Optimization Problem #3 - Making a Rain Gutter

[iiottoii]

If only you were right handed=p

[TheDuskMar]

Hehe, I think it would be easier to utilize the identity sin(2x) = 2sin(x)cos(x)

[ImJustAbi]

@TheDuskMar I was thinking the same thing, saves a lot of time.

[RECxLESS]

i think the only dislikes your videos get are from angry math teachers that are jealous of your awesome teaching abilities :)

[00Dusk]

lol, middle finger?

[angelovss]

instead of doing this as a rectangle with triangles cant you view it as a trapezoid?

[samuelpalka]

Why would anyone dislike this? You help me study so much for finals!

[baseball101star]

Couldn't you use Pythag to find the height in terms of width?

[mirako347]

Oh my gosh I would of sworn the first thing I saw was a face. The angles are eyes the lines are the eyebrows and the swigging lines the mouth.

[beiyifa]

i hope this is what will be on the exam XD

[sueishungry]

our AB Calc class went through Related Rates before going through this on a crappy textbook... nonetheless I didn't do well.

[SantosJoss]

why u r no in my class!!!!!!!!!!!

[FiorituraVilly]

how do you do optimization problems without derivatives?

[feiunot]

my rain gutter is flat :D

[mistersirisaacnewton]

ay, dios mio.

[ICarnag3I]

@DeathIzurfriend this is harder

[TheSke7ch]

I have a quiz in Calc 3 covering Calc 1 & 2. I felt like I forgot a lot of the stuff. Just watched your vids and did a few practice problems for the harder concepts, now I am ready.

Keep it up!!

[kebakent]

That is one angry Pokemon

[FlipsterLombax]

I had me saying SOCCAHTOA

[santaclassic]

I just got 100% on my mid-term thanks to you sir. Thanks from Canada!

[MrHav1k]

YOU SIR ARE AMAZING! I'M GOING TO ACE MY FINAL TOMORROW BECAUSE OF YOU!!!

<3 YOU (no homo)

[1brightshadow1]

NICEEE! (fabolous voice)

[shrimfririceeeee]

you might've factored wrong or maybe i'm wrong

[pballer000]

I wish you were my calculus teacher !!

[VxGIBSONxV]

Why is the derivative of sin theta cos theta?

[urta93]

This is EXACLTY what I need, omg thank you

[patrickJMT]

@urta93 no problem

[GoodyearBandit]

@patrickJMT Thank you again man, God bless.

[TheMysteriousAtheist]

good math videos. By the way you sound almost exactly like Mr Vandreesen from Beavis and Butthead haha

[kristinnnxox]

FUCK YES

Thanks for these videos!

[MrMateynikolov]

The graph looks like a really angry face!!!

[stargazer793]

also cos x = 1/2 at 5Pi/3 . Just wanted to let people know. So unless you are given an interval which does not include 5Pi/3 then you would normally list both these answers

[1966zaim]

Thanks .May God reward you.

[AnimangaArtist]

That was...beautiful.

I understood it completely.

Thank you so much for posting this optimization problem video, along with the others!

I feel more confident about my quiz tomorrow. :)

[StrawberryCheckers]

These videos are so helpful, they really have been saving my life lately! Thanks

[pimp2611]

Why do you only get 10 min??

[patrickJMT]

@pimp2611 those were the old youtube rules. they have since changed.

[jamchua93]

how can we check if it is the maximum or the minimum?

[lifemakesmelaf]

wait how can you ensure that its a maximum?

i mean couldnt it be a minimum?

dont you have to do a first derivative test?

[laputahayom]

bender approves of this video.

[marshvegaslimelight]

love it! you should see this problem we did today though, it was demonic- it was a cylinder in a sphere, it was super annoying

[Zyntle]

thanx patrick i had the last 2 problems 4 my tuts u really helped me

[O0oSorousho0O]

10:01-10:04 You sounded funny when u said it lol

[vd853]

all four teta angles are equal? how?

[O0oSorousho0O]

@vd853 Remember the "Z" pattern in Gr 9 Geometry?

[jazzysax102391]

Quite the beast of a problem

[Hackiesacker007]

Awesome explanation!

Thank you!

[PiningSapience]

I never know what were talking about in class until I look it up on your site. I'm surviving calculus because of you, thanks soo much!

[RyanEnvy]

the two T's on gutter look like Pi! :D

[gsharpshooter80]

hahah the problems looks like an angry face screaming making a rain gutter !

[darn111]

@gsharpshooter80 hahaha that's very funny

[gsharpshooter80]

@darn111 haha

[kyootaay]

I love you.

[sapphirexsunset]

if the 10m of the side-lengths of the gutter werent given - just that the total had to be 30, would using trig or pythagorus be easier? (on the areas/relationship of the triangles - w and h)

[hsb225623]

wouldnt u want to find volume of gutter? not area

[webmastertool]

@hsb225623 If you optimize area for a flat shape, when the shape turns 3d it is automatically optimized for volume.

[hsb225623]

wouldnt you want to find the volume? not area

[popcornredbag]

couldn't you have just used Pythagorean theorem instead of sin and cos? it would have been way easier.

[Ufaqueiqbal]

thnxx :)

[gespilk]

I wonder how the solution would look like if instead of gutter we have a canal to dig and we have to minimise the cost of building it. In this case given are the max width of the canal and the minimum throughput of water. The question is what shape would minimise the cost of concrete used to isolate the canal plus what shape would be cheapest to dig (complex shapes are more expensive I think). This is more like a real life engineering optimisation. Could give us some pointers in another video.

[gespilk]

I thought that semi-circle would be the shape that provides maximum volume for a given perimeter. At least that what they tell us is good for space domes (min surface max volume).

I could guess the shape of the gutter here is approximation of a circle.

[DragBag2000]

Whoops, one mistake. You would actually have to do 90 - arctan(w/h), since arctan(w/h) will give you the measure of the angle from the normal, in this case 30 degrees.

[DragBag2000]

In addition to solving the equation in terms of theta, you can also use the pythagorean thereom to find h or w in terms of the other variable, take the derivative with respect to whichever variable you chose to solve for, and then use that to find the optimal height or width. From there you can apply pythagorean thereom again to find your other variable, and then you could calculate theta by taking the arctangent of your (w/h) values.

[lilsamuraijoe]

That rain gutter is staring at me with devil eyes.

[jojoAlltheway]

@lilsamuraijoe oh yeah devil eyes! its scary as you thought it would be !

[xdashdave]

this will help with my exams the day after tomorrow

[MrSickygnargnar]

very helpful videos. thank you

[45caliberluv]

I'm a junior in HS and I'm first in my class of 400 students. I have a perfect record (no grades lower than an A so far) I'm taking AP Calc this year and was having some trouble, which I'm not used to. I'm lucky enough to have most things academically come natural. These videos have helped tremedously. My teacher explains things in a much more complicated manner. Appreciate the time taken to make them. Great study tool!

[4Shabani4]

nice job on your academics from University of Wisconsin.....

[thebrightnightsky]

I swear to God this guy is a better teacher than my Calc Teacher...he can't teach for life!! THANKS PATRICK!!!

[maggiekmays]

I love how you do every single step!!

[cheatingvid]

zomg, thank you (x10000)

[bxdiamonddd]

do you have any tips to starting the question? thats what i have most problems with, understanding what the question is asking me

[Holliman123]

tisk tisk u did not talk about the whole right angle so that u can use that triangle area rule very naughty at least should have the small squares there

[Lunchsacks]

i like how 2 of the three poblems you are doing are the ones done in my calculus lecture!

[thrashmeta1]

haha the finger

[NeoXC]

Holy...wow, I hope I never see this kind of problem on one of my tests.

[legram13]

btw how did you come up with 3 10cm? is it in the given? have you considered other way of dividing the 30cm? just curious though.

as always thanks for the free vids! you surely help a lot specially me!

[werenothere]

The piece of metal was given at the beginning of the problem to be a total of 30cm. And also given was the fact that the metal was to be bent into 3 equal parts.  3 x 10cm

[dJAYMist]

its given that u must divide into 3 equal pieces out fo 30cm

[bxdiamonddd]

its in the problem, there is also a diagram to illustrate it.

[zstanacev]

ok,ali kako montirati takav oluk?

[greatmoose]

ZZZZZzzz but it was helpful :D THX!

[elementoxygen]

Great video :D

I loved all of it!!

[PhoenixSparker]

i love it.

[Ahhhhlecks]

no joke i did this question for an assignment on saturday.. really wish i had found this video first :(

[xxk4ixx]

that's the more complex kind of optimization, there are also ones with cones and cylinders which are also very tricky

[yaguang]

Whoa. Impressive question! Never knew optimizations could be applied to angles

[ArrudA666]

the only part that confused me, which i guess i never learned, was how did you know that cos^2theta + sin^2theta =1 ? is that just common knowledge?

[patrickJMT]

it is one of the first trig identities that one learns; it is one of the pythagorean identities

[ArrudA666]

thanks ill look into that. i must have missed that class

[aznwoowooo]

@patrickJMT lol u cant have gone thru algebra II without cos^2 +sin^2 =1

[O0oSorousho0O]

@ArrudA666 Yes. Try testing that eq'n with a calc you'll see the proof

e.g.

sin^2(0) + cos^2(0) =1

0 + 1 = 1

and

sin^2(90degrees) + cos^2(90degrees) =1

1 + 0 = 1

[enodatube]

@ArrudA666 that is a restatement of the pythagorean theorem.

[steam118]

if i get a question like this on my test tommorow im fuked

[333329753]

lol!

[Grobannela]

haha

[matty2k001]

@steam118 Lol I got my cal 1 final tomorrow :P

[INS1cells]

qustion: how would you do a second dervative test on this problem?

[djjm11]

hi...great videos!

hmmm...i think you can avoid the derivation of trigonometric stuff by using the Pythagoras Theorem...just like:

total area=10w + wh

then build a triangle and by the definition of pythagoras theorem:

10^2= (w^2+h^2) and get the equation of "h"

now you can "plug in" it: total area=10w + w([10^2+w^2]^1/2) and derivate it... once you get the solution of the equation you solve cos^-1(the solution)

[kallo1234]

very interesting problem

[0oBrokensmileo0]

You Rock !!

Thanx a bunch 4 all of uR amazing vids..

u dont know how much this helps ^_^

[gellybelly2]

That's an interesting problem. Thanks for posting!. Pretty cool a bit of trig, calculus, trig identities. Great explanation :).

[patrickJMT]

thanks gelly : )

[gam3fr33k]

lol You gave us the finger. Thanks for the tutorial though

[patrickJMT]

yea, i noticed that too! : )

subconscious 'up yours'? : )

or just an accident....

i wonder

[FlavouredVitamin]

@patrickJMT Something we need to ask Freud!

You are absolutely amazing!!

[dragunov3rlo4d]

can u please make more optimization vids? for example how to find the maximum area of a rectangle/trapezoid inscribed in a semicircle problems etc

[okwuoc]

Thanks bro for posting. This is very charitable of you. God bless you.

[patrickJMT]

glad it helps everyone!!

[stmc247]

DUDE! thank you so much!!

[xroyaldevilx]

Thanks for the video.

[Nandine2]

thank you so much for these videos, you have really helped me with my maths! way better than my maths teacher!!!!