💧 Making a Rain Gutter 💧

[@alexthompson9409]

Dude is so smart. Wish i could borrow his brain for tests.

[@Happycamper059]

I currently have a 57% in my calculus class because my professor is garbage and an unfair grader, and I need a 78% on my final to pass. I honestly feel confident in getting this score thanks to your videos. Much love :)

[@patrickjmt]

@urta93 no problem

[@darksideguy]

I can not thank you enough for these videos (and the rest of your calc 1 series for that matter). Between my best in person math teacher I've ever had and you on youtube, nothing in calculus I've experienced fazes me (yet).

[@lanfordvideos]

I feel like my total cranial capacity is doubling for every ten minutes of watching PatrickJMT work these problems. Optimization and related rates problems seem to be about the toughest quagmires that derivative calculus has to offer.

[@Shidabood]

ah hell nah bro fr said quagmire who else but quantum physics

[@fenderbender23]

Patrick, I owe my A in Calculus to you. Thank you for being my primary source of calculus expertise this semester. For whatever its worth, I sent you a 15 buck donation. You're the man! Keep up the excellent work.

[@patrickjmt]

glad i could help :) thanks a bunch for the donation!

[@patrickjmt]

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

[@junioraugustoperez6212]

1:04 oops!

[@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.

[@patrickjmt]

yea, i noticed that too! : ) subconscious 'up yours'? : ) or just an accident.... i wonder

[@WildThobson]

I hope your making more money then a highschool teacher. Your videos are so easy to follow, so simple, and so helpful. I've learned more in 2 hours of watching your videos then i have from 10 classes of Calculus

[@patrickjmt]

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

[@teuffelowo]

You just saved my Calculus' final.I just saw all the optimization plus all the related rates videos. Totally worth it.

[@zzpatrick1]

Hey, Patrick I love all of your videos! Im just in pre-cal and I love optimization problems and this one blows my mind! Great job! Thanks for all of your wonderful lessons!

[@pucca8441]

0:44 tell me i'm not the only one that sees a face. :]

[@santaclassic]

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

[@pipertripp]

I ended up using the trig identity cos^2(theta) - sin^2(theta) = cos(2*theta). You end up with cos(2*theta) = -cos(theta), which is 60 deg. The quadratic you ended up with is easier IMO, but this other approach worked out too.

[@patrickjmt]

@1212naked i suggest a little shrine to start.... :)

[@johanalviz1716]

0:05 the devil is in the math. Amen.

[@redblack8766]

Am I the only one who thinks the drawing looks like a pair of angry eyes ?

[@stillalive4513]

Now that you mention it .___.

[@AeroeGraphix]

I cannot unsee this now.

[@kimjongun2524]

I THOUGHT IT WAS RINNEGAD TURNS SHARINGAN HAHAHAHAHA

[@Duncebunken]

This guy does a really good job! I just wish he would explain setting the problem up in more detail and finish the problem completely because the goal of the problem doesn't seem as realistic as it does in my math class. For me, it doesn't just end with the critical value, but more so a perimeter, area, volume, or a more extended answer. Regardless, these videos are really helpful. Keep it up!

[@Zyntle]

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

[@tracerbullet44]

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

[@patrickjmt]

glad it helps everyone!!

[@sylviao9752]

this video got stuck and I have been trying to replay it over and over again but it still gets stuck when its at 7:57..i really wanna watch to till the end patrickJMT

[@bryantlee1710]

This is definitely challenging, but man are you a good explainer! Thank you so much! Attempting to become a Materials engineer and you my man are helping me through Calc 1:)

[@шавкатнаджметдинов]

Good luck man i am attempting electrical engeneering)

[@katelynmh]

You really helped me through Calculus last year. Thanks!

[@patrickjmt]

that has to be one of the best comments ever :)

[@patrickjmt]

i think that is a good way to use the videos ;)

[@yvonnekavithe6247]

man, I need a repeat of the cosine theta and sina theta's derivaives joh

[@patrickjmt]

thanks gelly : )

[@xxk4ixx]

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

[@Nandine2]

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

[@yaguang]

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

[@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

[@supperd0n]

When you're dealing with cosine or sign you should use exact values. Just think the numbers prettier he don't have to deal with any signs to the negative or driving sin. That's just what I did.

[@youmah25]

in 9:10 we can subtute cos(theta) by X the equation will became: 200*X^2+100X-100

[@jeryk421]

You are incredible! We in Puerto Rico love u man!

[@AndrewLee-wl6cn]

He could not have explained this any better! This was on point! I'm seriously considering giving this guy $1 per month. Patrick, is there any way you could add a graph? Function A for 0 less than or equal to theta less than or equal to pi/2?

[@youngdonlee495]

You are truly a Godsend. God Bless You. You should be teaching at an university.

[@SiddhantEkale]

Hey Patrick! In this problem we want to maximize the quantity of water i.e. the volume of the water hence how can maximising the area maximise the qty of water..since volume would be area into height of the gutter..

[@GoodyearBandit]

@patrickJMT Thank you again man, God bless.

[@xxCCBBxx]

Patrick JMT 2012 for president

[@gellybelly2]

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

[@lilsamuraijoe]

That rain gutter is staring at me with devil eyes.

[@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.

[@123rimsha]

For some reason, I read the title of this video as "Optimization Problem #3 - Making it Rain"

[@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

[@Masonggg]

please tell me how to maximize the area of such a shrine

[@AkingAquila]

You have to think about the context. eg if you have profit, you wouldnt wish for your business to run at a loss. you'd want to find out where you'll get maximum profit. Same for cost of materials. if you want to build something, you'll look for the dimensions that use the least materials, right ? (because more materials = more money, which i'm sure given the current economic situation, you do not want. ) so in general, i'd say you should think "would this benefit me or would this be bad"

[@Eeeeeeeeerie]

how do you do optimization problems without derivatives?

[@urta93]

This is EXACLTY what I need, omg thank you

[@Infranco10]

your videos are really usefull references, thanks a lot for your dedication

[@omjnrg111]

How do you know when something is asking to be maximized or minimized?

[@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)

[@ArrudA666]

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

[@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!

[@savitribaiphulepuneunivers1461]

Please make video of minimization for the same problem

[@xdashdave]

this will help with my exams the day after tomorrow

[@muigaimwaura2379]

The cross-section is a trapezium. It's easier to use that and the formula for the area of a trapezium.

[@boody8beloved]

10 minutes limit !! I would give you all my time Pat , just keep going :")

[@mohamadamierasyraf5976]

wait, if you already set the rectangle to a certain height, wont it be affected when you changes the angle? i mean, the flatter the angle, the less height.

[@jamchua93]

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

[@salmanhaidar3877]

How do I solve it if there isn't a 10 value, just a variable a for each line?

[@baseball101star]

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

[@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?

[@ChadisRad100]

Why do you not have to take the derivative of 100 in front of the cos or sin. Is it not a product rule?

[@zahraalzuraijawi9062]

finding the area of the trapezium would've also worked

[@matchew422]

how do you know if the hypothenus of the triangle is 10?

[@riohina0730]

our class use this kind of problem but instead of that, we’ve used the area of trapezoid.

[@sueishungry]

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

[@superbros1690]

I wish I have good memory, I keep forgetting Identities and all the important rules.

[@elementoxygen]

Great video :D I loved all of it!!

[@demebox3607]

Lmao when I heard the 10 time limit. Still saved me a decade later.

[@bebexc143]

what is the question? thank you!

[@cnp5729]

Would you help me in solving my optimization problem?

[@vd853]

all four teta angles are equal? how?

[@XZeniXTaniX]

-flips out the middle finger as a pointer- & -slips out a 'whoops' for reassurance of the otherwise case-

[@Hackiesacker007]

Awesome explanation! Thank you!

[@gsharpshooter80]

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

[@inejio8794]

Thank you sir for your video!

[@ataraxic89]

Can someone help me, I worked this myself before watching and got the same derivative, 100cosx-100sin^2x+100cos^2x=0. Next I moved the -100sin^2x to the other side and divided by +100cos^2x, which gave me 100cosx=tan^2x. Why doesnt that work?

[@justabi_sings]

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

[@enodatube]

@ArrudA666 that is a restatement of the pythagorean theorem.

[@xxberryyxx]

is it just me or does the picture look like a mischievous cat? XD anyways, thanks a lot patrickJMT! ur videos helped a lot!

[@TheMysteriousAtheist]

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

[@Borjigin.]

If you were to use product rule, the derivative of 100 = 0, so that would still just be 100*(the derivative of sin or cos).

[@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?

[@kebakent]

That is one angry Pokemon

[@MrSickygnargnar]

very helpful videos. thank you

[@timjohnson2559]

This stuff is so hard :( It wouldn't be so bad if there were a standard or general way of doing each and every single one. :( :( :( I have a test on this tomorrow!!! And related rates!!!!! :( :( :(

[@tofo7151]

related rates for me is easier now this optmization is so hard for me

[@Borjigin.]

Because the 100 is a constant, not a variable. You don't use product rule when taking the derivative of 2x^2 because 2 isn't a variable. Same logic applies.

[@patrickjmt]

awesome! :)

[@шавкатнаджметдинов]

Thanks a lot! You are very helpfull!

[@TheFalloutnewvegas]

These videos are why I have a 97% in Calculus. :)

[@xroyaldevilx]

Thanks for the video.

[@anathorsis]

thanks a lot buddy, keep it real yo

[@aymanwaseem1735]

Why is it that you took the hypotnuese as 10 but refused to take the height as 10 too?

[@ACTlVISION]

The hypotenuse was made from "bending" the segment that was 10 units long, same segment so length is known. The height is unknown at that point because it's a function of the angle.

[@Quichey2]

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