Mixing problems with separable differential equations (KristaKingMath)

► My Differential Equations course: www.kristaking...
Learn how to solve mixing problems using separable differential equations
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@bobbyoctaviano2661]

Just watched it again to lock it down. Your organization and fluidity in lecture is very good. If you plan to teach, good on you. Thanks again. B

[@kristakingmath]

+Bobby Octaviano I'm glad I can help through the videos!

[@bobbyoctaviano2661]

Thanks so much again. Bobby :)

[@MaxUP2]

Wow! you are a lifesaver. You and Patrick are the best. I like the way you explain without skipping steps. Thank you.

[@kristakingmath]

You're welcome, I'm happy to help!

[@cadeemmusgrove7791]

you are not only very clear, but you are beyond helpful... *nothing but praise and thanks*

[@kristakingmath]

i'm glad the videos are helping!! :D

[@chrisdesmon779]

This was by far the best explanation for how to solve a differential equation that I have ever seen. Thank you got making the video, it really was super helpful.

[@truongngo638]

I am a teacher myself and you are the only person that has structure in your explanation.

[@dv5855]

Well presented Krista. When at University a female in one of the Chemical Engineering courses was mentally very quick with correct responses - you bring to mind an earlier experience. Keep up the good work. Looking forward to additional video.

[@jasminesondhi6048]

only video on this that made sense, no one else explained the ln and then e bit, assumed i knew the formula. Thanks!

[@kristakingmath]

awesome! i'm so glad it helped!!

[@thecoolshaws]

Have struggled all semester with mixing problems and this just made it click. Life saver.

[@kristakingmath]

+Daniel Jo Nell Shaw I'm so glad it helped!

[@joyfisherback5335]

All my classmates need to see this video!!! Awesome job explaining!

[@Mr.EazyM_]

Thanks! You save lives. I like how you explain things step by step and make the problems much easier! I wish you were my professor :)

[@kristakingmath]

Mohammed Ahmed Thank you very much! I'm honored to be able to help.

[@superkooliodude20]

I can literally write a page saying thank you, but that would be too lengthy! You explained this in a simple step by step way that it made perfect sense! Now, I am able to solve any problem that has to do with this type of problem! Again, thank you soooo much!

[@kristakingmath]

So glad I can help! I really appreciate the comment! :D

[@quinny01able]

I always search for your lectures. You have a good way of teaching that makes it understandable. Also thanks to you 'Euler method' is now a bonus for me, so easy.

[@kristakingmath]

Awesome! And thank you so much, I'm honored!

[@bobbyoctaviano2661]

Thank you Miss. Your a very thorough tutor. I appreciate your time. Cheers. Bobby :)

[@moknowsnick16]

Very clear and concise. Thanks Krista

[@lisaallen4427]

Great Job Krista!! Thanks for all of your help! I tried the Bamboo with sketch! I will give it a shot this summer. Great videos. Your interactive components are where Mobile learning is at! Beautiful Mathematics!

[@kristakingmath]

+Lisa Allen Thank you so much Lisa! Good luck with the Bamboo... it takes a little getting used to, but once you get the hang of it, it works great! Enjoy... :D

[@kristakingmath]

You're so welcome! :)

[@CubanSauce]

U, u r making a damn difference! Without u I would be a frustrated as hell. Thanks for all the time u put into these videos.

[@toadzapper]

at min 1:26 you introduce variable "y" as "concentration", even though it's actually the "mass" or "amount" of salt. concentration implies you divide amount by volume. this leads to confusion with the actual true concentration that is also important in the problem.

[@gmkpremier]

Yeah, I was just about to say that. I think what she meant is that it models the amount of dissolved salt in the tank. Which would make sense

[@vanessafujikomukoko9315]

Wow! Thank you Krista you are truly a lifesaver!! I finally get it !

[@kristakingmath]

Oh good! I'm so glad the video made it finally make sense! :D

[@kristakingmath]

I'm so glad I could help! :)

[@arifhakiminadnan4880]

This video helps me to understand the mixing problem vividly. Thanks a lot for it :) . Now Im prepared!

[@kristakingmath]

Yay! I'm glad it could help!

[@robertsonjoshua87]

Just got that "Ah-ha" moment. Amazing work Krista.

[@kristakingmath]

I love that! :D

[@sulaimanalessa5002]

At 02:11 you said: "y(t) is the function that models the concentration".. Why you did not consider y(t) to be the function that models the Amount of a substance in the tank instead of considering it as the concentration function? Thankss!

[@kristakingmath]

That's what I mean when I say concentration. I'm talking about the amount of the substance we're interested in, at any given point in time.

[@kristakingmath]

Your nice comment is all I need! :D But if you feel so inclined, you could donate or join integralCALC Academy. ;)

[@akshaysood6666]

If only you were my Calculus Teacher. Thank you sooo much for this.

[@kristakingmath]

you're welcome! i'm glad it helped! :D

[@amerajama4006]

YOU SAVED MY LIFE TODAT THANK YOU SO MUCH !

[@ThePinoyMamba]

Love this problems! Thanks Krista

[@MiamiGeneralContractor]

Thanks so much, I have my 2nd test on monday of MAP 2032 and this mixture problems is one of the topic, you did a great job!!!!!!! thanks so much!!

[@kristakingmath]

Glad you liked it! :)

[@moinaction]

You're are a life saver. What I spent hours trying to understand in the text book, you made it easy in less than 11 minutes. More grease to your elbow. Thanks a bunch. How can one donate to you so you can be able to continue raising funds for your material and supplies?

[@kristakingmath]

Aww thanks! I'm so glad I could help. If you really wanted to donate, you could always join my Academy here ;) integralcalc.com That definitely helps!

[@Postcalculus]

Khan and Krista are good enough. Vi Hart, who teaches at Khan Academy could be the third person who could join the team. Really nifty in the way they use the mouse instead of the pen, along with a transcript that runs at the bottom and there is no need for anyone else. They have no arrogance, but all the wisdom of a teacher. Whenever I have faced a problem I have found a solution from them, and Krista has been humble enough to take feedback, while answering each doubt. Few teachers do that.

[@jimcar53]

By a long way the best explanation. I finally get it. Thanks.

[@tresteinjordklatt8133]

When you have *e^ln(input)* the *e^ln* doesn't become 1, because 1^input is always 1. Since *e^(input)* and *ln(input)* are inverse functions when you have *e^(ln(input))* the *e^ln* cancles and you get *input* Comment to what was said on 4:46, its a very good video explaining this :)

[@kaziabir1]

Sometimes I use your videos as lullaby for myself...

[@tonAlts]

Thank you!!! I have exam on this later and you are a really great help. Thank you! :)

[@kristakingmath]

You're welcome, good luck on your exam!

[@SpacePunk1000]

excellent video with thorough explanation! subscribed! thanks!

[@kristakingmath]

:D

[@trucvynguyen4269]

that is awesome video that really helps me out, so thank you very much. i just have a question at 9:00 that you are talking about getting off +/- when you solve for absolute value. i mean why do we only take a positive value and not considering the negative one?. i appreciate your help. :)

[@lonewolf1175]

Is there any way we could see a problem with the volume in the tank being a variable? That would be awesome... Regardless, your videos are awesome! Much appreciated!

[@peterh.1521]

Excellent video on a classic DE-problem. Even a kid can follow. :) I wish I did have pedagogical teachers like you in the courses on math, it would be much more educational. As it often is (for many I presume) is that the teacher have difficulties to explain in a way so the students can understand. The elementary mistake I think many teachers do is to believe that many students automatically understand this and that...and so on, but the student often don't do that, so the teachers assume wrong and the possibilities to follow is therefore interrupted (and no, not all is asking because they think they are the only ones who do not understand). You avoid this elementary mistake very much Krista, and therefore many likes your videos. :) Keep it up! /Pete

[@kristakingmath]

+peter hansi Thank you so much, Pete, I'm glad you like my style!

[@josephalbertrubante2208]

wow, I finally found the perfect video for my problem>> Thank you very much for the thorough teaching.. :) ++Hoping there's also a video for Escape velocity problems but thanks anyway.

[@liamrobinson6226]

Great video, but do you know how this might change if your in flow rate is less than your out flow rate?

[@mcgarettsteve9077]

really really amazing...i was busting my brain trying to solve questions like this...thank very much...:)

[@XX-sf1eh]

Awesome. Thanks a lot for your videos 😀

[@keremoflu]

Hi, i can understand your videos very well even i'm intermediate level in english. thanks for your labor.good luck:)

[@charlesrivet3246]

How should I proceed when it's about mixing gases and percentage instead of masses in kg?

[@zJeffreyz]

Extremely helpfully

[@ForceTranq]

Thanks for a great explanation... you're good.

[@baivabjena1438]

This was so helpful revising for my mid terms. Thanks a ton.

[@kristakingmath]

You're welcome, I'm so glad it helped! Good luck on your midterms, I hope they go great! :D

[@baivabjena1438]

Thanks. :D

[@dannyrodriguez5338]

What would happen if the initial conditions of the tank were fresh water? Wouldn’t C go to zero making the whole equation zero? That doesn’t make physical sense to me.

[@curtisslasserre921]

Once again, thank you!

[@kristakingmath]

Ha...Sorry about that situation, but I'm glad I could help! :)

[@OAKZD1]

when dealing with mixing problems do we always deal with separable equations

[@solariaeuropa3669]

Thankyou Kristaaaaaaaaaaa!

[@kristakingmath]

:D

[@MrGuardianAngel11]

Mathematics has never looked prettier.

[@alangiovaniromay5115]

Great lecture. Thanks

[@kristakingmath]

Glad you liked it, Alan!

[@kristakingmath]

you're welcome! i like them too!! :)

[@kristakingmath]

right back at ya!! :)

[@kritinvij]

Which software are you using? And, are you using a touch screen?

[@kristakingmath]

yep! :)

[@robinankartoft759]

Hi Why are you not devideing rate in with 1000 L?, I got wrong answer on a test and the teacher said that I needed to divide the concentration in which was 1 g/L with 500 L in my case

[@computer3990]

uhm.. well rate in is usually given so you dont have to divide it in V.

[@TheDrob81]

Do you have 9.1 modeling with differential equations

[@PLP0321]

Always helpful!

[@kristakingmath]

:D

[@grandorottcod1]

Hi, I got a little confused with this problem. Part 1: Mixing Problems with Differential Equations I am just wondering why he is not considering the concentration of the rate out as A/100GAL

[@grandorottcod1]

Hi I think I got it the reason is because in your problem the rate coming in and coming out is the same so dv/dt=0 The volume is always in your case 1000 L of solution. In this problem the volume changes.

[@kristakingmath]

That's awesome! :)

[@gur0004]

Hi isn't supposed to be ln15?

[@midyan11]

How can I pay you for this amazing work?

[@kristakingmath]

it's not a touch screen... this is how i make my videos: integralcalc(dot)com/how-i-create-my-videos/

[@aviattri_9]

i liked the video at first then after t min again unliked it and liked it again. tq soo much for this

[@delonthompson9631]

love this video

[@kristakingmath]

:D

[@khairulazwari3348]

Hi, what's software did you use?

[@kristakingmath]

I explain here :) www.kristakingmath.com/blog/how-i-create-my-videos

[@Wolfstar26]

i don't mean to start beef or anything but you're honestly a better teacher than patrickjmt (although patrick is still wonderful of course). your organization and explanations are perfect.

[@kristakingmath]

I'm so glad you like my style of teaching! Patrick is amazing, and I'm honestly glad that he's an option for people on KZbin. :)

[@mikechowmanho]

Good ! Nice video. Better than my Maths professor lol

[@kristakingmath]

+mikechowmanho Glad I could help!

[@kristakingmath]

yes! like the x-men, or the power rangers, or the a-team, but geekier! :)

[@CubanSauce]

If you only had let's say 500 gals full out of 1000, would y(t) be over 1000 still? Or would it be over 500?

[@danielolivera2618]

omg ur good thank u so much i have a test tomorrow. please speak louder!! :)

[@joesit]

turn ur fucking volume up

[@danielolivera2618]

yes thats what i really ment to say

[@narcssius]

Yesssss

[@ahrims221]

I love you

[@ahsan3691]

You and Patrick JMT have the same problem. However, you two have different solutions. He got C= ln(15) while you have C= 15. Who's right? Edit: Nevermind, you two have the same final answer. Just go about it a different way. Thank you.

[@adilsaleem3756]

patrickjmt and you should get married to produce good math teachers

[@brakatsuuu00]

and their kids will no longer need to go to school except in exams

[@AhmedAlbadwi]

You and a PatrikJMT has the same problem to be solved !!!1