomposition im familiar with

but also, I dont see how this can be solved that way as no matter I cant find a proper function

(we are told to solve it with substituting sqroot(x) and partial fraction decomposition)

[serene junco]

That seems to check out, but no it is not partial fraction decomp

And I agree, partial fractions doesn't really seem appropriate for this integral

[astral holly]

okay so my confusion was warranted^^ thought i was missing smth

atp i might just ask the prof, since noone seems to believe its appropriate^^

[serene junco]

Yeah I mean, after you do u=sqrt(x), the denominator is already linear

And, the degree of the numerator is higher, so you'd have to divide first, but you'd still only have u+1 as a denominator for the remainder

so there's nothing to decompose

[astral holly]

yeah I think ive solved this like 2 ways already but none of them involved decomposition^^ bummer

[serene junco]

Could just be a mistake in the question, yeah I'd just ask your prof

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@astral holly Has your question been resolved?

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[noble mural]

Help me find what’s wrong

[noble mural]

I thought I might had to factor -4 out

I think this step is the reason why but I don’t understand why I have to take this step.

And Photomath doesn’t tell me unless I pay for plus.

<@&286206848099549185>

[lone heart]

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.

[noble mural]

Mb

[buoyant saddle]

y they divided by 2?

ur work is hard to read

they divided by 2 simplify it

because there was a factor of 2 on both sides

it looks like u squared both sides but didn’t square the 4 on the left

and only squared the square root

yea that’s ur mistake

u squared both sides but didn’t square the -4

should by (16)(8m+1)

[noble mural]

Yea

[buoyant saddle]

@noble mural

[noble mural]

You mean divided by -2?

[buoyant saddle]

yea same thing

[noble mural]

Alr I’ll get back to you after doing that

I for some reason wrote in my notes to not do that

[buoyant saddle]

strange

it’s wrong

[noble mural]

!close

.close

[lone heart]

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[wide onyx]

.close

is 0.3 comp or stretxh

[wide onyx]

what r the transfomrations being applied here

[hard prawn]

it's 2^x shifted 2009 units to the right, compressed by factor of 0.3 vertically, and shifted 40 units upward

[wide onyx]

okk

[wide onyx]

if less than 1 comp?

[hard prawn]

yes

[lone heart]

@wide onyx Has your question been resolved?

[lone heart]

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[zenith flax]

Can I get some help with explaination on this?

[unkempt mica]

start by splitting the integral

[zenith flax]

how exactly would i go about doing that?

would it be

hold on

[mystic swallow]

yes

[zenith flax]

Okay, how what would i do with that

[mystic swallow]

okay so remember how an integral is just the area under the curve?

use that

[summer dirge]

use the definition of f on each interval

[zenith flax]

yes

that uh

confused me

wdym use it?

[mystic swallow]

e.g. if 4 is larger than x, the value of f(x) is 4

[zenith flax]

gotcha

[mystic swallow]

so the integral from -1 to 4 is 4 x 5 units

[summer dirge]

for the first integral, turn f(x) into 4

[mystic swallow]

exactly

[summer dirge]

for the 2nd, turn f(x) into x

[zenith flax]

and then id use the property of

4(b-a)

for the first one

confused on what id do with x for the second one

[mystic swallow]

okay

so what's the integral of x

or the antiderivative

[zenith flax]

1

oh

[mystic swallow]

no?

[zenith flax]

1(b-a)?

[mystic swallow]

no?

[zenith flax]

wait

sorry

wait ewait

[mystic swallow]

the ANTIderivative of "x"

[zenith flax]

1/2x^2

[mystic swallow]

yes

0.5x^2

so now plug the b - a thing ther

wait brb

back

so now do you know how to evaluate the integral?

[zenith flax]

im still confused

so

i got 28 with the left side

[mystic swallow]

okay

[zenith flax]

or well -1 to 4

[mystic swallow]

what?

how did you get 28-

[zenith flax]

4(6-(-1))

[mystic swallow]

hang on-

but we SPLIT the integral

[zenith flax]

since i 4 as the f(x)

[mystic swallow]

remember??

[zenith flax]

yes

hold on

[mystic swallow]

BUT f(x) = 4 only when x is lower than 4, so 4-6 doesn't count here

[zenith flax]

sorry i put the wrong numbers

running off of no slepe rn

[mystic swallow]

lol

[zenith flax]

20

[mystic swallow]

yes

[zenith flax]

okay

[mystic swallow]

dude tbh get some sleep first

[zenith flax]

now with .5x^2

what to do

oh wait

[mystic swallow]

after this go directly to bed

yea so just input the rest of the values here

[zenith flax]

dont worry i have 4 more questions ive beens tuck on

[mystic swallow]

LOL

[zenith flax]

[mystic swallow]

dw i'll help

im here all day

[zenith flax]

I'm a bit confused on inputting into .5x^2

[mystic swallow]

okay

[zenith flax]

I do know the rule of putting the .5 to the outside

[mystic swallow]

okaty

*okay

the integral of f'(x) dx from a to b is just f(b) - f(a)

[zenith flax]

oh

gothca

brb

[mystic swallow]

we know that "x" is the derivative of 0.5x^2

[mystic swallow]

kk

[zenith flax]

got it

[mystic swallow]

what is it?

[zenith flax]

30

[mystic swallow]

total integral?

[zenith flax]

litereally getting screwed over by this one

[zenith flax]

Yes that was the answer after adding them together

[mystic swallow]

wait for the 0.5(6)^2 - 0.5(4^2)

[zenith flax]

no

it was 10

[mystic swallow]

okay wait i havent done it myself

yea ok

30

[zenith flax]

Now for htis one

[mystic swallow]

can u just pin this problem

[zenith flax]

yes

.close

[lone heart]

Channel closed

Closed by @zenith flax

Use .reopen if this was a mistake.

[mystic swallow]

tbh idk what the midpoint rule is either-

[zenith flax]

uh

uh

[mystic swallow]

well that works

.close

nope

[zenith flax]

.close

[mystic swallow]

HEH?!

okay

what-

[zenith flax]

#help-11

[lone heart]

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[faint lynx]

For Variation problems

[faint lynx]

If asked "The time spent varies directly as the speed of the car"

Can i write it as a=kb

or does it have to be t=ks

[charred jewel]

as long as you know what each variable means, doesnt really matter

[faint lynx]

ok ty

.close

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[languid sable]

can someone offer me a different take on the concept of vectors, and vector fields? all the tutorials on youtube are kind of roundabout and i don't really understand them

[placid zinc]

You'll have to be a bit more specific. Anything in particular you're having trouble with?

[languid sable]

mainly just how they relate to calculus in particular, as in line integrals and stuff

[last ether]

Alright so line integrals, basically imagine a line. Imagine wind blowing against that line. The wind is the vector field, line is path. Measure how the wind kinda acts upon the line

[languid sable]

so in vector fields, is there anything that defines it or is it chaotic

[last ether]

Well it's typically defined

It's just a "set" of vectors

Like take <x + y, y - x> for example

Meaning at every point (x,y) there's an associated field

But in general

There's wind

There's some path or line or whatever

[languid sable]

so every single point has a vector in a vector field right

[placid zinc]

A vector field is a function Rⁿ → Rⁿ (at least in your usual calc class)

[languid sable]

and is there any GENERAL order to the field or is the order just the scalar of each individual vector

[languid sable]

sorry im selftaught lmao idk this

[last ether]

It's usually defined. Like they will give you a vector field

[languid sable]

so theres a general order to it?

whats the form

[last ether]

Wdym form

Form of a vector field?

[languid sable]

is every vector independant or does the whole field follow an order

[placid zinc]

Is there a general order to most functions? Like, what's the order of y = sin(x)?

[last ether]

Ever vector is dependent on the point it's tail lies at depending on how the vector field is defined

[languid sable]

so every vector starts at the end of another?

[last ether]

Like if I gave you a field F = <x - y, xy> what's the vector at the point (1,2)?

A vector is just a direction with a magnitude

[languid sable]

mhm

[languid sable]

im just starting fields could u teach me how this works

[last ether]

Just plug in (x,y) = (1,2)

So <1 -2, 1(2)> => the vector at (1,2) for the associated field is <-1, 2>

[languid sable]

i see

[last ether]

Nothing crazy

If you do this for all point

You get a lot of vectors

[languid sable]

ohh i see

[last ether]

,w plot vector field {x-y, xy}

[ocean seal]

Results provided by WolframAlpha

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

Requested by umbraleviathan

[languid sable]

is that the scalar or something

im a little dull sorry

[last ether]

The point is just a location

Kinda like a position vector I guess

It's not really a scalar

[languid sable]

is there anything that defines the vector itself

so the scalars

[last ether]

Has magnitude and has direction

Scalars don't have direction

[languid sable]

wait wrong term

magnitude

is there a way u can tell that

and direction as well

[last ether]

Length of the vector

[languid sable]

but from the field given is there a way

[last ether]

Direction is usually compared to how many degrees from the positive x axis

Well

Yeah

If you plot a fuck ton of vectors

You can kinda trace the arrows

Start at one point

Follow the ardows

You get a possible path

[languid sable]

i see so theres no numerical way just from a field given right

[last ether]

Wdym numerical way

[languid sable]

like a formula or anything

[last ether]

For?

[languid sable]

finding the direction and magnitude from a given field

[last ether]

A field is like a set of vectors

You don't find the "direction and magnitude" of the whole field

We can measure it's flux or general direction

I guess

Not meausre

Like qualitatively describe

[last ether]

Like this spirals out

We would say that its flux is negative

But I mean

[languid sable]

what i mean is theres no way to find out if for example if you have a distance 1 from the origin, all of the vectors starting at that point have a certain direction relating to their starting point or something?

[last ether]

,w plot vector field {1, 1}

[last ether]

There can only be one vector for one point

[languid sable]

yeah

but if theres a ring in which all points are the same distance from the origin you cant find the direction?

of the vectors on those points

[last ether]

You can find the magnitude and direction of a specific vector if you:

• Know the field
• Know where the vector starts (its tail)

[languid sable]

oh i see

how would u do that

[last ether]

Well if you think about a vector, it's just a linear combination of some orthogonal bases

So if you use Pythagorean theorem

[languid sable]

wouldnt u need the end of the vector then

[last ether]

You'll get that if you have a vector that's <a, b>, its magnitude is just sqrt(a^2 + b^2)

Which is nice because

If you have a vector, v, in any dimension

It's magnitude is sqrt(v • v)

[last ether]

No

[languid sable]

so <a,b> is the starting point of the vector right

[last ether]

<a,b> is the vector itself

[languid sable]

so what do they stand for

a and b

[last ether]

You can get <a,b> from plugging in the starting point into the expression of the field

[last ether]

x component, y component

Could be anything

[languid sable]

doesnt a vector have direction and magnitude? how do two values define the whole vector then

[last ether]

I just explained...

Alright

A vector tells you how to move like

Lemme draw this out

Like let's start with the basics

[languid sable]

oh so its the length

i was getting it confused sorry

[last ether]

If you were given a vector <1,1>, you would move 1 to the right, 1 up

[languid sable]

yeah i get it now

;-;

[last ether]

The length is magnitude

[languid sable]

i see i see

mk thanks

[lone heart]

@languid sable Has your question been resolved?

[lone heart]

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[lone heart]

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[alpine sable]

im stuck, I put a^2 and b^2 into pythag in my calculator and i don’t get a whole number, am i supposed to using pythag?

[coral flower]

its still correct tho

sometimes numbers can come in sqrts

[alpine sable]

did you also get 17.691...

where do I go from that

[coral flower]

thats AB

u can keep it in sqrt or use 17.691

[alpine sable]

okay thanks that was correct but im lost now on how i would find ac and bc

well AB and BC were right but AC isnt 5

[vapid lance]

yes

ac is root 313

yes

[alpine sable]

can u show me how you got ac and ab

[vapid lance]

srry i thought 13 was hypotenuse

[vapid lance]

So

they have given

TanA

As 13/12

And the trignometric ratio formula for tan is?

@alpine sable

[alpine sable]

Opposite over Adjacent

[vapid lance]

Yes

tell me what the opposite side and adjecent side is

[alpine sable]

opp is 13 adj is 12

[vapid lance]

In triangle abc

[vapid lance]

yes TanA = 13/12 =Opposite Side/ Adjecent side

just substitute

done

Opposite side =BC
adjecant side = ac

BC= 13
AC =12

[alpine sable]

so basically

where i wrote the 12

is AC

and thats the answer?

[vapid lance]

Correct

[alpine sable]

ohh ok thank you

[vapid lance]

Not necessarily that you will always get a whole number as hypotenuse Or any other side btw

[alpine sable]

oh okay

.close

[lone heart]

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[soft timber]

i need help with this im not exactly sure how to do it

[lone heart]

@soft timber Has your question been resolved?

[lone heart]

@soft timber Has your question been resolved?

[soft timber]

.close

[lone heart]

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[lone heart]

@left dawn Has your question been resolved?

[left dawn]

No

[lone heart]

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[steep cove]

what is the measure of acute angle ABC?

[lone heart]

@steep cove Has your question been resolved?

[lone heart]

@steep cove Has your question been resolved?

[naive valley]

!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 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

[steep cove]

1

[naive valley]

maybe draw a segment from O to B, what can you then say about triangles OAB and OBC?

wtf

[wraith meteor]

what

[naive valley]

what is that spam

[wraith meteor]

anything wrong

thats not spam

its a note

he asked for it

[naive valley]

i'm not gonna download it but i hope you didn't just paste a full answer

[wraith meteor]

oh its not

[naive valley]

ah ok

why is this happening haha

[steep cove]

There both right triangles

[unkempt sundial]

[steep cove]

If the angle O is 90 then is the angle B 45?

[wraith meteor]

exactly

[steep cove]

now what

[wraith meteor]

wdym now what

thats the answer

[steep cove]

ok

ty

[wraith meteor]

so

any payment?

[naive valley]

^ you mean angle P?

oh wait, B on your original figure, nvm

[steep cove]

.close

[lone heart]

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[steep cove]

On b) it says 5 cm of radius

[trail spade]

what should be the answer of q) Taj Mahal is located on the right bank of Yamuna in a vast Mughal Garden that encompasses nearly 17
hectares of area. It is one of the world’s seven wonders as declared by UNESCO as a world heritage site.

a. The Taj Mahal stands on a square platform that is 95.40 m on each side. What is the area of this
square in square metres?
b. The floor area of the main building is 3214 m2

. What is the area of the part of the platform that is not

covered by the main building?
c. If 1 hectare = 10,000 m2

, find the area of the Mughal Garden in square metre.

[lone heart]

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[spice rain]

For a n-digit number which leftmost digit is 1, if the leftmost digit is now put at the rightmost, the new number formed is 3 times the original. Find the minimum value of n.

[spice rain]

The answer given is n = 6
I just don't know how to show proof on that 💀

<@&286206848099549185>

[lone heart]

@spice rain Has your question been resolved?

[trail spade]

what should be the answer of q) Taj Mahal is located on the right bank of Yamuna in a vast Mughal Garden that encompasses nearly 17
hectares of area. It is one of the world’s seven wonders as declared by UNESCO as a world heritage site.

a. The Taj Mahal stands on a square platform that is 95.40 m on each side. What is the area of this
square in square metres?
b. The floor area of the main building is 3214 m2

. What is the area of the part of the platform that is not

covered by the main building?
c. If 1 hectare = 10,000 m2

, find the area of the Mughal Garden in square metre.

<@&286206848099549185>

[charred jewel]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[lone heart]

@spice rain Has your question been resolved?

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[dapper patio]

currently trying to use gaussian elimination to calculate the determinant, but when i put it into calculators to check for my answer, i realize that something always goes wrong with my calculations so i get a completely differnet determinant, any help?

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@dapper patio Has your question been resolved?

[dapper patio]

<@&286206848099549185>

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[copper compass]

1 fourth times X + 1 sixth times X + 1 half times X + 5 = X
The X is 60, but i dont understand why the x is 60

can someone help me?

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[lone heart]

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[gritty crystal]

Hey, for question 4 part i, i’ve got the first derivative and set equal to zero but how do i solve to get max and min?

[gritty crystal]

wants the answer in radians in terms of pi *

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[lofty heath]

How do I do parts B and C. I did part A and I think it’s correct

[lofty heath]

For Part C I factorized the equation and for x = 5 or -1

Still stuck with part B

[keen summit]

wait bro

lemme check

so bro as per i have seen

there are 2 intersection points

[lofty heath]

Exactly

[lofty heath]

(-1 , -5) and (2.5 , 2)

But idk how to solve part B

[keen summit]

yup

now if you plut these x points in the eqn

therefore it will satisfy this equation

[lofty heath]

So like this?

[keen summit]

exactly

now you can see for the x = 2.5 and -1 the equation becomes zero both sides. so it means the equation has 2 roots as 2.5 and -1 and therefore the equation is satisfied by these 2 values

i hope you got it 🙂

if not then dm me i will give you written solution

[lofty heath]

Thank you so much!

I understood 🙂

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[bold jolt]

How can I prove that the empty set is unique using the Extensionality Axiom which is ∀u (u ∈ X ↔ u ∈ Y ) → X = Y.

[lone heart]

@bold jolt Has your question been resolved?

[bold jolt]

<@&286206848099549185>

[rain holly]

suppose that Z is a set and φ(phi) is a formula in the language of set theory. Suppose A and B are two subsets of Z satisfying the axiom of specification for the formula φ. A and B consist of exactly those elements of Z that satisfies φ. In particular, A and B consist of exact the same elements. By extensionaly, it can be concluded that A=B

we can use this principle of extensionality, which states that two sets are equal if and only if they have the same elements

[bold jolt]

Yeah

But it doesnt make sense because the axiom says for any u but a u does not exist becuase nothing belongs to the empty set

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[rain holly]

optionD) 1009?

just substitute 1008 in the second equation as the first equation

[polar echo]

correct how did you solve it

[rain holly]

and divide by root of a

you will get a equation like a+root(a)+1

got it?

[unkempt sundial]

you are quizzing us? 😭

[polar echo]

yeah thanks a lot

[livid sage]

they are asking for reasoning

[polar echo]

i tried that before but for some reason i didn't get the answer from there

[rain holly]

maybe you did it in a rush

[polar echo]

lol i just have lot of test exams to do before uni exams

[polar echo]

im kind of tired ngl

[unkempt sundial]

i see, goodluck

[polar echo]

thanks a lot

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[hollow bay]

how would you graph this?

[ebon sparrow]

you already have the information but do you know how graph it?

my idea is, use transformation rules or key points

whatever you think the best works for you to start sketching the graph

[hollow bay]

can you tell me what to do

idk what youre talking about

[ebon sparrow]

^

[hollow bay]

#help-0 message

what are those

[ebon sparrow]

do you know what transformation rules are in general?

[hollow bay]

no

[ebon sparrow]

this I mean

[final hatch]

How is -5,5 a vertical asymptote

[hollow bay]

those are 2 verticle asymptotes

[hollow bay]

oh so they cross x axis at -5 and 5 ?

[final hatch]

They don't

[hollow bay]

yea idk but to find verticle asymptotes you solve for x = 0...

im not sure how to graph it could someone please help?

im also not sure why zeros is referring to the numerator either

[final hatch]

No, you find the zeros for denominator ~ ( x = 0 )

[hollow bay]

ok ?

what is that i never have seen it before

thats what i meant

[hollow bay]

anyway how would you draw the graph with this info???

[final hatch]

basically what you know from function domain

in order to start drawing

[hollow bay]

can you please explain using the picture i provided

assuming that is all the info i haev

have*

this is a new topic for me

and we whaven't gotten this far yet

if you can't do it that's fine

<@&286206848099549185>

[balmy pendant]

yes?

which one?

[hollow bay]

can you help.. i dont understand how to graph this

[hollow bay]

this ^

[balmy pendant]

idk this, 😊

[hollow bay]

ah man

should i ping again then?

[balmy pendant]

dunno

[hollow bay]

<@&286206848099549185>

[faint hawk]

sup

oh

okay what are you struggling with

[balmy pendant]

this

[faint hawk]

no like what did you try

[hollow bay]

i figured out the vertical asymttoes and the zero and long behavior ... dont know how to graph it

[faint hawk]

find the derivatives and double derivative

[hollow bay]

what??

we havent even done derivatives yet

[faint hawk]

that way you will know if its concave up or concave down

ahh

okay

[hollow bay]

yea i thinkk thats the next topic

or the one after

[faint hawk]

right

okay I might not be able to help right sorry

[hollow bay]

thats ok

[sand hatch]

I can help it think

[hollow bay]

ok great

[sand hatch]

You need to graph it right

[hollow bay]

yea

idk how tho like where i should start

[sand hatch]

Make to straight dotted lines at x=-5,5

[hollow bay]

i marked the verticle asymptotes

ya i did this

and horizontal at 0

[sand hatch]

Function goes to infinity there

[hollow bay]

ok this is the part im new to

how did you figure that out

ohhh

like

i think i get it

[sand hatch]

Ya

Function go straight up

[hollow bay]

but how do you know if its under the x-axis or above it

[final hatch]

Find limit when x tends to -5 / 5 both sides

[sand hatch]

Cuts at infinity

[final hatch]

They should go either negative infinity or positive infinity

[sand hatch]

Ya left hand limit and right hand limit

[hollow bay]

idk what that is/means

how do i find that

[hollow bay]

if it goes to infinity there , it goes to neg and pos infinity right?

[sand hatch]

Ya

[hollow bay]

so it would get ely close to thte y and x axis at 0 and -5 and 0 and 5

[sand hatch]

Put a value closer to 5 you get it is positive or negative

[hollow bay]

?

ya im tryng to figure out if the line goes to inf or -inf at -5 and 5

[sand hatch]

At goes to infinity at -5,5

[hollow bay]

so how do we know inf and not -inf

[sand hatch]

Like going upward

[hollow bay]

yes how do we know

[sand hatch]

Like if we put 4 in function we got positive value

[grand tiger]

sad thing is calculus is needed

all the explanation samurai is trynna give u

is derived from calculus

[hollow bay]

ya im in pre-calc with applications for calculus

[grand tiger]

id suggest first learn applications of derivatives

only then graph plotting concepts start to come

[hollow bay]

well im just going in the order my teacer is going in tbh

[grand tiger]

yes that only

[hollow bay]

i have a lot of other hw

[grand tiger]

ohh

[sand hatch]

Find value at x=0

Marked it

[hollow bay]

-25*

well its -7/-25

right?

[sand hatch]

7/25

[hollow bay]

is that what you mean?

yea

so thats pos

ok

what does that have to do with -5 and 5 tho lol omg

[hollow bay]

so as it approaches 0 it goes to inf is what you're saying

bc wen its 0 it is pos

[sand hatch]

No I 0 is just a point

It gives us where it cut y axis

It cuts x axis at 7

[hollow bay]

ok

i got that from my answer

[sand hatch]

-5 it is going -infinity downward

At 5 going+infinity upward

[hollow bay]

ok but youre not rly explaining how u find that out

can you possibly explain it?

[sand hatch]

If you don't want to use limit

[hollow bay]

idk what limit is

[sand hatch]

Choose a closer point to 5

Like 4

[hollow bay]

i dont have any points

you mean x value?

[sand hatch]

Ya choose a value for x which is close to 5

Like 4

At 4 function is positive

So going upward

[hollow bay]

are you plugging in 4 to the equation like (x-7)/(x^2-25) ?

[sand hatch]

Ya

[hollow bay]

so 4-7/4^2 - 25

[sand hatch]

Ya

1/3

Positive

[hollow bay]

ok so i need to check a couple values?

or just one

[sand hatch]

No just one close value

It give you an idea

Now do this for -5

[hollow bay]

its undefined

25-25 = 0

?

[sand hatch]

At -5 it is going to infinity

[hollow bay]

no its undefined

you cant divide by 0

[sand hatch]

0/0 is undefined

1/0 we say infinity

[hollow bay]

anything divided by 0 is undefined

[sand hatch]

We are going off topic