Related Rates - Conical Tank, Ladder Angle & Shadow Problem, Circle & Sphere - Calculus

[@TheOrganicChemistryTutor]

Related Rates - Free Formula Sheet: bit.ly/48hJymz Final Exams and Video Playlists: www.video-tutor.net/ Calculus 1 Final Exam Review: kzbin.info/www/bejne/jZ6lq6B-p9pqbtk

[@NicaKasende]

Hey, thanks for ur awesome videos. I recently posted some questions. Would you be able to answer them. Thanks in advance

[@sccm100]

This section is the hardest section in calculus 1. It's not really that hard after you know how to do it, but at the beginning it feels like rocket science.

[@jocoolshow]

i find limits, intergrals/anti derivatives and optimization to be harder

[@Vishuddha12]

Integrals is Calc II

[@jayseth9251]

Wait really. Jeez. IB HL Math is going to make uni calc a breeze.

[@jackychan4899]

Hard integrals are calc 2, we just learned usub in my calc 1 class and Riemann sums

[@treyrichmond747]

ruby_kid I’m in ap calc n he teaches it’s basically calc bc bc the whole second semester is u sub, ip, n integrals

[@elenagentry8774]

I’m crying right now. It’s 6:30 am and I’ve been up since 2:30 because I couldn’t fall back asleep due to nerves from having a math test I don’t know two shits about. I’ve been watching your videos for the past hour and a half and I actually understand. For having slept 7 hours within the last 48 hours, thank you from a mentally and physically exhausted scatterbrained 17 year old. Seriously- thank you!

[@ahmedmurtazamalik]

How did it go?

[@ARCHIlAND24]

Actually i feel every word you wrote iam the same 😢😢😢😢

[@nahthatscrazy]

@@ahmedmurtazamalik it probably went terrible tbh, not trying to bring them down but they were ill prepared. Not necessarily their fault though

[@lex-zx5hl]

@@ahmedmurtazamalik you find out

[@virp9632]

​@@nahthatscrazyI disagree... it's no one's fault but his. one doesn't start studying for the test 48 hours before it starts.

[@milisia7726]

i can't believe you do chemistry, physics, and calc!!! is there anything you don't know? thank you so much you're a gpa saver!!!!!

[@John-bq1lp]

he does biology now

[@scottwillard7998]

He doesn't do programming or Data Structures and Algorithms :/

[@christ8590]

@@scottwillard7998 Yea, but it wouldn't but much of a jump for him at this point. Programming is based off math.

[@dranoc5879]

@@scottwillard7998 He does, he has a separate youtube channel called TheNewBoston. He does c++, c#, java, etc

[@scottwillard7998]

@@dranoc5879 they're not the same channel are they? Two totally different voices

[@codyroman602]

Organic Chemistry Tutor deserves an award. His help with literally every subject is unmatched. Before you mention khan academy, they are incomparable.

[@ayushvaidya6608]

IKR khan is very shitty

[@allucard1018]

Khan academy is actually a better teacher in certain aspects. Ngl organic chem tutor is good to just know how to solve the question. Khan academy dives a lot deeper into the concept and that isn’t rlly required for chem and math

[@frehiwotgetachew542]

I personally prefer organic chemistry over khan academy

[@frankyan3500]

let me be honest OCT is far better than Khan.

[@hannahwatermelon]

This video alone is saving me. I mean, almost every single one of his videos are amazing, but related rates in particular is so difficult to wrap my mind around, and the fact that he included so many examples, is a blessing for real. My teacher only showed us 3 examples, which was really great, but then the homework had examples we hadn't covered yet, and there are so many ways these problems can be written, I'm so glad he went over all these different types. Sincerely, thank you so much.

[@Vyap2702]

my teacher showed 1 example and that's it lmao xed

[@gluebroken2369]

True

[@badkgaming5122]

@06:35 origin and moving point on graph @11:08 radius of circle is decreasing. How fast is area and circumfuses changing given radius. @16:07 Surface area of a ball decreases at a rate. How fast is diameter changing given radius @19:46 side length of square increases at rate, how fats is area and perimeter changing given side length @23:20 balloon filled with gas at rate, how rate of raidus given radius @27:11 side length of cube increasing at rate, what is rate of surface area and volume given side length @31:11 ladder leaning against house. Slides down wall with rate @46:12 gravel is being dumped at a rate forming a concial pile whos base is 2x height . How fast is height changing given height. @54:48 water is leaking out conical tank at rate, given height and raidus

[@brandonlowwww]

respect bro 😎

[@sandratran5090]

gods work 🙏

[@GloomyPie1]

You saved me so much time

[@probablysam2744]

Thanks broski 😘

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Legend

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out of all the tactics i have tried, there's only one tactic that worked for me, and that tactic is YOU!!!!, you are so good!!!! at your work, thank you so much

[@Coreyahno]

This section proved more difficult than anything else I had done up to this point in math. Really struggled with the concepts. But after about a week of obsessive studying and watching this video at least 3 times it is actually easy for me now! It’s crazy how once something clicks and makes sense it seems so simple that you wonder how you didn’t understand it from the beginning. Thanks as always for your content.

[@drewbasile4055]

It's a great feeling once gained knowledge clicks and becomes second nature.

[@andrewmartinez9262]

You gave me the highest grades in my chemistry class last semester, so I was tremendously excited to see that you do calculus as well.

[@CieKayy2000]

Andrew Martinez sana all

[@ResidentTitan]

1:19:05 The values of x and y should be switched. x = 120 miles and y = 90 miles since dx/dt = 40 mph (going east) and dy/dt = 30 mph (going north). This makes dz/dt = 50mph. Overall a really great video that helped me understand related rates a lot better. Thank you!

[@Slayest_doctor]

Yeah I noticed that mistake 😅 But he(or she) is a great smart person 😅

[@christianjosephmondejar4383]

Yep made me check again 😆

[@PrivacyTerms911]

she?????????????? @@Slayest_doctor

[@forthehomies7043]

lol hey you never know what gender someone identifies as. jk but in all seriousness it is a black dude @@PrivacyTerms911

[@christianmangrobang3061]

I knew it, thought I was wrong 😅

[@Sonny2009]

By far, he has to be the best when it comes to teaching Calculus. A lot of other teachers failed to explain the concept or take things from ground up. But he explains everything very CLEARLY.

[@JesusRodriguez-dc7of]

It's been a minute since I learned these early calculus concepts and it feels so good to understand this concept so easily now since it was a confusing nightmare when I first learned it lol. As always, OCT deserves a Nobel Prize for the number of stem graduates he's produced since he started this channel.

[@karimasa9066]

I keep praying for you every time you save my grade. I couldn't know what to do in calculus without you. I like your voice and the way you explain lessons. many Thanks for helping the student to learn a lot.

[@boredmonke2959]

I'm on Calc 2 now but I came back here to thank you from the bottom of my heart. I almost got a perfect score on the finals because of you. I just cannot believe it to this day LOL. As I'm typing this comment, you're still saving my ass on Calc 2 with your videos. You're a legend

[@wolfxlover]

The best part about your videos, is that every time I have watched the full video, I have left completely understanding. This lets me learn in peace, knowing that everything will be fine afterwards. What's really great is that I can watch any video of any subject I haven't studied yet, and then know the mathematics for solving the problems before ever even approaching the subject at university. They're that clear.

[@bigshaqsmathematicalinstit3318]

Undergraduate math student here. When I was taking AP Calculus AB back in high school this was the hardest topic that I encountered in the whole course.

[@yazeedalhokail1011]

I will forever and ever be thankful for your existence in our world, may god bless your beautiful soul.

[@abbeytwoods]

Every time I watch my teacher's lecture videos I am so confused but then I watch your videos and it all makes sense. Corona made college impossible but now I think I can make it through online college!!

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College teacher teaches like if you already learn everything u need to learn for learning this unit. This guy teaches assuming us didn’t do to well in the previous year about the course and point out every possible problems we might have as a beginner which is so awesome!

[@comprehendnature2404]

@@Karlleagueoflegends I agree totally with you.

[@liamnicholas97]

I cannot thank you enough for your dedication to teaching. I haven't studied math formally beyond GCSE level, which in the UK ends at 16. I continued biology and chemistry at A level (aged 17-18 years). I undertook a bachelor's degree in biomedical science, then worked for a few years toying with the idea of studying medicine. I finally realised my passion lies in questions and not answers, and thus decided to embark on the journey to become a research scientist. I am now studying an MRes in Regenerative medicine and devices, which is essentially synonymous with biomaterials and tissue engineering. I realise that to become a successful scientist, I must improve my mathematical reasoning and advance my knowledge base. Through your videos, I have progressed beyond what I thought I was capable of. I study in my own way, opting for practice problems over lectures - I learn the concepts through mistakes in practice problems as data shows the yield for learning is rather high in this manner and retention of concepts can be improved. I had never studied this topic before yesterday, and now at 52 minutes into the video, I have made enough mistakes to successfully complete the inverted conical flask question without assistance relying on my own logical reasoning and employing the rules picked up from previous problems and other videos. I feel so happy to be able to apply these concepts to solve real-world problems. It's also been rather fun to go backwards after videos and learn the theory after learning to apply the rules - it seems to make sense faster and consolidate what has been learned. Honestly - thank you, mate.

[@emptiness6022]

the first few minutes of this video finally made me understand implicit differentiation. very good stuff

[@alexmartinez3683]

you know that feeling when you find this the day before the exam and you wish you found it sooner?

[@mynameislol12345]

literally me right now

[@charmlesscharacter]

Yoooo I found this 7 hours before my finals

[@SydneyMadueke]

Major final tomorrow, I'm crying bittersweet tears

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YOOOOOO LITERALLY ME right now 1 HOUR BEFORE the finals. I hate myself

[@contentwatcher111]

Faith Manalo did it help?

[@shodimutosin8271]

i remember in my last semester before i started Organic Chemistry tutor i had only 24 out of 50 and i needed a B at least in my overall score, then i began watching your videos and i had about 84 out 100 in my exams, i should have gotten about 90 and above but i made silly mistakes but i was grateful to God for your videos and intelligence and i eventually made a B, if i had watched your videos earlier i would definitely make an , from Chemistry to maths and to Physics your videos have been very helpful, in class i dont worry too much if i dont understand cos i have an excellent tutor at home, so happy to have met you on this platform. thanks

[@fet1612]

The Organic Chemistry Tutor is doing a great job. I encourage all Calculus students to watch this great assortment of work of his that he has laid out for us all.

[@bullittsandbullets1821]

Hello sir, I appreciate your videos a lot. I am a chemistry major so I have to take multiple levels of calculus and chem. Your videos have allowed me to pass calculus and ace multiple chemistry exams. I wish my professors could explain concepts as well as you do. Thank you for allowing me to be very successful in college.

[@vai570]

Can't thank you enough man. This stuff just wasn't clicking for me, but I get it pretty well now. Watched the entire video, and I'll check out some of your others as well. Great job.

[@mirnaalnahi9316]

THANK YOU SO MUCH!!! I've literally had problems understanding this my entire life just because none has explained it to me the way you did!! You made it finally feel logical and easy and it's working on all problems I'm applying this to! Thank you from the bottom of my heart!!! Gonna become a construction engineer just because I watched your videos!!!

[@laraschwartz457]

me sitting down crying before starting this video with a calc test in 5 hours not ready for it

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me rn omfg

[@lachlancroll2386]

Thank you so much! this video is so much better than my proffessors, btw at 1:18:50 I think you might have mixed up x and y. Thanks again

[@patrickong7157]

Yeah he did mix them up.

[@debbie6571]

yupp

[@JaronCarter]

I literally came to the comment section to post this same thing. Glad I wasn't going crazy. Changes the answer to 50.

[@mahmoudwahidi8873]

i was losing my mind thank you

[@ash39877]

i was just checking comment to see if anyone noticed or if im tripping lol

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Legit don’t learn anything from my teachers but one 1 hour video from this guy teaches me everything it takes a teacher to do in a week

[@annieocho2456]

You are amazing! Literally saved me from failing my exams! God bless you!

[@TheOrganicChemistryTutor]

Thanks.

[@menglu464]

Dude you are the tutor GOD this lecture is awesome practically covered everything related rates.

[@sokhuorchiv1298]

My cal final is literally tomorrow. ❤️ this video saves my life

[@iturbo5733]

I was relieved to find I am able to solve these problems in the video successfully after pausing the video when the problem is introduced. I've found that there can be several specific paths to the right answer, all of which are mathematically correct, but can cause some confusion and frustration for those starting out with this section of Calculus I. This is a section that takes a lot of practice to fully grasp and thank goodness for videos like these.

[@kateraburrows4092]

This video was definitely a life saver, didn't understand this a tap after class and rewatching the class recording, but came here and wow thank you is an understatement!

[@l.mcghee3146]

I'm literally sitting in calc ignoring my shit teacher and watching this.

[@damienfernando1553]

know those ones man

[@Jose-oy1ow]

@@damienfernando1553 fr, I'm here re learning this for finals cause my calc teacher did fuck all over this chapter.

[@DuskyHuskE]

Bro I sit in class and draw in my notebook cuz I haven’t known how to do these this whole week

[@nickoemmanuelvillacruz3090]

I guess we are all the same but my situation is my professor didnt attend 7 consecutive meetings lol

[@stevefeynman4888]

I skipped all of my calculus courses and watching this.

[@yashkhanchandani4520]

*This man taught me more about related rates in 2 hours then I could've ever imagined, thank you bro*

[@Charlie-rh8od]

Dude... thank you so much. I thought this impossible but this video made me realize it actually makes complete intuitive sense. For anyone struggling, just follow along with the first few problems and then they get real easy.

[@calibree2001]

I can fully understand this section now, just two days ago I had no idea what my instructor was explaining to us. Your videos are a total game changer, thanks!

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You're hot

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The fact that you've significantly helepd thousands of students, makes you incomparable to those who have latin honors out there. You're something special Bro.

[@ScarxxAssassin]

I didnt understand this concept even with tutoring and lectures, but I watched 7 minutes of this video and it all made sense. Thanks homie

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you saved both my chemistry and calculus! Love you !

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Am young Malawian ...your videos are so plenty and easy understandable...

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At this point I am going to have to make a special dedication to you on my degree. I have been using your videos all through calc 1 and they have really been helping. Thank you so much.

[@arudevi_]

i just had a related rates quiz today, and your video literally saved my grade!! thank you:)

[@saintanselmclassworkstuff6739]

Yet another night before an exam this guy restores my hope. Thank you for your vids; my GPA wouldn't make it without you

[@Ren-ml3tk]

I'm a UBC undergrad student studying commerce. This is saving my life. Thank you so much

[@mae7838]

Related rates were challenging for me but you made it seem simple which helped me ace my midterm😊😊

[@ChompNom]

the hardest part is finding out what you need to find and forming the functions

[@squidward9358]

Agreed

[@christianc.7084]

One thing I noticed at 1:21:00 you used the wrong variables. 90 should be multiplied by 30, and 120 by 40. This would change your final answer to be 50 mph, not 48.

[@rinoinso5221]

I also noticed this one haha. Its good to double check hehe but still thanks to the video.

[@mad-rx7wm]

I thought I was wrong when he didn't correct it, but I am still glad this guy is here, he has been a huge help

[@omarsamy1144]

same I got confused lol but he is a great teacher tbh

[@mariecool6567]

same situation, got confused but still got the overall thought

[@nathancreager1522]

agreed

[@user-sf9gs2pg1b]

You explain this SO well. I was completely confused in my classes, but this video makes so much sense.

[@ralphcesaryabut6668]

this is the longest 1hout and a half of my life but it is one of the most important 1 hour and a half to pass Calculus

[@surememilkbag5703]

After watching 10 minutes of this video, I learned more than my teacher had taught me after 6 hours of teaching!

[@hamzaalaudi1184]

Wallahi you are a calculus-life saver, I have a big Calc final tomorrow so God bless your soul dude. Thank you!!

[@Isp510]

Thank You, sir, for your help. I wish my math teacher could explain half of this in the class... As many said it already, you, indeed, are a life saver.

[@DatBallaProductions]

You really are the goat, explains it so much easier and understandable than my teacher!

[@johnlestergino8645]

In that problem about two cars travelling north and east respectively, x should be 120 and y is equal to 90. In 1:18:30, you used the rate of change of y in getting the value of x which is 30mph instead of 40mph which is the true rate of change of the x. Therefore, the final answer should be 50mph instead of 48mph.

[@arjunshah7138]

Thank you for this comment. I too got 50.

[@meronamsamho9410]

You are a life saver, the way you put helps me formulate what i need to do and then its just algebra with derivatives. This is gonna save me on my AP calc test tomorrow

[@jacksonabiusi2400]

this is probably a top 5 calculus video of all time

[@mynameislol12345]

omg thank you so much for this, i can literally pass my exam tomorrow for sure

[@saeedahamad8928]

Am taking calculus 1 and this part is the hardest one for me I don’t do well with word problems but after watching this video I can’t thank you enough thank you from the bottom of my heart

[@ahyessa2567]

This video deserves more views. Thank you so much

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best tutor on YT❤

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I love you so much Organic Chemistry Tutor

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bro you are actually the best teacher ive ever had thank you sooo much

[@jiabaozhao5920]

Thanks bro. You teaching better than my AP calculus teacher

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I honestly love you, passing calculus and i'm kinda of liking it too :))

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This is a great channel to get better understanding for math topics

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I can not believe myself, I can finally solve wordy problems. All thanks to you sir, I really appreciate the videos and the teaching.

[@aservant1284]

You are the teacher that only comes once in a generation

[@TheFarmanimalfriend]

If variables have units attached it is easier for me to do the math correctly and to know immediately if I have set up the problem as needed. This is really a good set of problems. I am seeing problems that can be solved by calculus everywhere.

[@SalahHAlsaadi]

My outlook on this topic changed after watching this clip on KZbin. I don't know if it was easy or if I understand the topic perfectly now

[@-a5624]

you are the best! Seriously carried me through grade 12 chem and now making things crystal clear in first year calc!

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This is honestly the best channel ever.

[@TheCriticalThinkerSocrates]

You are saving my brain in relation to Calculus right now, thank you!

[@jiadavid]

watching these videos really help me review a lot! I found out that reviewing online with videos, then checking if I did it right or wrong is the best way for me to learn. Thanks again

[@wallyduboss9464]

I just love this guy's teaching style. Should be a teacher.

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this is literally so easy omg, i really appreciate your way of teaching, you teach in a really simple manner. thank you so much!

[@anastasiaanautodidact9856]

I could listen to that soothing voice for hours

[@lora7938]

Thank you for saving my grade. I’m forever grateful

[@djm6683]

Thank you so much. I has been so confused over the last few days in calculus and this helps a shit ton. I'm probably going to watch the full hour and 50 min cuz of how worried I am about my test

[@ikoooy9212]

still the best prof than any actual profs

[@LoverIsaDayy]

This video is like the chocolate milk for youtube education. This helped me so much, thank you

[@elliza124]

In 1:21:38 the velocity are interchanged, should be 90x30 and 40x120. With final answer equal to 50.

[@mackx4933]

DUDE THANK YOU!! Watching this video 30 minutes before my calculus test!

[@NicaKasende]

😭but the vid is more than an hour

[@mackx4933]

@@NicaKasende 2 times speed

[@ajm7318]

You mixed up x and y around the hour and 20 minute mark! But thank you for your help your videos are so much more useful than my professors and tutors!

[@_DearDarling_]

Me in geometry rn and I understand nothing at all! But you make me understand

[@vl8891]

idk why or how but everytime he says "round 2" or "round 3" or something similar it just makes me smile, feels like we're going into a bossfight

[@aznman85]

Thank you for this lesson you made related rates so much easier for me.

[@kaeyynn]

Just learned this in class and had no fucking idea what my teacher was saying. All my classmates were like “Oh! I get it!” But I was completely dumbfounded. Thank you, really.

[@aldrineuri122]

Same

[@marthineangelfabico8646]

Reading the comments before watching the video, I trust that I can finish my homework after watching this almost 2 hour long lecture. :)

[@anthonyrodriguez6497]

How in the flying fuck does this guy make math look so easy. I barely look at my teachers lectures anymore

[@Piocoto123]

Thank you sooo much!! My uni professor is very good but with this topic in particular I had difficulty but it took only the first 12 minutes to actually get a neat understanding

[@fet1612]

Time-stamping will save many students time and energy to locate any specific problem. >>> 1. Finding dx/dt, dy/dt, and dz/dt - Pythagorean Theorem - Right Triangle Trigonometry 3:04 2. How to find the rate of change of the distance between the origin and a moving point on the graph if the y-coordinate is increasing 6:26 3. The radius of a circle is decreasing at a rate of 4cm/min. How fast are the area and circumference changing when the radius is 8cm? 11:04 4. The surface area of a snowball at a rate of 6 square feet per hour, how fast is the diameter changing when the radius is 2 ft? 16:06 5. The side length of a square increases at a rate of 3 inches per second, how fast is the area and perimeter of the square changing when the side length is 5 in? 19:42 6. A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute (cm^3/min), how fast is the radius of the balloon changing? 23:18 7. The side lengths of a cube are increasing at a rate of 5 cm/s, How fast is the surface area and volume increasing? 27:11 8. A 13-foot ladder leans against a house. The ladder slides down the wall at a rate of 3 ft/min. How fast is the ladder moving away from the base of the wall when the foot of the ladder is currently 5ft from the wall? How fast is the area of the triangle changing? How fast is the angle between the ground and ladder changing? 31:08 9. Gravel is being dumped from a conveyor belt at a rate of 100 cubic feet per min (ft^3/min) forming a conical pile whose base diameter is two times the altitude. How fast is the height changing? 46:04 10. Water is leaking out of an inverted conical tank at 500 cm^3/min. The tank has a height of 24 cm and a radius of 6cm. Find the rate at which water is being poured into the tank if the water level is rising at 15cm/min. 50:07 11. A street light is mounted on a pole 24 ft tall. A man 6ft tall walks away from the pole at a rate of 4ft/s. How fast is the tip of his shadow moving when he is 20ft from the pole? How fast is the length of his shadow changing at this instant? 58:17 12. A spotlight shines on a wall 18m away. If a 2m tall man walks toward the building at a speed of 2m/s, how fast is the length of his shadow on the building changing? 1:05:00 13. Two cars are moving starting from the same point. One travels north and the other travels east at 30mph. At what rate is the distance between them changing? 1:16:04 14. At 1:00​pm, ship B is 150 miles from ship A. Ship A is moving 30mph north and ship B is moving 20mph south. How fast is the distance changing at 3:00pm? 1:22:13 15. Airplane Problem - Travels Horizontally at an altitude of 3 miles. Radar Station Below. 1:29:24 16. Airplane Observer Problem - Rate of Change of Angle of Elevation - Angle Between Ground and Observer. 1:33:19 17. Baseball Diamond Square Problem - Speed in ft/s. At what rate is the distance between first base, home plate, and second base changing when he is halfway. 1:39:55 18. Water trough problem. 1:47:10

[@paathunax9204]

thank you

[@alexobrien7612]

you deserve the world, organic chemistry tutor

[@hazemaglan8664]

At 1:28:58, the answer is 57.735, not 27.735. Thanks for the great efforts!

[@destinyjoygesite7910]

I got 69.33 here :'))

[@destinyjoygesite7910]

Okay uhh I think his solving is correct tho. I just realized my wrongs. z^2 = x^2 + y^2 z^2 = 150^2 + (60+40)^2 Z = 50sqrt13 or 180.27

[@Cilantro3311]

This channel has saved me so many many times! Thank you thank you thank you!!

[@KINAKENVICTORMURITHIEEG]

i like the way in the middle of the lesson u remind usof some formulaes and steps lec

[@fritz4468]

Thank you so much for helping us understand calculus! I understand your simplified explanation a lot better than my prof. to be quite honest.