This calculus video tutorial explains how to solve related rates problems using derivatives. It shows you how to calculate the rate of change with respect to radius, height, surface area, or volume of a sphere, circle, cone, etc. This video contains plenty of examples and practice problems such as the inverted conical tank problem, the ladder angle problem, similar triangle shadow problem, problems with circles, spheres, cubes, cones, squares, and triangles and so forth.
Here is a list of problems.
1. Finding dx/dt, dy/dt and dz/dt - Pythagorean Theorem - Right Triangle Trigonometry
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
3. The radius of a circle is decreasing at a rate of 4cm/min. How fast is the area and circumference changing when the radius is 8cm?
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?
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 ?
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?
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?
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?
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?
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.
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?
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?
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?
14. At 1:00pm, 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.
15. Airplane Problem - Travels Horizontally at an altitude of 3 miles. Radar Station Below.
16. Airplane Observer Problem - Rate of Change of Angle of Elevation - Angle Between Ground and Observer
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
18. Water trough problem

Views: 178160
The Organic Chemistry Tutor

This calculus video tutorial explains how to solve the shadow problem in related rates. A 6ft man walks away from a street light that is 21 feet above the ground at a rate of 3ft/s. At what rate is the length of the shadow changing? At what rate is the tip of the shadow moving? You need to understand similar triangles and how to set up proportions in addition to knowing implicit differentiation and derivatives.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
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Views: 46394
The Organic Chemistry Tutor

Before you start solving you should:
___________________________________
1) READ the questions once, even twice.
2) UNDERSTAND what you need to find
3) WRITE what you are given + the equations for simple shapes
** Now you can start using the first step in the time stamp to jump ahead and see if you got the same answer as we did. If not you should watch the video from the beginning and NOT jump ahead**
TimeStamp !
1:34 - Solution begins. Press here only after you did the first 3 steps
3:37 - Second step. Find the "Volume of a Cone" - (Solution 5:13)
5:40 - Third step - Take the derivative of the volume with respect to time - (Solution 7:22)
7:35 - Fourth step - Find the rate at which the water level is rising by plugging "h" - (Solution 8:20)
---------------------------------------------------------------------------------------------------------------
Now try to solve it on your OWN! Don't just "understand"... PRACTICE!!
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Views: 13178
AF Math & Engineering

This is a video tutorial about the concept and application of time rates.
Created by: Maquilan, Michael Joseph R., Ortiz, Meggy C., Gonzales, Venice Ariele V., & Cando, Philip P.
BSCS-CS 2-2
*Enjoy watching!!!

Views: 18322
DIFF CAL BSCS-CS 2-2

Ang differential calculus na lesson na ito ay nagpapakita kung paano sumagot ng mga related rates problem ng sphere, cones, and ladder problem. Sa pag solve ng related rates problems, ginagamitan ito ng implicit differentiation with respect to time: d/dt
00:32 1. A = π r^2
03:02 2. A = 2πrh
08:27 3. Spherical Balloon
13:59 4. Cone-Shaped Paper Cups
21:09 5. Sliding Ladder Problem
For more videos, visit: www.numberbender.com

Views: 5455
Numberbender

Finding the rate of change of an angle that a falling ladder forms with the ground.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates-intro/e/analyzing-related-rates-problems-equations?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/v/rate-of-change-of-distance-between-approaching-cars?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates-intro/v/analyzing-related-rates-problems-equations?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
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Views: 19669
Khan Academy

This calculus video tutorial explains how to solve related rate problems with airplanes. The first problem asks you to determine how fast the distance between the airplane and the radar station is changing given the altitude and the horizontal speed of the plane. The situation of the second problem is two planes traveling toward each other intersecting at a common convergence point. This problem asks you to determine the rate at which the distance between the two planes is changing given the speed of each plane and the distance from the convergence point in miles.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
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Views: 8941
The Organic Chemistry Tutor

What's going on everybody, I am back with another practice word problem. This one deals with Distance, Rate, and Time. One key thing to remember with problems dealing with these things it to know the formula D=Rt, where D is the distance traveled, R is the rate or speed, and t is the Time. Remember, you MUST keep the units the same. For example, if Time is in hours, and speed is in Miles per hour, then D has to be in Miles. You may need to convert as well, for example, from minutes to hours and so on. I hope these videos are helpful and valuable to you, if so, click the like button and subscribe.
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Views: 16151
Jay Lawson

This calculus video tutorial explains how to solve problems on related rates such as the gravel being dumped onto a conical pile or water flowing into a conical tank. You need to know the formula for the volume of a cone and you need to know how to employ implicit differentiation to solve these related rates problems.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
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Views: 16924
The Organic Chemistry Tutor

What's the relationship between how fast a circle's radius changes, and how fast its area changes? Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates-intro/v/analyzing-related-rates-problems-expressions?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-applied-rate-of-change/v/derivative-and-marginal-cost?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
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Views: 384382
Khan Academy

This calculus video tutorial provides a basic introduction into related rates. It explains how to use implicit differentiation to find dy/dt and dx/dt. It contains a few examples and practice problems on derivatives and related rates.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
Access to Premium Videos:
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Views: 53743
The Organic Chemistry Tutor

This video explains how to determine the rate of change of the distance between two ships moving in different directions.
Site: http://mathispower4u.com

Views: 27124
Mathispower4u

Now that we understand differentiation, it's time to learn about all the amazing things we can do with it! First up is related rates. Sometimes the rates at which two parameters change are related to one another by some equation. With our newfound understanding of implicit differentiation, it's not too hard to find this precise relationship so that we can do important scientific calculations. Check it out!
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Views: 54639
Professor Dave Explains

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Linear Equation , Word Problem #7 : Work, Rates, Time To Complete a Task.
Here we are given that a person can complete a task alone in 32 hours and with another person they can finish the task in 19 hours. We want to know how long it would take the second person working alone.

Views: 25570
patrickJMT

A problem on how to determine the rate of a reaction given a) the balanced chemical equation, b) the change in concentration for ANY reactant or product, and c) the time interval during which the concentration changes.

Views: 68183
Ben's Chem Videos

In this video we solve a related rates problem about a trapezoidal trough - the cross-sections are isosceles trapezoids. This is one of the harder related rates problems but it's not so bad if you cut up the trapezoid a little bit. This is a challenging AP Calculus or Calc 1 problem.

Views: 1937
turksvids

You're on a ladder. The bottom of the ladder starts slipping away from the wall. Amidst your fright, you realize this would make a great related rates problem... Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/e/related-rates-pythagorean-theorem?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/v/related-rates-of-water-pouring-into-cone?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/v/rate-of-change-of-distance-between-approaching-cars?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 498446
Khan Academy

This calculus video tutorial explains how to solve the ladder problem in related rates. It explains how to find the rate at which the top of the ladder is sliding down the building and how to find the rate at which the area formed by the ladder is changing. In addition, it explains how to determine the rate at which the angle formed by the ground and the ladder is changing with respect to time using derivatives and implicit differentiation. This video contains one example problem with many parts.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
Access to Premium Videos:
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Views: 40217
The Organic Chemistry Tutor

Ang calculus lesson na ito ay nagpapakita kung paano magsolve ng related rates problem sa involving area of a circle and volume of a sphere.

Views: 1923
Numberbender

This calculus video tutorial explains how to solve related rate problems dealing with the area of a triangle. The first problem asks you to find the rate at which the area of a right triangle is changing. You need to use the product rule using the rates at which the base and height of the right triangle are changing. The second problem asks you to find the rate at which the area of a triangle is changing using the area formula with sines. You need to familiar with the derivatives of trigonometric functions such as sine and cosine. This video contains plenty of examples and practice problems.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
Access to Premium Videos:
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Views: 6027
The Organic Chemistry Tutor

Hello everyone, and math students! This is my very first animated math video and I hope it helps out visually. And welcome to my channel.
This uniform motion (problem 1) involves traveling in the same direction, solving for "how long" one moving object traveling until it meets up with the second moving object. This problem is also called "distance rate time problem" or "uniform rate problem."
[Thank you for watching, and please subscribe, it will mean a great support to me and this channel.]
RECAP: This is an algebra problem. It's a "distance" word problem, and solving for "how long." It uses d=rt (distance equals rate times time).
The actual problem from the video:
"Car 1 starts from point A and heads for point B at 60 mph. Fifteen minutes later, car 2 leaves the same point A and heads for point B at 75 mph. How long before car 2 overtakes car 1?"
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Views: 135999
tossinthetube

This calculus video tutorial explains how to solve the distance problem within the related rates section of your ap calculus textbook on application of derivatives. This video explains how to find the rate at which the distance between a moving point on a curve and the origin changes with respect to time. The second problem asks you to determine the rate at which the distance of two cars is changing if one car travels east and the other travels north. The third problem asks you to determine how fast the distance between two ships is changing if ship A travels south and if ship B travels north. You need to be familiar with the pythagorean theorem and implicit differentiation. This video on related rates contain many examples and practice problems.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
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Views: 7009
The Organic Chemistry Tutor

The Chain Rule is a powerful tool in solving time rates problems if coupled with a calculator that is capable of differentiation.
Related Links:
https://www.mathalino.com/node/965
https://youtu.be/mn6Stc7JUcU
Background music: Finding Me by Eveningland available as royalty free music in YouTube Audio Library.

Views: 2961
MATHalino

As you pour water into a cone, how does the rate of change of the depth of the water relate to the rate of change in volume. Created by Sal Khan.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/e/related-rates-advanced?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/v/speed-of-shadow-of-diving-bird?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-derivatives/ab-related-rates/v/falling-ladder-related-rates?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 633143
Khan Academy

This calculus video tutorial on application of derivatives explains how to solve the angle of elevation problem in related rates. It discusses how to determine the rate at which the angle of elevation changes given the altitude of the airplane and the horizontal speed at which it travels in miles per hour. You need to know implicit differentiation, right triangle trigonometry, 30 60 90 reference triangles, derivatives - power rule, and that's about it.
Calculus Video Playlist:
https://www.youtube.com/watch?v=1xATmTI-YY8&t=25s&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv&index=1
Access to Premium Videos:
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Views: 10161
The Organic Chemistry Tutor

This lesson shows how to use implicit differentiation with respect to time in cones, ladder, sphere, and circle problems.
00:36 1. A = π r^2
02:57 2. A = 2πrh
07:47 3. Spherical Balloon
11:37 4. Cone-Shaped Paper Cups
18:44 5. Sliding Ladder Problem
For more videos, visit: www.numberbender.com
AP Calculus AB and BC

Views: 785
Numberbender

This video provides a basic example of a related rates problem involving the rate of change of revenue.
Site: http://mathispower4u.com

Views: 13429
Mathispower4u

🌎 Brought to you by: https://Biology-Forums.com
🤔 Still stuck in math? Visit https://Biology-Forums.com/index.php?board=33.0 to start asking questions.
In related rate problems, there are two quantities changing with time. The rate of change of one of the quantities is given, and the other must be found.
A procedure that can be followed is:
a. Locate the given rate. Since it is a rate, it can be expressed as a derivative with respect to time.
b. Determine the unknown rate. Express it also as a derivative with respect to time.
c. Find an equation linking the variable in the given rate with that in the unknown rate. If there are other variables in the equation, they must be eliminated by means of other relationships.
d. Take the derivative of the equation with respect to time.
e. Substitute the given values and solve for the unknown rate.
Source: Technical Mathematics with Calculus, 3e. Calter & Calter.
Q. A 20.0-ft. ladder leans against a building. The foot of the ladder is pulled away from the building at a rate of 2.00 〖ft.〗∕〖s.〗 How fast is the top of the ladder falling when its foot is 10.0 ft. from the building?

Views: 18
Study Force

Using the formula for finding distance we can determine Usian Bolt's average speed, or rate, when he broke the world record in 2009 in the 100m. Watch.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/rates_tutorial/e/rate_problems_0.5?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/rates_tutorial/v/finding-unit-rates?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/ratios_and_proportions/v/solving-ratio-problems-with-tables-exercise-3?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
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Views: 320475
Khan Academy

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Buy my book!: '1001 Calculus Problems for Dummies' - you can get it on my website: http://patrickjmt.com/
Related Rates Problem Using Implicit Differentiation - For more free math videos, visit http://PatrickJMT.com
Happy studies!

Views: 516103
patrickJMT

Visit http://ilectureonline.com for more math and science lectures!
I will calculated the dy/dt=? of aater runner out of a funnel, r=3ft, at the moment of the water level of h=4ft and DV/dt=-0.1ft^3/s.
Next video in this series can be seen at:
https://youtu.be/9iNjYU0VYQ0

Views: 6022
Michel van Biezen

This video provides an example of how to determine the rate of change of profit with respect to time.
Complete Video Library at www.mathispower4u.com

Views: 10503
Mathispower4u

Sometimes you'll need to solve for multiple parts of the equation before getting at the answer. Here we solve for average speed, but first we have to determine total distance and total time.
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/rates_tutorial/e/rate_problems_2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/unit_conversion/v/converting-pounds-to-ounces?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/rates_tutorial/v/finding-unit-prices?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra
Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Subscribe to KhanAcademy’s Pre-Algebra channel:: https://www.youtube.com/channel/UCIMlYkATtXOFswVoCZN7nAA?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 479030
Khan Academy

#draw2picturesforrelatedrates
related rates: volume of a spherical ballon,
rate of change of the radius of a spherical ballon,
selected hw solution: http://www.blackpenredpen.com/math/Calculus.html,
follow me: https://twitter.com/blackpenredpen,
blackpenredpen
straightforward math lessons
tags: u sub, u substitution examples, integration techniques, what is u sub, how to use u sub, integral calculus, calculus 1 integral problems, calculus 2 integral problems, calculus with blackpenredpen, integration by parts examples, integration with trig sub, integration with partial fractions, hard integral problems, understand integrations, related rates: volume of a spherical ballon

Views: 6618
blackpenredpen

The following video goes through a related rates problem involving water being pumped into a cylinder.

Views: 48153
DrPhilClark

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Related Rates # 7 - Ladder Sliding Down Wall, Finding Rate of Change of Area Under Ladder. In this example, a ladder is being pulled away from a wall causing the ladder to slide down the wall. We find the rate of change of the area underneath the ladder.

Views: 171096
patrickJMT

http://www.rootmath.org | Calculus 1
This problem is very similar to filling a pool but with an added consideration. This is a very typical related rates problem for a Calculus 1 class. You may find a problem like this on a test or exam.

Views: 50909
rootmath

🌎 Brought to you by: https://Biology-Forums.com
🤔 Still stuck in math? Visit https://Biology-Forums.com/index.php?board=33.0 to start asking questions.
Q. A conical tank with vertex down has a base radius of 3.00 m and a height of 6.00 m. Water flows in at a rate of 2.00 m^3∕h. How fast is the water level rising when the depth y is 3.00 m?
A procedure that can be followed is:
Step 1: Locate the given rate. Since it is a rate, it can be expressed as a derivative with respect to time.
Step 2: Determine the unknown rate. Express it also as a derivative with respect to time.
Step 3: Find an equation linking the variable in the given rate with that in the unknown rate. If there are other variables in the equation, they must be eliminated by means of other relationships.
Step 4: Take the derivative of the equation with respect to time.
Step 5: Substitute the given values and solve for the unknown rate.
Source: Technical Mathematics with Calculus, 3e. Calter & Calter.

Views: 21
Study Force

► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
Related rates problems are an application of derivatives and implicit differentiation that allow us to figure out how fast one thing is changing in relation to how fast something else is changing. For example, we might be interested in how fast an airplane is traveling compared to how fast the angle between the plane and an observer on the ground is changing.
Related rates problems allow us to do that by using implicit differentiation. We'll usually take the derivative of the equation, taking the derivative of every variable with respect to time t. Then we'll plug in for what we know and solve for the value we're interested in.
The key to related rates problems is getting the right equation set up. You need to figure out what equation you can write that will include the value you need to solve for. In addition to that, you may have to come up with a second equation that will give you the value for a missing variable that you need to plug into your first equation.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com
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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: http://www.kristakingmath.com
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GOOGLE+ // https://plus.google.com/+Integralcalc/
QUORA // https://www.quora.com/profile/Krista-King

Views: 11957
Krista King

Applications of the chain-rule and implicit differentiation in order to solve calculus related rate problems. Scenario: A ladder is sliding down a wall. Note: An animation is included!

Views: 20690
MyTangentialThoughts

Visit http://ilectureonline.com for more math and science lectures!
In this three part Calculus series I will cover how to solve problems with multiple rates of change and each rate of change affects the other.
Next video in this series can be seen at:
https://youtu.be/73GnajJ9jVM

Views: 6075
Michel van Biezen

Subscribe Here http://goo.gl/2XXaLS
For more cool math videos visit our site at http://mathgotserved.com or http://youtube.com/mathsgotserved
RELATED RATES
#1 Circles Oil is dropping from a punctured tank onto a circular oil pool on the ground with radius r. Find the following and state their meanings and units.
a) dr/dt
b)dA/dt
c) How fast is the radius changing when the radius is 2 cm and the area is changing at 20p cm2/min
#2 Cones:A conical pit is being filled with concrete. The pit has a base radius of 10 cm, and a depth of 30 cm. The pit is being filled so that the height of water rises at 2 cm/sec. Find the following in terms of V and h, (include meaning & units).
a) dh/dt
b)dV/dt
c) How fast is pit being filled at the point in time that the water level is 4cm.
#3 Spheres A sphere being inflated at 10ft^3/sec How fast is the radius increasing once the radiums is 4ft ?
#4 Ladder: A ladder 13 ft long is sliding down a wall. At the moment the base is 12ft from the wall, the base of the ladder is moving at 5 ft/sec. How fast is the top of the ladder moving at this moment?
#5 Boat and Winch: A winch 20 feet above sea level is used to reel in a rope connected to a boat at 2 ft/sec. How fast is the boat moving when the rope is 45 feet in length.
Ice Cube: An ice cube melts uniformly at a rate of 27cm3/sec. If the cube retains its perfect form while it is melting, at what rate are the sides shrinking when each side is 3 cm long ?
#Inverted conical Tank: water runs out of a conical tank at 7ft^3/min. The tank has a base of 10ft and a depth of 12 ft. How fast is the water level rising when the water is 5ft deep
#7 Trapezoidal Trough:The ends of a horizontal water trough is an isoceles trapezoidal prism. The length is 8 feet and the lower base is 4 feet. The upper base is 10 feet and the depth of the trough is 2 feet. If the water level is rising at 3 feet/min, when the depth of the water is 1 foot, how fast is water being poured into the trough?
#9 Hot air Balloon:A hot air balloon is rising vertically from a level platform. A range finder 400 feet from the lift point is tracking the hot air balloon. At the moment the angle of elevation of the range finder is 60 degrees , the angle of elevation is increasing at .10 degrees/minute. How fast is the balloon rising at that moment?
Consider a sphere of radius 10cm.
If the radius changes 0.1cm (a very small amount) how much does the volume change?
Water is draining from a cylindrical tank at 3 liters/second. How fast is the surface dropping?
Truck A travels east at 40 mi/hr.
Truck B travels north at 30 mi/hr.
How fast is the distance between the trucks changing 6 minutes later?
A particle moves along the curve C ú »" Ä B fi As it reaches $
the pointa b #fl $ fl the y-coordinate is increasing at a rate of
4 cm/sec. How fast is the x-coordinate of the point changing
at this instant?
3. Suppose where is a constant and when
4. Two cars start moving from the same point. One travels south at
60 m/hr and the other travels west at 25 m/hr. At what rate is
the distance between the cars increasing two hours later?
5. A plane flying horizontally at an altitude of 1 mile and a speed
of 500 mph passes over a radar station. Find the rate at which
the distance from the plane to the station is increasing when it
is 2 miles away from the station.
6. A conical water tower has a height of 12 ft and a radius of 3 ft.
Water is pumped into the tank at a rate of 4 ft /min. How fast is $
the water level rising when the water level is 6 ft
A man walks along a straight path at a speed of 4 ft/s.
A searchlight is located on the ground 20 ft from the path and is kept focused on the man.
§
§At what rate is the searchlight rotating
when the man is 15 ft from the point on
the path closest to the searchlight?
A police cruiser, approaching a right-angled intersection from the north, is chasing a speeding
car that has turned the corner and is now moving straight east. When the cruiser is 0.6
mi north of the intersection and the car is 0.8 mi to the east, the police determine with radar
that the distance between them and the car is increasing at 20 mph. If the cruiser is moving
at 60 mph at the instant of measurement, what is the speed of the car?
The voltage V (volts), current I (amperes),
and resistance R (ohms) of an electric circuit like the one shown
here are related by the equation V IR. Suppose that V is
increasing at the rate of 1 volt sec while I is decreasing at the
rate of 13 ampsec. Let t denote time in sec.
A trough is 15 ft long and 4 ft across the top
as shown in the figure. Its ends are isosceles triangles with
height 3 ft. Water runs into the trough at the rate of 2.5 ft3min.
How fast is the water level rising when it is 2 ft deep?
Sliding Ladder A 13-ft ladder is leaning against a house (see
figure) when its base starts to slide away. By the time the base is
12 ft from the house, the base is moving at the rate of 5 ft sec.

Views: 23654
maths gotserved

A classic example of a related rates problem.

Views: 20393
Kris Kissel

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Related Rates using Cones.
Gravel is being dumped into a pile that forms a cone; how quickly is the height changing?
A problem from UT-Austin calculus 1 course, homework #8.
For more free math videos visit http://PatrickJMT.com

Views: 337660
patrickJMT

This calculus video tutorial provides a few practice problems on related rates such as area, volume, circumference, and surface area.
Topics include:
1. Finding dr/dt
2. Area of a circle
3. Circumference of a circle
4. Inflated Balloon Problem
5. Volume of a sphere
6. Melting Snowball Problem
7. Surface Area of a Sphere

Views: 14026
The Organic Chemistry Tutor

A related rates problem on rate of change of the length of the shadow of a man walking away from a lamppost.
Download the free Calculus I e-book accompanying this playlist at:
http://bookboon.com/en/a-youtube-calculus-workbook-part-i-ebook
Please share!
Full Calculus I playlist:
http://www.youtube.com/playlist?list=PL265CB737C01F8961
Calculus II playlist:
http://www.youtube.com/playlist?list=PLm168eGEcBjnS6ecJflh7BTDaUB6jShIL&feature=em-share_playlist_user
Support my work on PATREON: https://www.patreon.com/calculusvideos

Views: 37570
calculus videos

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Related Rates Involving Trigonometry - A problem from UT Austin Calculus 1, HW #8.
For more free math videos, visit http://JustMathTutoring.com

Views: 200951
patrickJMT

► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
Understand one of the trickiest applications of derivatives and implicit differentiation, related rates.
Review the spherical balloon and leaning ladder examples to get a better grasp on related rates.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com
● ● ● 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: http://www.kristakingmath.com
FACEBOOK // https://www.facebook.com/KristaKingMath
TWITTER // https://twitter.com/KristaKingMath
INSTAGRAM // https://www.instagram.com/kristakingmath/
PINTEREST // https://www.pinterest.com/KristaKingMath/
GOOGLE+ // https://plus.google.com/+Integralcalc/
QUORA // https://www.quora.com/profile/Krista-King

Views: 175794
Krista King