help-10

[sinful kraken]

ill fail my uni classes

its 2 am finals xD

[timid silo]

yikes

[sinful kraken]

follow my instructions tho

wait nvm

[timid silo]

.close

[obtuse pebble]

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[sinful kraken]

ignore what i said i read ur question really quickly

[timid silo]

its ok

ima just fail

fuck life

[sinful kraken]

what grade r u in ?

[timid silo]

freshmen

[sinful kraken]

u prob wont fail

[timid silo]

yea this qustroin worth 10 points

out of 20

10 mc

[sinful kraken]

tbh i dont understand what they want

[timid silo]

its ok

thx anyway

[obtuse pebble]

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[ionic wren]

how did they arrive at this ?

[plain stag]

sin(n*pi) = 0 for any integer n

[ionic wren]

tysm

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[fresh acorn]

<@&286206848099549185>

[gilded needle]

!status

[obtuse pebble]

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

[fresh acorn]

1

[gilded needle]

do you know the formula for the CDF of a normal distribution?

[fresh acorn]

this?

[gilded needle]

yea

and then do you know how to compute that probability?

in your case, you want P(75 < X < 85), which is equal to P(X < 85) - P(X < 75)

[fresh acorn]

wait wrong

the other one

[gilded needle]

which you can then put into standard form using the above formula

[fresh acorn]

this one?

[gilded needle]

sure, that's the same as what you have above, no?

[fresh acorn]

ooh yea

but the question is 75-80

[gilded needle]

yea

[gilded needle]

^

[fresh acorn]

aaaah

[gilded needle]

btw, <= vs < doesn't matter for a continuous distribution like this one

in case that's what is causing confusion

[fresh acorn]

the drawing part

[gilded needle]

what is up with question c, there are some weird typos

"3X0"?

[fresh acorn]

390

yea

[gilded needle]

and "eye Statistics"

[fresh acorn]

the shit didn't load in docs

[gilded needle]

ahh i see

computers causing mayhem

[fresh acorn]

statistics lesson

lmao

when the teacher tried hard to use English

[obtuse pebble]

@fresh acorn Has your question been resolved?

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[obtuse pebble]

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[timid silo]

how does one get the parts circled

[timid silo]

shouldnt A intersect B / B intersect A = 1/4

[royal basin]

there's a technique they used here called the Bald-Faced-Lie method

[timid silo]

what?

[royal basin]

whoever wrote this fucked up their arithmetic.

[timid silo]

yeah i think the answer sheet is wrong

and it gaslit me

i was so confused for a moment i thought i couldnt count

so the right answer should be 1/4 right

[royal basin]

P(A & B) is 1/4 yes

[timid silo]

😓

so first answer is 1/2

second answer is 1/3

[royal basin]

yes

[timid silo]

thanks mate

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[tacit vapor]

Hello, I would like to ask a question regarding C = max{|alpha|, |beta|} here, why can it be written as -C <= fn <= C and what does C = max{|alpha|, |beta|} here mean?

I would also like to ask why are the red underlines parts included in the proof, rather than just saying that C is the max of the absolute value of L - 1 and L + 1 only?

Thank you very much

[tacit vapor]

Here’s a full picture

[obtuse pebble]

@tacit vapor Has your question been resolved?

[tacit vapor]

<@&286206848099549185>

[wintry swift]

assume alpha = -10. beta = 3 -> C = 10.

C is the greater value from alpha and beta without signs.

[tacit vapor]

Ahh I get it now, thank you very much @wintry swift 🙏

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[static fulcrum]

Is this normalized form correct?

[royal basin]

do you have a definition of "normalized form" on hand?

as in, specifically for that boxes-with-numbers-and-signs thing

[static fulcrum]

this?

[steep harness]

Oh is this a signed float?

[royal basin]

ok sure but you've normalized the mantissa to the range [0.1, 1)

is that what you're supposed to do?

[static fulcrum]

Not specified, this is the problem.

[royal basin]

so your book never specifies whether the mantissa of a number in normalized form must be read as between 1 and 10 or between 0.1 and 1?

or did you just not catch the point in the book where that's defined?

[drifting wraith]

you don't even have a solved example?

[static fulcrum]

0.1 and 1

[royal basin]

ok, in that case another issue exists

you didn't chop 0.2134650987 to four digits correctly.

you rounded instead.

[static fulcrum]

I think I didn't really get the concept then.

Trying to find a good explanation

[royal basin]

there is nothing to get

you just erase the digits past the last one

[static fulcrum]

okay

many thanks @royal basin 👍

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[torpid tapir]

Solve for a to achieve highest local area

[wary vigil]

you can set up a formula for the area

and you can then look at that and take the derivative with respect to a

to check how the area changes when a changes

and then do the normal local maxima thing

@torpid tapir

[torpid tapir]

I wont get the correct answer

[wary vigil]

how come?

[torpid tapir]

No idea

I can check when I get a geogebra computer

[steep harness]

Integrate from a to 2a, then simplify, then differentiate wrt a to find extrema

[torpid tapir]

From a to 2a? Not the opposite?

I integreted with 2a on top of the integral

[steep harness]

Yes, that's correct. "From a to 2a" means with a lower bound of a and upper bound of 2a

[wary vigil]

what did you get with that integration?

[torpid tapir]

I dont have my papers left, but I think I got 10e^(-0,1a)-10e^(-0,2a)+1/(2a)

[wary vigil]

that is correct

now derivative with respect to a of that

[steep harness]

Wait, are they asking for two decimal places? Rude. Rounding sucks

[torpid tapir]

I think I got 2e^(-0,2x)-e^(-0,1x)-1/(2a^2)

[wary vigil]

i got that too

[torpid tapir]

Also hate rounding

[steep harness]

Why do you have x and a?

[torpid tapir]

That =0

[wary vigil]

although x = a

[torpid tapir]

typo

Then I get this stupid equation

[steep harness]

Find your critical points, test for maxima

[torpid tapir]

So I got another lesson rn

I can either end the chat or continue, but doing math slowly

Nvm got the answer

The eqyation overloaded the calculator so it could calculate the maxima

Ty for your help, love spending 1 hour doing same math 4 times and it turns out the calculator lied

[wary vigil]

that does not look right though

this is the equation

[torpid tapir]

Oh right

Forgot to add -1

And multiply first two polynomes by two

[wary vigil]

4

[torpid tapir]

You swuared the 2

[wary vigil]

(2a)^-1

-1(2a)^-2

right?

times 2

nvm

[torpid tapir]

Let me checl the answr

[torpid tapir]

Why are the graphs so differebt

Im lowkey retardez

Did the same mistake twice

So my og calculator failed at drawingthe function

Ty for the help, answer is 6,7 because of the equation

!close

1 sec

.close

[obtuse pebble]

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[verbal niche]

how do you do this

[verbal niche]

I know it has to do with expected value, but i think i just need to see the solution and i'll remember what i was supposed to do for it

[plain stag]

It will indeed involve computing an expected value

Your first step should be computing the probabilities of winning each of the prizes

[wooden marten]

expected value of how much the prizes will cost them?

[plain stag]

(And the probability of winning nothing)

[verbal niche]

would this be hypergeometric?

nvm

[wooden marten]

the assumption I believe is that someone will win every prize

[plain stag]

Yes all prizes will be given out

[wooden marten]

so, no probability here

ig OP figured it out and is doing the math now

[plain stag]

Yes probability

[wooden marten]

mmno

[plain stag]

There are a little over 100k prizes and 2000000 tickets; not everyone will win a prize

[wooden marten]

but this is from the company's perspective

[plain stag]

Oh wait nvm, no probability

But similar concept

[verbal niche]

oops

oh no probability

[wooden marten]

indeed

[verbal niche]

would you just add up all the potential loss then find the mean?

[plain stag]

I misread the question

[wooden marten]

company already bought the prizes, will give them all away, and already got its revenue

[wooden marten]

funnily enough if it had asked "how much does person who buys 1 ticket expect to lose" then you would probably do it with probability but you could also do it this way because loss is the same as per-ticket gain from the company's perspective

[wooden marten]

why divide by #prize

[verbal niche]

thats how you get how much they get per ticket?

oh

sorry

[wooden marten]

all you need to find is the company's profit

[verbal niche]

but its asking how much they make per ticket

so you would divide by 2 mil

[wooden marten]

ye

[verbal niche]

yay ty

I think i asked before and I'm allowed to keep this open if i need help with another question right?

[obtuse pebble]

@verbal niche Has your question been resolved?

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[dense lodge]

not sure what to do for part b

[high lily]

in general how would you determine x-intercepts of a curve

[dense lodge]

yeah nvm

i thought it was a harder problem

thanks

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[static fulcrum]

Is this correct?

[static fulcrum]

I think it is wrong though.

[ivory trout]

Are you supposed to use IEEE754?

does that ring any bells?

[static fulcrum]

No, I am a beginner and not even finding any good resource to understand rounding and chopping.

[obtuse pebble]

@static fulcrum Has your question been resolved?

[static fulcrum]

.close

[obtuse pebble]

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Channel closed

Closed due to the original message being deleted

[grizzled hound]

.close

.close

[obtuse pebble]

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[vernal turtle]

3b^2|5c^3 divided by 9b|25c

[untold flax]

?

you realize what you said reads as 3 b squared divides 5 c cubed divided by 9b divided 25c

[vernal turtle]

3b^2/5c^3 divided by 9b/25c

[untold flax]

right htat makes more sense

[vernal turtle]

3b square over 5c cube divide by 9b over 25c

[untold flax]

ok what have you tried

[verbal niche]

doesnt | means given that

[tame narwhal]

not in this context

[vernal turtle]

bruv idk am i supposed to change divide to times or smt

[verbal niche]

what are you solving for

or just simplifying

[vernal turtle]

simplify

[verbal niche]

like this right?

[vernal turtle]

its divide sign

[verbal niche]

a fraction is dividing

[vernal turtle]

ok if it works

it shld be 5b over 3c square

[vernal turtle]

5c cube

[verbal niche]

how would you solve this

[tiny seal]

Reciprocate 3/2 and multiply

Basically

Do 1/2 * 2/3 instead

[vernal turtle]

yes

[verbal niche]

why dont we do the same here

[tiny seal]

We do

[vernal turtle]

so 25c on top and 9b below?

[verbal niche]

mhm

[vernal turtle]

then cross multipication or smt?

[tame narwhal]

no, just multiply and simplify

[vernal turtle]

??

5c cube times 25c?

[tiny seal]

No

[tame narwhal]

reciprocal is key here

[tiny seal]

Reciprocate first

[vernal turtle]

wtf is that

[tiny seal]

Flip the fraction

[vernal turtle]

.

[tiny seal]

Reciprocal of a/b is b/a

[vernal turtle]

3b square over 5c cube times 25c over 9b

[tame narwhal]

yes

[vernal turtle]

ya then how continue

[tame narwhal]

how would you continue w/ any 2 fractions being multiplied?

[vernal turtle]

cross multiplication???

[tame narwhal]

what is $\frac{a}{b} \cdot \frac{c}{d}$

[warm shale]

cwatson

[vernal turtle]

abcd

[tame narwhal]

?

[vernal turtle]

bruv idk 💀

[tame narwhal]

what is $\frac{1}{2} \cdot \frac{3}{4}$

[warm shale]

cwatson

[vernal turtle]

6 over 4

[tame narwhal]

no

[vernal turtle]

3 over 8

[tame narwhal]

yes, how'd you do that

[vernal turtle]

3b square times 25c over 5c cube times 25c over 9b

[tame narwhal]

can you post the original so I don't have to scroll up?

[vernal turtle]

3b^2 over 5c^3 divided by 9b over 25c

[tame narwhal]

ok

so after multiplying by reciprocal we have $\frac{3b^2}{5c^3} \div \frac{9b}{25c} = \frac{3b^2}{5c^3} \cdot \frac{25c}{9b}$

[vernal turtle]

ye

[warm shale]

cwatson

[tame narwhal]

so you can cancel terms now

[vernal turtle]

oh

aight so 3b over 5c square times 25 over 9?

[tame narwhal]

yes looks right so far

[vernal turtle]

$\frac{3b}{5c^2} \cdot \frac{25}{9}$

[warm shale]

Lucas the rizzasaurus-rex

[vernal turtle]

yes

[tame narwhal]

now simplify more

[vernal turtle]

idk

[tame narwhal]

yes you do

look at the integers

[vernal turtle]

5/3?

then b over c square?

????

[tame narwhal]

yes

[vernal turtle]

$\frac{b}{c^2} \cdot \frac{5}{3}$

[warm shale]

Lucas the rizzasaurus-rex

[vernal turtle]

thi?

this?

[tame narwhal]

yes but just combine it into one fraction

[vernal turtle]

ok

[tame narwhal]

the same you did when I asked you what (1/2) x (3 / 4) equals

[vernal turtle]

$\frac{15m^2}{8mn^3} \cdot \frac{4}{5mn}$

[warm shale]

Lucas the rizzasaurus-rex

[vernal turtle]

$\frac{15m^2}{8mn^2} \cdot \frac{4}{5}$

[warm shale]

Lucas the rizzasaurus-rex

[vernal turtle]

i need help again

[tame narwhal]

where did the "mn" in the bottom go?

[vernal turtle]

i ate it

[tame narwhal]

how about first just simplify the integers

[vernal turtle]

how do i do that

[tame narwhal]

the same way you did the last problem...

[vernal turtle]

oh

$\frac{5m^2}{4mn^2} \cdot \frac{1}{1}$

[warm shale]

Lucas the rizzasaurus-rex

[tame narwhal]

15/5 = 5?

and 4/8 = 4?

[vernal turtle]

mb 💀

$\frac{3m^2}{2mn^2} \cdot \frac{1}{1mn}$

[warm shale]

Lucas the rizzasaurus-rex

[tame narwhal]

the first denominator should be 2mn^3 right

you had mn^3 before

[vernal turtle]

oh yea

$\frac{3m^3}{2mn^2} \cdot \frac{1}{1mn}$

[warm shale]

Lucas the rizzasaurus-rex

[vernal turtle]

aight

wait

$\frac{3m^2}{2mn^3} \cdot \frac{1}{1mn}$

[warm shale]

Lucas the rizzasaurus-rex

[vernal turtle]

ok now its correct

[tame narwhal]

ok, now you can multiply denominators together. remember rules of exponents

[vernal turtle]

whats the rules

[tame narwhal]

$x^a \cdot x^b = x^{a + b}$

[warm shale]

cwatson

[vernal turtle]

damn idk whats that

[vernal turtle]

is it 2 mn ^4?

[tame narwhal]

almost

you have the n right

[vernal turtle]

oh

the m can get eaten too

[tame narwhal]

well just focus on the denominator first

what is $2mn^3 \cdot 1mn$

[warm shale]

cwatson

[vernal turtle]

2mn^4

[tame narwhal]

no again

you have 2 "variables" here, m and n

[vernal turtle]

3 mn ^4

[tame narwhal]

no. you're saying 2*1 = 3?

[vernal turtle]

2mn^3

[tame narwhal]

what is $m \cdot m$

[warm shale]

cwatson

[vernal turtle]

m square

[tame narwhal]

yes

what is $n^3 \cdot n$

[warm shale]

cwatson

[vernal turtle]

n^4

[tame narwhal]

and what is 2*1? obviously it's 2, you had it earlier

put them all together now

[vernal turtle]

2mn^4

[tame narwhal]

no... you got each of them correct individually

[vernal turtle]

wut

[tame narwhal]

what is m*m

[vernal turtle]

m square

[tame narwhal]

yes

what is 2m * 1m

[vernal turtle]

2m square

[tame narwhal]

yes

what is (2mn^3) * (1mn)

[vernal turtle]

2m^2 n^4

[tame narwhal]

yes

now we have $\frac{3m^2}{2m^2 n^4}$

[warm shale]

cwatson

[vernal turtle]

mhm

[tame narwhal]

so how can you simplify that

[vernal turtle]

u take the m square out

[tame narwhal]

right

[vernal turtle]

aight i got it

ok thx

.close

[obtuse pebble]

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[obtuse pebble]

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[left hornet]

$\int_{a}^{t} \sqrt{1 + f'(x)^2}dx = L$

[warm shale]

ArianKG

[left hornet]

How can I find t with respect to a, L, and the function f?

[serene dawn]

Something tells me this isn't your actual question. What are you trying to do?

[left hornet]

yeah, exactly

the XY problem screaming..

[serene dawn]

I've never seen that before, thanks for teaching me that problem

[left hornet]

Actually, I'm trying to calculate the point that, if we take a distance L in a function f at a, we'll get to that

[serene dawn]

So we start at a, we travel along the curve f for a distance L, what t coordinate do we land at

[left hornet]

?

That was a question, right?

If so, yeah. I want to do that

[serene dawn]

Well that is actually the question you initially posed so mb

[left hornet]

And a curve isn't necessarily a function btw

[serene dawn]

No?

[left hornet]

I mean

I said it inversely

[serene dawn]

You are travelling along a curve, if you weren't it wouldn't be parametised by a length

[left hornet]

Yeah

That is a curve

But not all the curves can be expressed as a function

[serene dawn]

Whether that is true or not I said that f is a curve (because it is)

[left hornet]

Yeah, that's true

[left hornet]

And I said that as a by the way, as you can see

[serene dawn]

Anyway I don't think there is a general solution to this. Sometimes you're going to need to solve it numerically but otherwise if you can find the integral then it simply becomes a case of solving for t in the integral. Even then sometimes you won't be able to solve for t without numerical methods

[left hornet]

I already can find t

There's enough root-finding algorithms to do so

e.g. binary search algorithm

[serene dawn]

Yes, that's what you need to do

[left hornet]

But I'm trying to do it mathematically, with the standard mathematical functions

[serene dawn]

You can't, not in general

[left hornet]

..proof?

[serene dawn]

Consider something that can't be integrated in terms of elementary functions. If you cannot perform the integral then you cannot solve for t analytically

$\int_{a}^{t} \sqrt{1 + f'(x)^2}dx = F(t) - F(a) = L \newline
t = F^{-1}[L + F(a)]$

[warm shale]

Jacks0n

[serene dawn]

If F is not invertible (if F even exists) how can you solve for t analytically?

[left hornet]

You could also write the sigma-definition here

[left hornet]

Anyway, it really has one answer, only one answer

When we say that a function isn't invertible, means that its inverse (by rotating it 90 degress) wouldn't be a function (but a curve, still)

And when we say that it's not a function but is a curve, if we look to the functions as a set of pairs, it means that, a value in the first parameter of a pair exists, that we can find at least one another pair with the same first value but the different second value
But since it has only one answer, this can't happen

[serene dawn]

Yep

[obtuse pebble]

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[lyric kelp]

Hello

I have an exercise i dont think i understand correctly

[lyric kelp]

Let (G, +) be an abelian group

Prove that G can at most be a Q-vectorial space

[kind hawk]

"at most" ?

[lyric kelp]

Thats what i dont understand

[kind hawk]

is this the exact wording of the problem?

[lyric kelp]

In french its "au plus"

[lyric kelp]

Yes

[kind hawk]

well the original is in french so its not the original

then again I dont speak french. maybe someone who does drops by

post the original statement

[lyric kelp]

In case youspeak french

Im quite confident in my ability to translate this sentence

"Prove that G can be provided with at most a structure of Q-ev"

Keeping the french word order

[kind hawk]

well as stated that is false

[lyric kelp]

Id say at most mathematically vague here

[kind hawk]

in every possible way I can think of meaning "at most"

[lyric kelp]

But those are exercices from a teacher in an excellent post highschool thing

So i dont think hed write something false

Help please

[obtuse pebble]

@lyric kelp Has your question been resolved?

[wintry swift]

maybe: https://les-mathematiques.net/vanilla/index.php?p=discussion/1814370#Comment_1814370

[obtuse pebble]

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[devout warren]

how do you know if its SHM or not?

I only know how to see the level of damping

[lyric kelp]

Merci

(Sorry for interrupting)

[lyric kelp]

Simple harmonic is no damping right

[devout warren]

yup

there isnt any

so would that mean that there would be no dx term?

[lyric kelp]

That would be weird

[devout warren]

I remember the form being something like that

[lyric kelp]

Whats the other option

Would mean theres no movement

[devout warren]

it may still be incorporated

just isnt explicit as a dx/dt term

[timber fox]

pretty sure

can't see it being anything other than 0, otherwise damping

[lyric kelp]

Lambda is 0

Thats the only option

[timber fox]

I would agree

[lyric kelp]

Otherwise no mouvement

[devout warren]

yeah thats true, the thing which slightly confuses me is that if we find the discriminant of the auxiliary equation, which determines the level of damping, even if the second term is 0, it would still be negative

which would imply underdamping

[timber fox]

yeah , not sure entirely

[devout warren]

but the answer does say lamda is 0

so I guess the principle is right

thank you guys for your help

.close

[obtuse pebble]

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[shadow lava]

How do we know to set P' = 0?

it's finding the maximum OR minimum, is it not?

where slope = 0

[dark stirrup]

yes

[shadow lava]

so how do we know if it's max or min?

[dark stirrup]

second derivative test can confirm if it's a local min or local max (or neither)

[shadow lava]

if P''>0, it's positive?
P''<0, it's negative?
P''=0, it's neither?

[dark stirrup]

P''>0 is a local min
P''<0 is a local max
P''=0 is undetermined (it could be min, max, or neither)

[shadow lava]

and we are talking about P'' = 60 - 2x here right?

[rigid pine]

You may not need to resort to the second derivative test. You may only have two points to consider.

[dark stirrup]

P'=60-2x

[shadow lava]

so P'' = 2?

so 2 is greater than 0, therefor it's a local min?

[tame narwhal]

watch your sign

[shadow lava]

oops

right

ty

-2

so -2 is less than 0, therefor it's a local max?

[shadow lava]

meaning what exactly?

[shadow lava]

this is technically not correct, the way i worded it?

[shadow lava]

wdym?

[dark stirrup]

Correct. It is not correct.

[shadow lava]

Hmmm

[tame narwhal]

well it's technically correct. if P'' > 0, it's positive...

[shadow lava]

lol

[dark stirrup]

wdym?

[tame narwhal]

second derivative tells you concavity up/down or inflection point

[shadow lava]

local max

means local maximum

to the graph

like the highest slope on the y axis, before it approaches infinity (if at all)

[dark stirrup]

local max means that it's a maximum value within some inteveral. The bounds of the interval are the neighboring critical points, or the bounds of the function if there are no neighboring critical points

[shadow lava]

this table helps me to understand

sum is constraint function

we know it has to equal 60

but we don't know what product is (yet)

x=30, y=30 is the correct answer to this

900 is the maximum possible with any two numbers that add to 60

[rigid pine]

You need to maximise the function f(x, y) = xy subject to the condition x + y = 60.
Eliminating y, we consider the function g(x) = x(60 -x) for all x.
Since the domain of the function g(x) has no boundary points, we know all the extrema will be exist where g'(x) = 0.
You've seen that it occurs only when x = 30.
Hence g(30) = 30(30) = 900.

You know you only have one extrema.

[shadow lava]

yeah exactly

we need to find both x and y first

kind of incredible you can do that just from one value.. 60

but that's the magic of math

i'm thinking about this problem via Cartesian plane

visually in my head

[rigid pine]

This is useful to classify the point you found.

[shadow lava]

btw, who is your avatar?

[rigid pine]

f(10, 50) = g(10) = 500.

[shadow lava]

Wolfenstein character?

[shadow lava]

wait why is it g(10)?

[rigid pine]

Since you only have one extrema and you've shown there exists a point (10, 50) where f(10, 50) < f(30,30) you have shown it's a relative (and absolute) maximum.

[rigid pine]

"You need to maximise the function f(x, y) = xy subject to the condition x + y = 60.
Eliminating y, we consider the function g(x) = x(60 -x) for all x. "

[shadow lava]

oh

[rigid pine]

A Escape from Tarkov character with a funny hat to me and my friends lol.

Here's the theorem they suggested for testing the critical points (where f_11 = f_xx, f_12 = f_xy, etc.)

[shadow lava]

Ah OK, my second guess would have been Metro games

[rigid pine]

I described the other way as this is additional theory you might not be aware of yet.

[rigid pine]

Never played that one. 🙂

[shadow lava]

these textbook definitions are the worst

i need to see it described, usually video works best for me

[rigid pine]

The one I linked?

[shadow lava]

anybody familiar with the sniper rifle bullseye symbol, and Tor?

[shadow lava]

just a general statement about textbook definitions being so convoluted (imo)

[rigid pine]

Do you consider this convoluted?

[shadow lava]

keyboard text is always more difficult to interpret for math

[rigid pine]

I mean the image lol.

[shadow lava]

yes

but it's OK, i don't need to understand it right now

[rigid pine]

Theorems are much easier to prove if you start with the hypotheses clearly presented.

[shadow lava]

just enough to get me through this final exam next week

[rigid pine]

Yeah. Avoid the second derivative test stuff for now.

[shadow lava]

watching this right now https://www.youtube.com/watch?v=lx8RcYcYVuU

i can answer most of the questions but when it comes to word problems i sometimes lock up and freeze

i guess it just comes with practice, the more you do, the easier it gets

there tends to be certain questions that are asked over and over again (for optimization with Calculus 1)

they aren't very original with the questions, from what i can tell, lol

like maybe 8-10 questions that get asked over and over again

just with different values

[rigid pine]

I hate those YouTubers generally but that's just me.

[shadow lava]

Professor Leonard is good

taught me stuff i will probably never used in math class, unfortunately, but still very good

[rigid pine]

I may just be a hater lol.

[shadow lava]

https://www.youtube.com/watch?v=WmBzmHru78w I will watch this one next

"Excited but nervous" ... hopefully that's a decent place to be for your exams!

"Excited and super confident" would be ideal

dunno if it ever feels like that

anyways, i gotta get back to studying

ty for the help!

.close

[obtuse pebble]

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[obtuse pebble]

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[astral aurora]

Can someone help me with it. This is the solution but i didn't understand what formula did they use?

[obtuse pebble]

@astral aurora Has your question been resolved?

[obtuse pebble]

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[small cobalt]

I'm asking this again, because I didn't get anything last time I asked. In this scenario, what would B's latitude and longitude be? I'm pretty confident I could solve this if I had the info.

[small cobalt]

I'm being tripped up because the problem says that A is 20N 18E, but it is at 0,20 in the graph

[obtuse pebble]

@small cobalt Has your question been resolved?

[small cobalt]

<@&286206848099549185>

[obtuse pebble]

@small cobalt Has your question been resolved?

[obtuse pebble]

@small cobalt Has your question been resolved?

[wooden marten]

probably a mistake
say A is 20N 0E

I don’t understand the diagram at all though

[obtuse pebble]

@small cobalt Has your question been resolved?

[small cobalt]

Yeah the diagram is a bit dumb

[obtuse pebble]

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[violet hull]

Can someone please help me with this question? Thank you.

A round trip in a helicopter lasted 4 hours. If the helicopter flew from the airport at 90km/h and
returned at the rate of 45km/h, what is its greatest distance from the airport?
A. 100 km
B. 110 km
C. 115 km
D. 120 km

[tiny seal]

im assuming we are headed straight for the airport then suddenly straight back, right?

D=ST
D distance, S speed, T time

it traveled the same distance there and back

[violet hull]

no

[tiny seal]

no?

[violet hull]

starts from the airport

[tiny seal]

right

point a to point b

then point b to point a

right away

right?

[violet hull]

assuming that yes

[tiny seal]

okay

can you see how to make a system?

[violet hull]

hmm

[tiny seal]

distance = speed * time

ill give you a hint

[violet hull]

okay

[tiny seal]

one distance is speed*(4-t)

[violet hull]

hmm

I don't really understand

what I am supposed to do

[tiny seal]

solve the system
distance = speed 1 * time 1
distance = speed 2 * time 2

we know speed 1

we know speed 2

we know the total time

[violet hull]

does it just keep going on?

[tiny seal]

time 1 + time 2 = 4

time 1 = 4 - time 2

[violet hull]

I am lost

sorry

[tiny seal]

its okay

where did i lose you

[violet hull]

is there anyway we could draw a diagram of some sort?

[tiny seal]

here

what would be better is all givens then ill walk you through it more thoroughly

total time = 4 hours
speed 1 = 90
speed 2 = 45
distance 1 + distance 2 = distance

distance = speed * time

okay

[violet hull]

ok

so

[tiny seal]

first

[violet hull]

mhm

[tiny seal]

total time = time 1 + time 2

total time = 4

[violet hull]

yes

[tiny seal]

that means time 1 + time 2 = 4

[violet hull]

yes

[tiny seal]

wait

[violet hull]

time as in

90 km/per hour?

[tiny seal]

we need to solve for 1 time

[violet hull]

per hour?

[tiny seal]

unknown right now

we just want 1 time

[violet hull]

okay

[tiny seal]

time 1 + time 2 = 4
time 1 = 4 - time 2

lets say time 2 = t for a variable

[violet hull]

t representing time?

[tiny seal]

yeah

[violet hull]

alright

[tiny seal]

we know 2 things
time 1 = 4 - t
time 2 = t

from there we can do
distance 1 = speed 1 * time 1
distance 2 = speed 2 * time 2

but remember

distance 1 = distance 2

[violet hull]

so they are equal

[tiny seal]

distance 1 : a to b
distance 2 : b to a

[violet hull]

got it

[tiny seal]

right

write out the equation so i can make sure you follow

[violet hull]

speed 1 * time 1 = speed 2 * time 2?

[tiny seal]

right

speed 1 = 90
speed 2 = 45
total time = 4
time 1 = 4 - t
time 2 = t

[violet hull]

• meaning multiply?

[tiny seal]

plug those in

yeah

[violet hull]

90 x (4 - t) = 45 x t?

[tiny seal]

i got the speed backwards

but yeah

90t = 45(4-t)

solve t

[violet hull]

90t?

[tiny seal]

90 * t

[violet hull]

where did we get that from

[tiny seal]

shorter

i got the 4-t and t swapped

my bad

[tiny seal]

so this one is right

lets go from here

[violet hull]

okay

so

[tiny seal]

solve for t

tell me what you get

[violet hull]

could you tell me what t represents again? sorry

[tiny seal]

time

[violet hull]

okay

so

[tiny seal]

time 1 specifically

so what did you get for t?

[violet hull]

still stuck

[tiny seal]

$90t=45(4-t)$

[warm shale]

Cycadellic

[tiny seal]

how do i get 45 inside the parenthesis?

[violet hull]

90t - 45 = (4 - t)?

[tiny seal]

no

try this

[violet hull]

parenthesis meaning?

[tiny seal]

( )

[violet hull]

alright

[tiny seal]

$a(b-c)=ab-ac$

[warm shale]

Cycadellic

[tiny seal]

distributive property

what do we get after we distribute on the right side of the =

[tiny seal]

in this one

[violet hull]

ab - ac

[tiny seal]

right

so

a=45
b=4
c=t

plug those into your term

ab - ac

[violet hull]

90t = 180 - 45t?

[tiny seal]

good

how do i get 45t on the other side

[violet hull]

90t - 45t = 180?

[tiny seal]

almost

not - because
whats -45 - 45

[violet hull]

90t + 45t = 180

[tiny seal]

yeah

now do distributive property, but backwards

$ac+ab=a(c+b)$

[warm shale]

Cycadellic

[violet hull]

135t = 180?

wait so what?

[tiny seal]

yeah

[violet hull]

okay

[tiny seal]

this is okay

how do i get the left to just t

[violet hull]

wtf

[tiny seal]

bruh

<@&268886789983436800>

continue

[violet hull]

alright

[tiny seal]

so how do i undo 135 * t

[violet hull]

hmm

[violet hull]

multiply?

[tiny seal]

whats the opposite of *

[violet hull]

divide

[tiny seal]

right

what do i divide off of 135t

to get t

hint: we want 1*t

[violet hull]

hm

[tiny seal]

135/what = 1

[violet hull]

135 itself

[tiny seal]

right

so

135t/135=?

[violet hull]

1t?

[tiny seal]

yeah

[violet hull]

but its 180

not 135

[tiny seal]

okay

so

135t=180

what do i need to divide by both sides to get just t

[violet hull]

135

ohhhhhh

that means

do we divide 180 by 135 too?

[tiny seal]

yeah

think of a scale

if i do one thing to one side, i have to do it to the other

[violet hull]

yes

[tiny seal]

that will keep the scale balanced

thats actually what algebra is based on

so t=180/135

[violet hull]

but dividing 180 by 135 won't give us a whole number

[tiny seal]

simplify it as much as we can

or

[violet hull]

12/9?

[tiny seal]

just type it into your calculator

[violet hull]

t = 12/9?

[tiny seal]

yeah but

we can keep going

[violet hull]

4/3?

[tiny seal]

yeah

good

so, time 1 = 4/3

[violet hull]

indeed

[tiny seal]

distance = speed * time

[violet hull]

distance 1

is

[tiny seal]

distance = 90 * 4/3

[violet hull]

yes

360/270?

distance 1 = 360/270?

[tiny seal]

no

thats 4/3

[violet hull]

oh

[tiny seal]

90 * 4/3

[violet hull]

so what do we do?

[tiny seal]

you did (90*4)/(90*3)

but $90\cdot\frac{4}{3}=\frac{90\cdot 4}{3}$

[violet hull]

yes

[warm shale]

Cycadellic

[tiny seal]

whats 90*4

[violet hull]

dot meaning?

[tiny seal]

times

[violet hull]

360

[tiny seal]

x is confusing so we use dots instead

[violet hull]

okay

[tiny seal]

||until you reach higher levels of math then we use x again for different multiplications||

so we want

[violet hull]

okay

[tiny seal]

360/3

[violet hull]

90

[tiny seal]

not quite

[violet hull]

wait

no

120

[tiny seal]

yeah

thats the distance of A to B

or

[violet hull]

alrighty

[tiny seal]

the distance to the airport

all good?

[violet hull]

distance to the airport?

[tiny seal]

(its your answer)

did it all make sense?

[violet hull]

it started from the airport

[tiny seal]

point A

[violet hull]

so airport is point a?

[tiny seal]

then it went to another airport

cant image a plane landing anywhere else

[violet hull]

so distance from point a to b is 90km?

[tiny seal]

no

[tiny seal]

we solved it earlier

[violet hull]

oh yeah

yes

120

120km?

[tiny seal]

yeah

[violet hull]

so the answer is d. 120km

[tiny seal]

did everything i told you make sense?

[violet hull]

yes it did

didn't know we had to represent time with t and distance with d

[tiny seal]

to recap, we found distance from speed and time, and we set the total time = 4, solved for 1 time and solved our distances because we knew they were the same

[violet hull]

yeah

thing it

these types of questions

times that I don't know where to start

[tiny seal]

yeah

thats why they have you doing them

[violet hull]

any advice?

[tiny seal]

you can only get better with practice

[violet hull]

indeed

[tiny seal]

practice practice

[violet hull]

alright

I will

Anyway

thank you so much for helping me

[tiny seal]

np

[violet hull]

really gave me a better thinking

hope you enjoy the rest of your day!

[tiny seal]

you too!

[violet hull]

.close

[obtuse pebble]

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[distant rampart]

I'm struggling with a question regarding a geometric series and was hoping someone could help me out. The question is as follows:

Given a geometric series where $a_3 = 6$ and $a_5 = 1.5$, determine the infinite sum of the series, i.e., find the value of $$\sum^{\infty }{i=1} a{i}.$$

[warm shale]

dgh

[upbeat gazelle]

Try to express the ratio of a_3 and a_5

That might help

[distant rampart]

to find r, we take the ratio of any two consecutive terms in the series, in this case, the ratio of a_3 and a_5 is:

r = a_5 / a_3 = 1.5 / 6 = 0.25

Like that?

[upbeat gazelle]

Here it does not give you r but r²

[distant rampart]

oh, how did you have in mind the expression of thee ratio would look like?

[upbeat gazelle]

Because 5-3=2

[distant rampart]

so it should be r = (a_5 / a_3)^(1/(5-3)) = (1.5 / 6)^(1/2) = 0.5?

[upbeat gazelle]

Yes

[distant rampart]

okay now that we have r, what's the next step?

and should r be ±0.5?

[upbeat gazelle]

Now you may want to find the multiplicative coefficient by computing a_3/r³

And once you have that you multiply it by the geometric series of parameter r which gives you 1/(1-r)

[distant rampart]

a_n = a_1 * r^(n-1)
n = 3, r = 0.5
=> a_3 = a_1 * 0.5^(3-1)

a_3 = 6 => 6/(0.5^(3-1)) = a_1

,calc 6/(0.5^(3-1))

[warm shale]

Result:

24

[distant rampart]

S = a_1 / (1-r) => 24 / 0.5 = 48

@upbeat gazelle

correct?

[upbeat gazelle]

Looks good

[distant rampart]

what's the difference between 1/(1-r) and a_1 / (1-r)

[upbeat gazelle]

1/(1-r) is the sum of r^n while the other is the sum of a_1r^n

[obtuse pebble]

@distant rampart Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[queen lark]

csc -5pi/6, can anyone help me with this??

[queen lark]

what i don't understand is why the answer is -2 instead of 2

[timid silo]

u know which quarter is it

[queen lark]

the 2nd right

[timid silo]

nope

its the 3rd

u are moving clockwise

not counter

because its negative

and csc is negative in the 3rd

[queen lark]

sry im confused

5pi/6 is 150 degrees?

[timid silo]

yes

but

its -5pi/6

so its -150 instead

[nocturne minnow]

You're forgetting that it's negative 5pi/6

[queen lark]

so i subract 150 from 360

??

[timid silo]

yes

or u move clockwise

[queen lark]

ohhhh

[timid silo]

instead

[queen lark]

i wasnt here for the lesson so this stuff was rly confusing

thank youu

[nocturne minnow]

If it helps, the unit circle is from 0 to 360, you can do 360 - 150 to achieve a positive angle

[timid silo]

or u have one more trick

sec and cos removes the negative

but others u can take it out side

[queen lark]

wait so it can be both positive and negative??

[timid silo]

so cos-pi

is cospi

and sin-pi

is - sinpi

[queen lark]

-blinks-

sec and cos....removes what negative?

[timid silo]

yes

the negative inside of it

[nocturne minnow]

Fyi the term is coterminal angle, -150 and 210 are the same angle

So that's why you can do 360 - 150 to get the same angle

As going clockwise 5pi/6

[queen lark]

oh ok so its just another way

[queen lark]

can you give me an example pls?

[nocturne minnow]

They just did

$\cos(-\pi) = \cos(\pi)$

[warm shale]

dldh06

[queen lark]

how is that possible

is that a rule?

[nocturne minnow]

Yes

[queen lark]

ahh more things to memorize

tyty

wait so when im calculating the coterminal do i write 360-150=210? cause isnt it supposed to be -210?

[queen lark]

are you still there?

[nocturne minnow]

The given angle is already negative, you want that angle to be between 0 degrees and 360. -210 is not between that, so it would be +210

[queen lark]

what if the angle was -210, that's not between 0 and 360 degrees??

[nocturne minnow]

Then you add 360 until it gets between 0 and 360

[queen lark]

ahh i think i get it

thanks again

[obtuse pebble]

@queen lark Has your question been resolved?

Channel closed

Closed by @queen lark

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