How to solve related rates problems! (cars approaching, water into a tank etc) Calculus 1 tutorial

[@blackpenredpen]

Here are the Time Stamps! (Q1) 0:04 circular metal plate (Q2) 5:57 water in a circular tank (Q3) 16:02 the ladder falling down (Q4) 24:21 two cars approaching to the same intersection (Q5) 32:38 two ships, one ship travels north the other travels south (Q6) 42:13 two sides of a triangles are changing (Q7.) 50:08 balloon rising up and angle of inclination If you like this video, be sure to subscribe for more math related content. Also help me to share this video with your calc classmates and teachers, thank you!

[@clashroyalepro9082]

Can you explain this sir please why the integration of sin6x is -cos6x/6 ? With proof .....

[@tomjohn3644]

When will the shirt in your profile pic be available to buy as merchandise?

[@aashsyed1277]

thank you so much! =D

[@JB1RD367]

Fantastic! I'm actually teaching this topic in two days and I'm going to use your method of explanation to help. The two pictures is a great idea.

[@blackpenredpen]

Johnathan Tafoya nice!! Let me know how it goes!

[@alinamoreno9235]

THANK YOU KING! you're saving both my grades and my sanity this semester

[@blackpenredpen]

Glad to hear 😃

[@tiredpoe5540]

Same I started to fall behind. Hopefully this would make me be ahead.

[@alissa7760]

You are a life saver 😭😭😭😭 and thanks for explaining every single step so well. It’s the video I’ve been looking for for hours and hours today..... finally found the video I was looking for 😭❤️ Love it!!! Please keep up the good work!

[@THotSouce]

You're ridiculously helpful man, thanks for this amazing content and your effort

[@rkumaresh]

With 7 different problems one can do any problem on related rates. All are great explanations . The ball problem could be done alternatively by differentiating the equation tan(theta)=h/500 w.r.to t where we should determine sec^2(theta) using the given information and then substituting into the derivative equation i.e sec^2(theta) times d(theta)/dt = (1/500) times dh/dt.

[@zynex9250]

This is a REALLY well made video

[@JamalAhmadMalik]

Thanks, at any rate!

[@blackpenredpen]

lol

[@xcalibur6482]

My math exam was good... but im not sure about a six mark problem... doesnt matter... exam or not... i will solve it... i will learn it... maths is about learning from mistakes 😊😊😊

[@rofl.connoisseur]

thats the spirit

[@rob876]

I prefer to derive the equations first and only plug the numbers in last of all. There's less chance of an arithmetical mistake that way. e.g. for the ships problem, I would get dC/dt = f(t) and then compute f(4).

[@satyam-jha]

I first tried to solve the following problems by my own then after looking at the solutions and YAY I succeeded in 6/7. Amazing content keep it up...😀😀😀

[@blackpenredpen]

Satyam Jha yay thank you!!

[@satyam-jha]

@@blackpenredpen just keep it up.. Proud member of calculus finisher.:p

[@johnabraham8520]

Satyam Jha which one you got wrong ?

[@drpeyam]

Neat! It’s almost as if this video and the 100 integrals video are... related 😉

[@blackpenredpen]

Dr Peyam Hahahhaha

[@belutcodm2850]

I find your videos to be really helpful so I'm here to leave my comment

[@LS-Moto]

I can't catch up with all these videos 😂 .... good luck to everyone writing calculus 💪

[@comprehendnature2404]

I think I understand it now. First, you find a geometric formula that apply to the problem, then convert it to a derivates problem, derivate it and make sure that you isolate the one you want to find. Its easy now that I understand it. I will work on more problems to make sure I get it right.

[@unknownme5930]

Please do more worksheet videos like this !! Its really helpful,thank you so much :))

[@NasirKhan-lq5jl]

I love the content!!! Can you please do some videos on Complex Analysis by any chance...

[@quixiee_]

Finally, things are making sense.. thank you 😊😊

[@ΆγγελοςΔημόπουλος-φ2δ]

Greek school books use this problems at the rate of change chapter.

[@epicfacelover]

Thank you for the help, literally all of these were on my homework!

[@con_el_maestro3544]

Sir, I got every single one of those questions wrong except for question 7, I think I get it now... There are no words to describe how grateful I am except to say THANK YOU ❤🔥

[@HorizonSpeed26]

on q5 I used the limit definition of the derivative lol. I think I might be a bit too ahead of myself with this stuff.

[@kauze8063]

ooooo. Related rates😉 my favorite

[@owenscinta1032]

so concise did better than a uni professor I pay 70k a year to be in his class.

[@alejrandom6592]

I can't believe I actually solved the first problem, I haven´t seen these before lol. I used integration to figure out that r(t)=0.02t plugged it into A=pi*(r(t))^2, so I got A=pi*0.0004t^2, then I set 60=0.02t to solve for t=3000 differentiating A I got dA/dt=pi*0.0008t, plugged in t=3000 into this derivative and got 2.4*pi :D

[@michaeldengg]

oh you shouldn't really use what t=, its much easier to solve it using just normal differentiation

[@gloriaa5857]

This video what so easy to follow, Thankyou!!

[@blackpenredpen]

Glad it was helpful!

[@alexgutierrez4547]

Thank you so much!! Helped so much

[@scrumptious1227]

I have a question on 30:28 about that sketch

[@diagasokhna5777]

car A and B( can you please check it again)!!! I f the car is heading north which means it's increasing, right? my final answer is 18mph.

[@blackpenredpen]

No, because they are heading toward the same intersection.

[@MusicalInquisit]

For question six, the units for the derivative of area with respect to time is not simply meters-squared per second. Because the derivative of area includes rad/s as a multiple, the unit for the change in area is in actuality (meters per second)-squared times radians

[@minlehya1163]

THANK YOU, YOU ARE THE BEST

[@multipleorganfailure3449]

Helpful for sure. Great video. Thank you.

[@fiona685]

Thank you so much for the amazing explanation! Simple and super clear!

[@mohittiwari8934]

Your favourite ? 1. Mathematics ? 2. Physics ? 3. Chemistry ?

[@blackpenredpen]

Math, easy!

[@forthesakeofscience961]

Physics

[@TheNachoesuncapo]

Meth

[@michaelhunt2222]

Mohit Tiwari maths

[@lalitverma5818]

Math

[@GeletomWAbebe]

From the 7 examples one or two of them will appear on our national exam (g-12) and i want to say thank u for your dedication

[@SarahStarmer]

Thanks this is very helpful.

[@slyanover]

Thanks, great explanation, especially the two diagrams.

[@Anna-qp1fi]

Thank you so much!

[@HeYoNiA]

Saved my skin! I didn't know what to do until I found this video, thanks man!

[@andrewbooths7099]

Very helpful. Thank you. Keep it up.

[@asiaakperov6479]

For question 6: how did you simplify the last bit --> 20cos(pi/3)(.06) become .6

[@ajanar]

1.199 in my calculator

[@samiadam3632]

20×.5×.6=6 COS 60=.5

[@einavrubin6353]

Thank you so much!!!!!!!!!

[@williamwelmans8648]

Thank you!

[@Jay-fo8tf]

Why do you use the chain rule in the first problem? It’s not a composite function to my understanding

[@newtonnewtonnewton1587]

Nice i am amath teacher its an easy quistion in our school here in jordan there is many quistion more difficult than this quistion

[@portreemathstutor]

Thank you.

[@ahmad_hun]

Sir are you using calculus and analytical geometry by Thomas ?? And I can't find play list can somebody help me ?

[@thrivikramsasapu2253]

i know its a bit late but generally when we think of a ladder and the bottom part is moving with a certain rate then the top part should also move at the same rate right ,if not can you explain what makes it move at different rate when compared to the bottom part...

[@michaeldengg]

I got every question right but Q2, Q5 and Q7... Thanks for the help though I sorta struggling on this subject...

[@gihanshamindadoowage7766]

Thanks this is very help full

[@gaurangagarwal3243]

21:02 oh I knew it atleast. 😁Just kidding. Btw awesome viddeo

[@catherinehill8198]

Thank you

[@science-y9209]

How did you randomly assume that it would be 12 oclock and not 11 or 1 oclock ... how can you be so sure.. please tell me.. (Q5)

[@Skankhunt-mv4vd]

This might be a stupid request, but heck it! I recently noticed that there is a very high chance that you get a pair of any two numbers (not taking the suit into account) in a deck of cards i.e. 2 and 2, queen and queen, 10 and 10 and so on.. I was trying to calculate an actual probability for this phenomenon and really struggled. I would appreciate it if you did a video over this problem, or if it seems really simple for your audience, a general probability video would be greatly appreciated. Thanks!

[@blackpenredpen]

Skankhunt 42 how many cards are we choosing?

[@Skankhunt-mv4vd]

blackpenredpen not choosing any number of cards. When u shuffle the deck, it is almost guaranteed that you will get a pair of cards that are the same when you go through the whole deck. all the 52 different cards.

[@soumikpal8910]

Sir can you please explain when 1^m=1^n (m is not equal to n) then it seems like m=n and we can prove every real number is equal to another real number . Btw love your vids 😇

[@NasirKhan-lq5jl]

Essentially what you did is took logarithm both the side to base 1. But it's actually not like that as logarithm base b is as 0 or 1 not =b. Or else you there would be troublesome situations like you have encountered.

[@typo691]

In order to get from 1^m=1^n to m=n, you would need to take log base 1 but because of the very problem you pointed out, log to base 1 is undefined

[@hamiltonianpathondodecahed5236]

@@typo691 u can also take log any base but it will end up log some base of 1 which is zero.

[@danielmacsai776]

One to any power is one

[@hamiltonianpathondodecahed5236]

@@danielmacsai776 what about 1^inf

[@gustavosedano294]

Very usefull before an exam

[@lalitverma5818]

Wow u r great teacher

[@namenlos4198]

Is it assumed in Q2 that the inverted cone is regular so that the apex lays in the middle of the base circle?

[@namenlos4198]

Or can we use Cavalieri's Principle to simplify the question?

[@gordonchan4801]

There is a slight error in the PDF document. The unit for question 7 should be "rad/s" instead of "ft/s".

[@johnnolen8338]

My geometric intuition stinks. For the two ships problem, I more likely than not wouldn't have figured out the ships' bearings relative to each other formed an increasingly large right triangle if I had not seen you work this problem a couple of dozen times. Therefore I decided to work it using vector algebra. Each ship has a position vector that explicitly depends on time. As such the difference in their positions is also a time dependent vector. The position of B relative to A is given by: R = 100 *i* + 60t *j* . The magnitude of R, the distance between the two ships, is given by |R| = sqrt[ 100^2 + (60t)^2 ]. Differentiating with respect to time gives the expression d|R|/dt = 3600t/sqrt[100^2 + (60t)^2 ]. Substituting t = 4 into this expression gives d|R|/dt = 14400/260 = 55.385 kilometers per hour. ◼

[@jammonmd]

Regarding Q2: Am I the only one who thought an inverted cone would have the large part on bottom? That would change the answer. Love your videos!

[@jammonmd]

In that case, I got dh/dt = 24/(13 pi)

[@babs8233]

I though the same thing! drew it like that too....

[@natejones8508]

ice cream cone is inverted, traffic road cone is regular LOL

[@jammonmd]

@@natejones8508 ice cream upper nappe; traffic lower nappe

[@jadensmith2191]

Why can't I use radius in question two?

[@alissa7760]

Can you please do the shadow related questions to please

[@otioti264]

Where can I find those pen?

[@Sidou_]

Please Can you show US the integral of sqrt(x)*cos(x)

[@jasonloftis9563]

Respectfully, I believe the answer to the ships problem is incorrect. I followed every step several times, down to the "use your calculator" part, and I get 73.8. Incidentally, I found another video involving the exact same question with the only difference being the ships' speeds, A being 35 and B being 25, and that video's solution is the one you presented. Did you alter the ships' speeds but forget to adjust the solution?

[@chikenwingsteve]

Nope. The correct answer is 55.4

[@cyan1153]

For question 2, is height measured in m^3/min or m/min? This question has been bugging me for a few days now.

[@raexn]

Height is one dimension. Therefore, m/min.

[@rik9833]

when you took the derative of the whole equation with respect to t at 3:35, why couldn't we take the derative of pie, which would be 0 because derivative of constant is always 0

[@waldo719]

Constants only turn into 0 when it doesn’t have a variable with it. You can also just imagine the constant beside a variable with zero exponent. [for example: (d/dx)3 is just the same as (d/dx)3x^0 since anything with zero exponent is just 1. Taking its derivative will just bring the zero down which is why we cancel constants when differentiating.]

[@forthesakeofscience961]

Hey hi answer this Can u pls do a differentiation under integral sign video plzz

[@JensenPlaysMC]

kzbin.info/www/bejne/aHu3qp5reKepm6s and kzbin.info/www/bejne/qWLdmYx6ad1po7s

[@saharhaimyaccov4977]

Can u show graph with I number ..?

[@aldricbenalan4755]

CHEN LU!!!!!!

[@neilgerace355]

4:07 What is this "chain rule"? ;)

[@ΧρυσοβαλαντηςΤασιοπουλος]

dA/dt is actually speed , velocity when you apply Pythagorean theorem you referred to distances and not velocity!!!!

[@joshuaargote3231]

Where do you even get these questions?

[@preciousjumuad2958]

I rushed answering coz I wanted to hear Doraemon theme song intro every cut XD

[@iCosmicRex]

shouldn't the answer at the end be 14/50?? or 7/25 if you simplify it. you have 140/500 so i think there is a slight error. amazing helpful nonetheless!

[@chikenwingsteve]

No. You are wrong. 1+1 = 2 2 x 500 = 1000 140/1000 = 7/50, not 7/25. Your welcome

[@ssdd9911]

i thought do be4 already?

[@clunkymonkey1403]

people in the us are taking this in college while I am taking this in 10th grade.......FUCK

[@n-clue2871]

pov: youre in elementary but you get a question right

[@ricktomev155]

Black pen blue pen

[@Wacko773]

Can I get your email?

[@HoSza1]

The ladder example is suspicious because the ladder will detach the wall at some point.

[@marcushendriksen8415]

Wow, you're really making me think about this. Common sense agrees with you that the ladder would detach from the wall at some point, but I'm not so sure. For the ladder to not touch the wall, the overall distance between x and y would have to increase, and I'm pretty sure that calls for an acceleration. The problem mentions a constant d/dt for x and y though, so no acceleration to be had there. I think in the real world, you're actually right, because such a ladder would have at least one acceleration acting on it. This is just one of those examples in which maths doesn't line up with reality.

[@marcushendriksen8415]

Now I think about it, this would be fun to point out in your answer in an actual exam, and to take it even further by assuming a frictionless and a uniform acceleration in the -y direction (of 9.8 m/s^2, of course)

[@marcushendriksen8415]

Hold on hold on hold on. After some actual hand-waving (in place of drawing diagrams, you see), I realized that even with an acceleration present, the ladder still shouldn't detach from the wall, at least, not until after y=0 (the ladder hits the ground.) I'm not able to explain why right now, because I don't fully know myself, but watch this space. Later - tomorrow, probably - I'll have worked it out and come back to show it.

[@assbeater5642]

I LOVE U

[@gaurangagarwal3243]

Who remember. Me ek udta sapna hoo jo aaj ban chuka hoo sach. Ab ye mera sapna hai ki sabke sapne sach me karu. Dora-e-mon.😂😂

[@maxhenderson1890]

I don’t like how in the question involving ships, it expects you to interpret that noon is “12:00”, when in fact, midday is 12.00

[@samilismaylov8585]

Thank you