help-17

[vast shale]

bruhhh

okay

thank you so much

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[queen path]

I think I'm lacking something in my understanding of algebraically proving these are symmetrical along the x-axis, y-axis, and about origin

For question A I tried solving for the x axis by replacing y with -y and ended up showing that the equation was not the same as the orignal

For the y-axis it was the same case

But I think it has symmetry about the origin?

Is my math just wrong or am I right

For B. there is y-axis symmetry but I'm not sure if it has x-axis symmetry nor origin symmetry

Because aren't even exponents always positive ?

[sinful kestrel]

yeah

replacing x with -x doesnt change the eq but replacing y with -y does

[queen path]

So A would be symmetrical about the origin

since I can divide -y by -1

er

multiply

B would then also have x0axis symmetry

Because even if I multiply the expression by -1 it will end up becoming positive since it's an even exponent?

I think I reasoned it out

Ty

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[sleek escarp]

Is the formula radius sqared

times height

time pi

times 1/3?

is that the formula?

[mighty nacelle]

yup

[sleek escarp]

wait

so then

9 times 4

is 36

then what?

[mighty nacelle]

pi(r^2)h/3

[sleek escarp]

36 times 1/3 or 36 times 3.14?

[mighty nacelle]

order doesnt matter

[sleek escarp]

ok

36 times 3.14

is

113.04

right??

can u check for me

then that

times 1/3

[mighty nacelle]

,w calc 36*3.14

[twin meteor]

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[mighty nacelle]

sounds good to me

[sleek escarp]

so

what is the exact answer?

when you multiply 113.04

with 1/3?

[mighty nacelle]

what do you mean

[sleek escarp]

on my calculator

1/3 is 0.33333333333333333

is repeated?

would I get an accurate answer?

[vast shale]

,w calc 113.04/3

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[sleek escarp]

Oh

that makes more sense

thanks

so 37.68 would be the answer then??

[mighty nacelle]

yeah, just divide by 3

[sleek escarp]

the volume??

[mighty nacelle]

yup

[sleek escarp]

thanks guys!!

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[mighty nacelle]

youre welcome!

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[arctic mantle]

wdym

x = x times the sqrt of (4 - x^2) ??

okay

simplify by dividing by x on both sides

[twin meteor]

guinearW

[arctic mantle]

yes

[strong grove]

im pretty sure u cant do that , u are removing a solution
x = x sqrt(4-x^2)
square on both sides
x^2 = x^2(4-x^2)
x^2 = 4x^2 - x^4
x^4 - 3x^2 = 0
x^2(x^2 - 3) = 0

[arctic mantle]

wait what-

no?

hang on-

no

4-x^2 = 1
x^2 + 1 = 4

[strong grove]

u divided x which meant that u removed a solution which is 0

[arctic mantle]

yea he's right

but is fine

[strong grove]

also u cant divide by x as we now know x = 0 and u cant divide with 0

[arctic mantle]

dude

there are two solutions

yk that right

no?

you can divide by x^2

then solve

dude

there are TWO solutions

which u arrive at thru different ways

you know one is 0

yes

here you can

[strong grove]

x^2(x^2 - 3) = 0
x^2 = 0 , x^2-3 = 0

u get 3 solutions

[arctic mantle]

what-

oh yea

he's right

look one solution is 0

[sonic zinc]

U can divide by 0 assuming x≠0
And then take a case where x=0 later

[arctic mantle]

but here you CAN divide by x^2 if x is non-zero, which, for this solution,it isn't

so x^2 - 3 = 0

now simplify, u get two solutions from this one alone

okay good

there's one more

what's (- root 3)^2?

yes

there are your 3 solutions

?

wdym

okay

so basically if u have two things that are multiplied

like (ab)

and then raise the entire thing to a power, like (ab)^n
that will be the separate terms to the same power

so (ab)^n = a^n times b^n

yes

np

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[broken garden]

I need help to see if I'm wrong on this or not

[broken garden]

The problem boils down to this "find the length of one part of vector a"

One of the steps to solving it is to find the area of triangle ABD while using similar triangle properties on the area of triangle PDC

My answer is shown as 64, cuz essentially you multiply the square of the ratio of the side length

[jolly lava]

is AB parallel to OC?

[broken garden]

However, the answer that's given is shown as 16, implying that the actual area is multiplied by the scale factor

[broken garden]

OABC is a parallelogram from the question

So it is

[jolly lava]

Ah ok

[broken garden]

The classmate I helped out on showed me this which is really confusing

Are vectors capable of doing something like this? I genuinely have no clue due to the lack of information of harder vector questions that weren't given

[jolly lava]

Looks like area ratio from length ratio with triangle similaritu

[broken garden]

It is yeah, I just don't know ehat to think of this at all

[jolly lava]

If you intepret vector length as triangle side length, no problem

[broken garden]

Is there an else situation where interpreting vector length as triangle side length is wrong?

[jolly lava]

If the vector is not the side of triangle

[broken garden]

Wdym by that tho

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<@&286206848099549185>

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[toxic prairie]

this questions is apparently solvable without a calculator to an exact value

so no trig functions with non-special angles

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[rotund blade]

Can someone please help me like I'm kinda stuck in the hours

So this is the example my teacher gave us but the prob is I was absent when he thought us that lesson 😭😭

[hardy vector]

It would be best if you gave specfic step

[vital cloud]

(also would be lovely if you provide the whole question from the start)

[rotund blade]

Scenario

arning institution, gelizing community. mpetence and fostering in Jesus Christ, one rest of creation.

O lumber + 5 hours $180 20 lumber+ 4hours $ 200

200 lumber and 80 hours

Tables = 10 lumber 10 = 100 lumber Shes 10 50 hours

100 lumber 30 hours left

SA

W

Departm

to be e

chara

JUSTI

attain

The carpenter can make tables or they can make bookcases. If they choose to make tables, it takes 10 units of lumber but it also takes 5 hours of labor to make $180 of profit for a single table. Alternatively if they decide to make a bookcase, it takes 20 units of lumber to make a bookcase but it takes only 4 hours of labor to make $200 profit for a single bookcase. The carpenter only has 200 units of lumber and 80 hours of labor available. The carpenter wants to make as much money as possible using only 200 units of lumber and 80 hours of labor. How many bookcases and tables should the carpenter make to make as much money as possible using only 200 units of lumber and 80 hours of labor?

Ok so this is the question and I'm kinda stuck in the hours....

Cuz like wait I'll show you guys my answerr

[hardy vector]

This stuff based on operations research. You could make use of the simplex algorithm. (I am guessing that might be a little advance). Alternatively there is graphical approach that you can take to the problem. But it might be a bit hard depending on the number of variables.

A good textbook to refer is operations research: applications and algorithm by Wayne Winston

[rotund blade]

Ohhh thanks I'll try reading it

If I have time....

[twin meteor]

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

[rotund blade]

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[flat fossil]

What does area under displacement-time graph give us?

[icy spear]

Meter seconds

There's no meaning to it

[flat fossil]

So nothing?

[icy spear]

Actually nvm

[vast shale]

it gives absement

[icy spear]

Absement is a thing

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[zinc timber]

somebody help, the answer is very simple but it seems like there are like dozens of steps. can someone explain step by step in the simplest way as I think im getting too far. if it really is just a long long question then its fine

[zinc timber]

its taken me like ages

[elfin surge]

!show

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

[zinc timber]

ok so the issue is for me

as you can see on the last step in the screenshot which is still sending

is that there is a bx^2 so i cant just take out the x and divide the rest out

and so if i divide it its like gonna be in the denominator making it more and more complicated

unless i just did it in a complicated way

soz i dont have clear workinga t all

[zinc timber]

Ok tysm

Its been resolved

[tribal moss]

yvw

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[dapper cedar]

Let f be continuous on the interval (0, 2) and g be continuous on the interval [1, 3]. What can be said about the continuity of the function f + g?
f+g is continous on [1,2), correct?

[distant eagle]

Yes

[dapper cedar]

ty

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[eager sentinel]

im having trouble with this. help would be appreciated!

[mild flower]

this integral doesn't really make sense

you have x in the bounds of your dx-integral

[eager sentinel]

we were given this as a question to solve as an extra

[surreal basin]

maybe they meant $\int_0^1\int_x^{\sqrt{2-x^2}}\frac x{\sqrt{x^2+y^2}}\dd{y}\dd{x}$

[twin meteor]

matt07734

[inner osprey]

that integral doesn't work very nicely either

[eager sentinel]

yeah thats it probably

[mild flower]

i guess you'd do the inner integral the same way you'd do something like $\int \frac{1}{\sqrt{1+y^2}}\dd{y}$ but those bounds are going to be Fun™️

[twin meteor]

ヘイリー

[surreal basin]

or you use polar coordinates

[mild flower]

oh yeah that's a better idea

[surreal basin]

switching to polar coordinates gets you this integral

[eager sentinel]

oh

how did that happen

[surreal basin]

you can start here to learn how to switch to polar coordinates https://tutorial.math.lamar.edu/classes/calciii/dipolarcoords.aspx

[eager sentinel]

alrighty then ill get to that

thanks for the link!

[surreal basin]

np

[eager sentinel]

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[vast shale]

Claim

[vast shale]

Hey! Is it okay if someone gives me a math problem?

Could someone give me a math (worded) problem to do with this please?

<@&286206848099549185>

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[gray veldt]

what did i do wrong?

I have do find the global maximum of a function given an interval

[outer warren]

extra - sign in your first derivative
didn't cancel the 2 properly
sqrt(4-x^2) isn't the same as sqrt(4) - x^2

[gray veldt]

could you showq where exactly?

[outer warren]

first few lines

issues appear in that order

I stopped reading after that

[gray veldt]

Up to this point the direvative is correct, no?

[outer warren]

oh, you had different results when doing the differentiation in a,b

that is the correct derivative, but you still had an extra - sign in the first line there

the issue with the square root still stands

when differentiating $\sqrt{4-x^2}$, why do you have
$$\br{\red{-} \frac{1}{2\sqrt{4-x^2}}}\cdot{(-2x)}$$

[twin meteor]

ℝαμΩℕωⅤ

[gray veldt]

oh yeah you're right

I see another mistake

let me redo it, and i'll send it again

almost there, but why is fmin= -sqrt(3) and not -2?

[outer warren]

x=-sqrt(2) is outside of the set domain

f(-sqrt(2)) will be undefined here

[gray veldt]

isnt the domain x <-2;2:>?

[outer warren]

no

reread the equation you're given in the question

you are given that $x \in [-1,2]$

[twin meteor]

ℝαμΩℕωⅤ

[gray veldt]

oh i see

i have to take it into account also

[outer warren]

work in part a) didn't get fixed, and for these types of multi-part question, there was no need to do the same thing again.

i.e if you differentiate properly in part a),
and part b) utilises the derivative, you could use that result directly

[gray veldt]

I see

so that's the correct domain

and I shouldn't take into account -sqrt(2) here

I understand now, thank you!

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[north elk]

1.f)

I'm not sure why the values aren't correct in the end

Been looking over and over to see where I messed up

Oops

i found it

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[compact isle]

Just need help wrapping my head around Trig Ratios and when to use them

[vast shale]

what do you have trouble understanding

[compact isle]

When given a right triangle and given information, I have trouble understanding wheter to use
Sin0= Opp/Hyp

or

Cos0= Adj/Hyp

or Tan0= Opp/Adj

ik how to opperate each ratio just not when to use them

[stuck quail]

It depends on the given problem

[tawny nacelle]

it totally depends on what you’re given, if you’re just solving for angles/sides of a right triangle

[compact isle]

Is there like a criteria to follow?

Ex. two angles and a side = use Sin

somethiing like that

[tawny nacelle]

well, it’s basically what you’ve written already

In your trig ratios

For example, if you have an angle and the side opposite to it, and you want to solve for the hypotenuse, then sin is the best (and actually only) option

I liked to think of the each of the trig ratios in terms of 3 variables

if you have 2 out of the 3 variables used in a particular ratio, you can use that ratio to solve for the last variable

if you only have 1 or 0, then you cannot use that ratio

[limber glade]

May I add something?

[compact isle]

yes please

[limber glade]

Okay, so the simplest way is imagine a building

That building has a height right?

Now what angle does the building make with the ground?

[compact isle]

are these labeled as you explained?

[tawny nacelle]

yeah

[compact isle]

so the third variable is the variable im tryna find

[tawny nacelle]

that would be the case, yes

[compact isle]

if i wanna find the Adjacent side

i would use

Tan

?

[tawny nacelle]

depends on the info given

cos may work too and tan may not

[limber glade]

I would suggest you not to try to memorize which ratio to use where

[tawny nacelle]

^^

[limber glade]

That's why I asked you to imagine a building

[compact isle]

that is what my objextive here is

usually math has clicked at some point

but you two have helped me

alot

thank you so much

i get it now

[limber glade]

Everytime you have a problem imagine you standing in front of a building at a distance

Mathematically, the distance of your foot from the building is base

Distance between your head and the head (top) of the building is Hypotenuse

And the length of the building is height

Then you can apply this logic at every case to check which of the quantity you have to find

But one thing to remember is in certain questions the height of the person is given then, you can no longer consider it a triangle it becomes a trapezium, with the person's height and building's height being parallel

[compact isle]

okok

thank you dude this acc helped alot

you can close this channel if you need

[limber glade]

.close

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[dusty crane]

can u help me @vast shale

[mild flower]

i think that would work yeah

[dusty crane]

hey i need help

[mild flower]

just kinda bash it out

[dusty crane]

i need help with finding the works

[mild flower]

!help

[vocal sleet]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[dusty crane]

but idk how to open a channel

[mild flower]

yeah

[mild flower]

go read the channel I linked

[dusty crane]

i opened

[mild flower]

hmm

each of those things has to be individually equal to 0

like it has to be 0 + 0i

no like

8yx - 4x = 0

[vocal sleet]

@vast shale Has your question been resolved?

[soft walrus]

(you'll get a system of equations with two equations and two unknowns)

[
\begin{cases}
4x^2-4y^2-4y=0\
8yx-4x=0
\end{cases}
]

[twin meteor]

PajamaMamaLlama

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@vast shale Has your question been resolved?

[quasi rover]

I would think by solving these equations you find solutions to the original one

The equation only equals 0 when you have 0 on both real and imaginary parts

So “trying to get them equaling 0” is the goal

And these equations are doing just that

[soft walrus]

that's a very valid reason where there's 4 possible w's yes :) also make sure to check those solutions too!

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[zinc quail]

Is this inequality true for n e N and x e R+? I'm having trouble verifying it 🦆

[obsidian stream]

Yes

[zinc quail]

how could you show it?

I tried eliminating the ln first:

but then I got stuck

[obsidian stream]

After taking the exponential, I would break it up into three cases, where x > e, x < e, and x = e so that you can factor out either e or x from both sides of the inequality.

That way you can factor out terms by doing things like: (x^n + e^n))^(1/n) = (x^n + (xe/x)^n)^(1/n) = x(1 + (e/x)^n)^(1/n). Then knowing that e < x makes it easy to eventually compare terms involving (e/x)^n and (e/x)^(n+1) after more simplification.

[zinc quail]

hm kk will try thanks

for x=e it's trivial

for the case x<e:

but for x>e I couldn't find an approach @obsidian stream 🦇

I might not be present anymore as I'm becoming sleepy, but any help will be highly appreciated :) (I've shown the initial inequality for x<=e, but not yet for x>e)

[hybrid flicker]

x>e is fairly similar, it's just e/x < 1 this time

[zinc quail]

oh? where can you use this estimate

[hybrid flicker]

Instead of factoring by e^..., you factor by x^...

[zinc quail]

and then the inequation holds? I've already closed my laptop as as it's way past night for me, but I'll get to finish writing it tomorrow

[hybrid flicker]

Vision this but with e/x instead...

[zinc quail]

ah yeah should have been blatantly obvious when I did the other way

thank thee

i should refill my battery

🐛

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[plush tundra]

How do I verify this by solving/simplifying one side only?

[plush tundra]

I’ve tried using Pythagorean identities but I keep going in a circle

[willow bridge]

,rotate

[willow bridge]

multiply by $1 = \frac{1-\sin \theta}{1-\sin \theta}$

[twin meteor]

LF

[willow bridge]

you should be able to use the pythagorean identity nicely then

[plush tundra]

So it’s better to simplify on the left side?

[willow bridge]

hm idk i havent thought of the other way

[plush tundra]

Its alright, thank you though

Ill try to work from here

[willow bridge]

cool lmk how it goes

[plush tundra]

Alrighttt

Should I keep it open then?

[willow bridge]

sure

[plush tundra]

Alright!

[willow bridge]

actually the other side is easier i think

[plush tundra]

That’s what my teacher said, but my partner and I went in spirals 😭😭

I’m probably missing something lol

I turned it to this

But the third term with the +1 messed us up bad

[willow bridge]

put everything in one fraction with only sin and cos

and then convert cos to sin using pythagorean

and simplify using pythagorean

[plush tundra]

I’ll try that after completing the left side

If I have sin^2 theta, can I factor it

I ended up with this

Wait wrong one

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@plush tundra Has your question been resolved?

[plush tundra]

<@&286206848099549185>

[plush tundra]

<@&286206848099549185>

[karmic forge]

You can us a^2-b^2=(a+b)(a-b) in denominator

[plush tundra]

Ohh so like it can end up as:

WAIT WITHOUT RHE 2

Wait my brain is very tired let me rewrite that

Oh wait it’s coming together

Thank you

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[modest otter]

I want to express that the result of 4/3 * any power of 2 will always be a rational number/never be a natural number. is this an acceptable way of saying that? is there a better way?

[willow bridge]

can you clarify?

where are you expressing that result?

[vocal sleet]

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[modest otter]

what do you mean?

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[modest otter]

.reopen

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✅

[hot bolt]

I got -1935/6. Which i understand is very off

[hot bolt]

do you need this room?

[modest otter]

I'll make a new one

[hot bolt]

ighty

<@&286206848099549185>

<@&286206848099549185>

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[cerulean tartan]

Hello I need help on a question

[cerulean tartan]

<@&286206848099549185>

[rustic bramble]

sorry, i can't understand the formula you write.

it seems to be a logarithm of the base 10? how to understand the number 24?

[cerulean tartan]

Hold on

Never mind this one

Not sure about number 2

<@&286206848099549185>

[vast shale]

Yo

Which one

Oh that one

[cerulean tartan]

Ye

[vast shale]

Damn that looks hard

I'm not good man

Idk why I chose help I regret it man

[cerulean tartan]

This is regular algebra 2

Not even honors

[vast shale]

Yeah I'm sorry man

[cerulean tartan]

It’s alright could you possibly get someone else then

[edgy gulch]

first of all, wait 15 minutes before pinging that

[rustic bramble]

g is the inversion map of f

[vast shale]

Bet

[rustic bramble]

i think the answer is 7

[cerulean tartan]

How come

[vast shale]

Is it alr if I just straight up ask the question?

[edgy gulch]

what is the relationship between exponentials and logarithms

[cerulean tartan]

Inverse

[edgy gulch]

and what happens if you compose two functions that are inverses to each other

[cerulean tartan]

They become the same

[edgy gulch]

no...

[cerulean tartan]

They cancel each other out

[edgy gulch]

and whats left

[rustic bramble]

it is an identical mapping bro

[cerulean tartan]

The original

[edgy gulch]

original what

[vast shale]

f(g(7)) = (2*7 + 3)^2 - 1 = 288

Guys

I don't wanna ping anyone so

@cerulean tartan I think I have it

[edgy gulch]

fuck did that came from

[vast shale]

Why do u care

It's not from me anyway

[edgy gulch]

also thats nowhere close to the answer

[vast shale]

So?

I didn't have anything to do with the answer I got

[edgy gulch]

so whats the point of putting it here?

[vast shale]

Bcuz I got it from someone

[rustic bramble]

take b = 7 as an example, g(7) = 1, and f(g(7)) = f(1) = 7

it is an identical mapping

[cerulean tartan]

Thanks Max

[rustic bramble]

😋 you are welcome

[cerulean tartan]

How come u don’t have helper role

[edgy gulch]

dont care about it

[cerulean tartan]

Are you qualified

[edgy gulch]

idk

[cerulean tartan]

Ty for the help, but you are not even an official helper so why are you complaining

[edgy gulch]

what was i complaining?

[cerulean tartan]

I just find that to be strange

maybe you should ask them for helper role

.close

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[icy moth]

Honestly have no idea how to do this once I get to integration.

[icy moth]

I get to my integration which is just $13\int_{0}^{a}\int_{0}^{b}(xy)dydx$

[twin meteor]

ImTallOk

[icy moth]

and is incorrect

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[worldly drift]

for the formula $n=dk$ can't n, d and k be integers?

[twin meteor]

Navee

[mental falcon]

!original

[vocal sleet]

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.

[worldly drift]

I read this statement in Basic Mathematics by Serge Lang

Let d be a positive integer and let n be an integer. We shall say that d divides n, or that n is divisible by d if we can write n=dk for some integer k.

[mental falcon]

so what's your question, why d is restricted to positive integers?

[icy moth]

Doesnt that fulfill your original statement

[worldly drift]

Yes

[mental falcon]

well, different definitions will be used in different contexts that allow for positive or negative divisors but oftentimes you'll see them restricted to positive in a lot of contexts, because if you're just talking about divisors of 10 you would get 1, 2, 5, 10 and it's just kinda superfluous information to also give -1, -2, -5, -10, but it really depends on context

the negative divisors would just basically be a mirror image

[worldly drift]

In this context the author of describing divisibility, I was wondering if I should take the positive integer part without thinking about it.

[mental falcon]

its like easier to just define it for positive numbers because that's what you want most of the time, if you ever need to consider the negative versions also its easier later to just say, ok consider the set of divisors plus the negatives of all divisors and now you've got everything

[worldly drift]

So if I cut the positive from the above statement, it still is true right?

[mental falcon]

wdym is it true? its a definition

the author is defining what he means by a divisor in the context of the work

[worldly drift]

Ok I'm lost 😭

[mental falcon]

its not a theorem where the author is saying ok I make this claim and then I'm gonna prove it, he's just literally defining what is going to be meant by a divisor from here on out, you can define things however you want

[worldly drift]

I don't see the word divisor anywhere in the text, so I'm assuming d is divisor? And what is n and k called?

Also is the author saying d is the divisor and it will be positive in the remaining of the book?

[mental falcon]

ok he doesn't use divisor, i didn't scroll up to reread so i was paraphrasing but he's defining what is meant by 'd divides n'

and by the word divisible

[mental falcon]

i dunno what else to say about this, i feel like youre just overthinking it, it's like if i say "ok what we mean by midpoint is the point halfway between the the ends of a line segment" now midpoint has been defined and you know what is meant by it from there on out

after that stamement for example i can say:
5 divides 10 or 10 is divisble by 5 because we can write 10 = 5 (2) where n = 10, d = 5, k = 2 according to the definition

[worldly drift]

the overthinking part can be true : \

so can I say

10 is divisible by (-2) because I can write 10 = (-2)(-5), where n = 10, d = -2, k = -5 according to the definition?

where the definition is the one from the text?

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[ancient adder]

i dont understand inequality

why did we neglect x^2 -x > -1

previously

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@ancient adder Has your question been resolved?

[vast shale]

we never neglect it, actually x²-x+1 >0 for any value of x, like whatever you put in x its always greater than 0 so we were only concerned with the less than 1 part

and to see why x²-x+1 is always positive see this,
x²-x+1 = (x-1/2)² + 3/4
and we know that a square of real number is always positive, so not only is x²-x+1 always greater than 0 it's greater than or equal to 3/4

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[dense hedge]

is this non calc?

[gloomy furnace]

I think

[dense hedge]

then just do it ?

[gloomy furnace]

I need help tho

[dense hedge]

with wat

[gloomy furnace]

With the question

[dense hedge]

its solve for x i assume

[gloomy furnace]

Yeah but idk how to calculate to the answer

[dense hedge]

wat steps have u done so far

[dense hedge]

have u learnt abt inverse trig functions

arccos

arcsin

arctan etc

[gloomy furnace]

Yeah

[dense hedge]

ok do arccos on both sides

[gloomy furnace]

K

[dense hedge]

then rearrange

and plug into ur calc

[gloomy furnace]

Like that?

Im able to calculate for quadrant 4 but not for quadrant 1

Nvm i got, sorry for bothering u

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[vast shale]

the question and my attempt

i cant understand tho lol

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[vast shale]

<@&286206848099549185>

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@vast shale Has your question been resolved?

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[frosty bobcat]

please help me with question 22!

idk where to start and idk how to get the answer lmao

[merry shuttle]

cosine rule

[frosty bobcat]

ik

the whole topci is law of cosines

[merry shuttle]

can you find cos(J)

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[small glacier]

how to solve this question

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[finite hatch]

hello

[finite hatch]

what did i do wrong

[finite hatch]

for part b

[vocal sleet]

@finite hatch Has your question been resolved?

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@finite hatch Has your question been resolved?

[finite hatch]

<@&286206848099549185> excuse me

[twin horizon]

-->
AP = -(i +4j) + q(2i + 5j)
-->
OB = 2i + 5j

$AP \cdot OB = 0 $

[finite hatch]

q(2i+5j)?

but why

-a +q(b)?

[twin horizon]

substitute value of b in -a + q(b)

q is a constant(scalar) so it multiplies all the terms in b

@finite hatch

[finite hatch]

ah i see

ook thnx

[twin horizon]

np

[finite hatch]

is it ok if i have 1 more questiojn

[twin horizon]

um yes

hopefully i will be helpful

[finite hatch]

did i do something wrong for this question

question 9a

wait thats a bad picture

[twin horizon]

thx much better

ok

if two vectors a and b

are on the same plane

[finite hatch]

yea

[twin horizon]

their dot product is given as |a| |b| cos $\theta $

;-;

[finite hatch]

ya

[twin horizon]

so let a be the first vector and b will be the second

making cos(theta) the subject of the formula:

[finite hatch]

i think i did dat here

[twin horizon]

cos(theta) = (a dot b)/(|a| |b|)

[twin horizon]

you forgot to put the sqrt 'sign'

[finite hatch]

why do i get math error

when i use sqrt

[twin horizon]

lemme check

[finite hatch]

oke

[twin horizon]

oh i see

[finite hatch]

hm?

[twin horizon]

you did 5 * 7

[finite hatch]

oh how do i multiply sqrts

[twin horizon]

you just multiply the numbers and put the sqrt sign over it

[finite hatch]

but i get math error with sqrt(35)

wait..

its 5 x 17

oh

..

i am sleepy ok

[twin horizon]

thats because its 17 not 7

[twin horizon]

lol

[finite hatch]

how come when i do it without sqrt

i get same answer?

[twin horizon]

GL! tho if you need any more help just ping me

[twin horizon]

?what

lemme see

[finite hatch]

oh nvm

i lied

[twin horizon]

lol

[finite hatch]

ok bai im sleeping now

cya

[twin horizon]

the angle is obtuse tho

[twin horizon]

bye

[finite hatch]

awkward

.close

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[craggy gust]

how do i solve this <@&286206848099549185>

[vocal sleet]

Please don't occupy multiple help channels.

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.

[toxic gate]

@craggy gust
What to do with that expression

[craggy gust]

solve it

i have to solve it basically

but i got confused with the 2

is it like an exponent? @toxic gate

[cursive turret]

yes

[craggy gust]

ohh alright

then i got it

thank you!

[toxic gate]

I did

Wait a min

I need help for the number 5 question, i tried but failed <@&286206848099549185>

[cursive turret]

1. this channel is occupied. take your own (-> #❓how-to-get-help )
2. only ping for helpers if no one responded your question for 15 min. @toxic gate

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[vocal sleet]

@vast shale Has your question been resolved?

[quasi rover]

This question seems to be oddly phrased

But considering the relevance of this question, I assume it means to estimate the limit of the function at point a

By using the order Tyler expansion at this point

@vast shale

Have you learnt Tyler expansion?

Is this something you have seen?

Then this formula should be what you use

What answer is 2x

Linearization is a way to estimate the value using “linearly close numbers”

Once you get the L(x) function, as shown above

Use “close up” numbers to approximate your value

I think is what this question means

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[open thistle]

Somebody can explain me pls

[iron parrot]

What do you get when you multiply the second equation by 2

[iron parrot]

What happens when you subtract that from the first equation?

[open thistle]

maybe this

[vocal sleet]

@open thistle Has your question been resolved?

[iron parrot]

what does $3a + 5b - 4c - (2a + 6b - 4c) = 12 - (-8)$ simplify to?

[twin meteor]

Dork9399

[open thistle]

maybe in a-b=12

[iron parrot]

yes

and thats your answer

[open thistle]

What would be the literal?

[iron parrot]

the rhs should be 12 - (-8), giving you 20 as your answer

[open thistle]

OHhh

thanks

.close

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[mellow geode]

hello, how do i prove that there's bijection between Q+ and N using cantor?

[hard atlas]

ok in what form do you know cantor

cause this is the way that I know cantor. the first one anyway

[mellow geode]

cantor diagonalization

[hard atlas]

well yes

[thin vale]

Prime factorization

[hard atlas]

that doesnt answer my question

in what way have you seen cantor diagonalization

if not in exactly this way to show a bijection from Q+ to N

[thin vale]

Denascite they probably have seen it in a proof that the reals are uncountably infinite

[hard atlas]

there are two cantor versions

[thin vale]

that's where I've seen it

[hard atlas]

the first and second diagonal argument

the first is that Q+ and N have same cardinality

the second is that R is not countable

I very much assume they are talking about the first

[mellow geode]

i don't know, probably what you're thinking about, we haven't seen it much

[mellow geode]

yes

[hard atlas]

can you write down exactly how you know cantor

[mellow geode]

i've just seen it with the cantor snake very briefly, i think to show that AxB is countable is A and B countable

[misty belfry]

the way I know is to write every element of Q+ as a/b in lowest terms and them map those points to a subset of Z^2 by a/b->the point (a,b) and then travel in a spiral from the origin

I think that might be what you want

[mellow geode]

what travel in spiral from the origin means? I find a bijection between Q+ and Z² and then how do i find the bijection with N?

[hard atlas]

with Q+ you are already only in one quadrant

and then you immediately use the snake thing you mentioned

[mellow geode]

ok

[mellow geode]

so for ex the bijection is f so f(1)=1 and f(1/2)=2, f(2)=3, f(3)=4, f(1/3)=5 etc...?

we just skip the diagonal?

[hard atlas]

well and we skip the other non reduced fractions

like 4/6

[mellow geode]

ok so that's all?

f(1)=1 and f(1/2)=2, f(2)=3, f(3)=4, f(1/3)=5, f(1/4)=6, f(2/3)=7, etc... mapping correct?

[hard atlas]

yes

[mellow geode]

thank you

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[hexed dagger]

How do I find where the particle is slowing down?

[heavy yoke]

find when the speed (magnitude of velocity) is decreasing

[hexed dagger]

So find the derivative then set it to zero?

[ornate ember]

That'll give you the critical points which will tell you where the particle's velocity is at 0. You also need to go one more step with a 2nd derivative and find the inflection points

[hexed dagger]

All I need is the critical and inflection points?

[ornate ember]

well kind of. You also need to consider the the particle starting at t = 0.

[ornate ember]

basically wherever you have a critical point you are changing from a positive and negative slopes. The inflection point is usually where the acceleration slows/speeds up.

BUT, since we're starting at t = 0, we can see that as we reach the first critical point that we're slowing donw

[hexed dagger]

The only inflection point is 4/3

[ornate ember]

yep, correct. The partical slowing down is from the inflection point to the critical point

[hexed dagger]

Wait so why (0,2/3) and (4/3,2)

Is it because t=0?

[ornate ember]

(4/3, 2) is because from the inflection point to the 2nd critical point at x = 2

from (0, 2/3), since we're starting at 0 and we're approaching a critical point, we have to slow down

[hexed dagger]

Ohh ok I think I get it

Thank you

[ornate ember]

yep no problem! 🙂

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[terse forum]

need help with these three questions

[terse forum]

[A=P(1+i)^n] or [A=\frac{R[(1+i)^n-1]}{i}]

[twin meteor]

アキラ (>_<)

[frozen shuttle]

6. would be 4000* 0.04^n (n is number of years) as it yould compunt each year

[terse forum]

so can i apply the first formula?

ok

but isn't it like 4000(1+0.04)^n?

where n is 10

[frozen shuttle]

yes

ofcourse

my bad

its increasing not decreasing

my bad

[terse forum]

okay no worries

what about the 7

[frozen shuttle]

FV = PV(1 + r/m)^mt u could probably use this formula

[terse forum]

idk what formula that is

can you latex it

our teacher will provide these formulas in exam so which one should i use for 7th question?

[frozen shuttle]

$FV = PV(1 + r/m)mt $

i dont get latex sorry

[terse forum]

,, FV = PV(\frac{1 + r}{m})mt

[twin meteor]

アキラ (>_<)

[frozen shuttle]

yes precisely

[terse forum]

honestly im not sure about this formula

we never learned this

[terse forum]

it is just either of these ones

[frozen shuttle]

yes

A=P(1+i)^n

and i=r/m i think

[terse forum]

I don't get it

[frozen shuttle]

i= is jsut the annual interest/how many times it's compounded per year

[terse forum]

10?

10/100 I think?

[frozen shuttle]

the annual interest is 4% right? and it's compounded every month so 12 months

hence 0.04/12

[terse forum]

4000(1+0.04)^n same thing for question 6? where n is 10

idk

[frozen shuttle]

FV= 4000(1+(0.04/12))^12*10

since it's compouned 12 times a year for 10 years

[terse forum]

can you use the formula ive showed you

plus i think it should be for this $$A=\frac{R[(1+i)^n-1]}{i}$$?

[twin meteor]

アキラ (>_<)

[terse forum]

[frozen shuttle]

hmmm

this is the same as the one you showed just rewritten

well i dont know waht your teacher tought you

but from my knowledge they are the same, jsut rephrased

where i=r/m and n=m*t

basiclly just more compact

[terse forum]

I don't think they both look same thing

the one you are using doesn't have an exponent of n

[frozen shuttle]

or rather the one you showed is jsut a special case of this one where the interest compounds once a year. hence, r/m= r and m*t=t if m is 1

n is just a special case of m*t when m is 1

if the interest compouns annually not monthly

do you see it?

[terse forum]

nope

[frozen shuttle]

hmm

[terse forum]

it just becomes more complicated

[frozen shuttle]

it does, since the question is more complicated.:/

let's start from the beginning

with your formula

[terse forum]

it's just average canadian math question

[frozen shuttle]

A=P(1+i)^n

[terse forum]

we're just supposed to use those formulas i showed you

[frozen shuttle]

yepp

[terse forum]

either the first or second

[frozen shuttle]

for this one we use first

[terse forum]

okay

[frozen shuttle]

we want to find A

P is 4000

[terse forum]

[frozen shuttle]

and i is not 0.04

since it is compounded every month

[terse forum]

hmm

[frozen shuttle]

so you have to divide 0.04 by 12, (12 months in a year)

[terse forum]

would be that n or i?

[frozen shuttle]

i

[terse forum]

okay

[frozen shuttle]

so then we have A=P(1+(0.04/12))^n

[terse forum]

,calc 0.04/12

[twin meteor]

Result:

0.0033333333333333

[frozen shuttle]

i'll use the fraction since it's more accurate

[terse forum]

can I just say the equation is 4000(1+(0.003))^n?

then the n is 10

[frozen shuttle]

you are right about the first part, however n is not 10

for the same reason that i wasn't 0.04

[terse forum]

why?

[frozen shuttle]

it compounds 12 times a year

[terse forum]

then what they meant by 10 years?

[frozen shuttle]

so it would compound 12 a year for 10 years

,calc 10*12

[twin meteor]

Result:

120

[frozen shuttle]

n is 120

[terse forum]

why did you divide 12 on 0.04 and multiplied 10 by 12

[frozen shuttle]

since the interest is split up for each month

you would have to multiply the compound period by the same amount

if it were to compound quarterly you'd divide 0.04 by 4 and then multiply 10 with 4 in order to balance it out

[terse forum]

ahhh I see I see

that makes sense

and finally last question which is 8

[frozen shuttle]

this probably uses the second formula

[terse forum]

yea i think so

[frozen shuttle]

so basiclly you start with an investment of 400, which compounds for the first year, then you add another 400 in year two nad so on

[terse forum]

is my equation looks 400[(1+0.06)^n-1]/0.06?

im not sure about n again

[terse forum]

yep i used the second one

[frozen shuttle]

the i is split up over 12 months too remember

[terse forum]

oh

divide by 12 again?

[frozen shuttle]

yes

[terse forum]

,calc 0.06/12

[twin meteor]

Result:

0.005

[terse forum]

okay so my i is 0.005?

[frozen shuttle]

yes

[terse forum]

and for n multiple by 12?

[frozen shuttle]

yes

and then -1

119

[terse forum]

how did you get 119

oh wait

[frozen shuttle]

my bad

[terse forum]

it's 10 multiplied by 12 right?

[frozen shuttle]

yes

and then the total of the upper function is -1

[terse forum]

okay so the final equation is 400[(1+0.005)^n-1]/0.005, where n is 120

correct?

ill latex it hold on

[frozen shuttle]

looks right

[terse forum]

,, \frac{400 [(1+0.005)^n-1]}{0.005}

hmm

latex fail

[twin meteor]

アキラ (>_<)

[terse forum]

ok there

[frozen shuttle]

it would have been the same thing

[terse forum]

can i just add 120 to n

and then find the answer?