Related Rates Example

For more related rates practice, check out the above link!

[rolandthebloxxer]

Thanks for making me remember why I majored math and calculus with fun problems like these after finishing my exams.
Here's hoping for a good thesis in a few.

[troybingham]

That was a good one. Good refresher. Thanks for running through that.

[EvansKazooCovers]

I hated related rates in high school...somehow you made it super interesting. Thank you Andy math

[alitraore]

Personally, i would calculate directly the derivative of x as t/√(100+t^2) where, using the assumption of a costant rate of y, i changed y itself with t (time in minutes). At the end, you just need to set this term equal to 0.5 and solve the equation. Nice video btw. Keep it up.

[OptimusPhillip]

If we take the vertical position of the red car as a, then we get x^2=10^2+a^2. Doing implicit differentiation, we can find that 2x*(dx/dt)=2a*(da/dt). We know da/dt=1, and we want dx/dt=0.5, so we can just plug those into the equation, and find that 2x*0.5=2a*1, or that x=2a.
Substituting 2a in for x gives us (2a)^2=10^2+a^2, or 4a^2=100+a^2. A little bit of algebraic manipulation later, and we see that a^2=100/3, or a=10/sqrt(3).
Plugging this back into x=2a tells us that x=20/sqrt(3) when dx/dt=0.5

[clayton]

From the problem statement we know x^2 = t^2 + 100. Take derivative of both sides with with respect to t. Solve for t. I get the same answer.

[elvkim]

These were my nightmare problems in college

[dalehjify]

Please done crucify me. At 4:00. How does taking away x² take .25 to -.75?

[starboy]

Holy ahit! I keep thinking slowly everything is gonna cancel at the end and we will be left with 0. 😂 How. Exciting.

[nabil]

Can you explain the lambert w function?

[syed]

I challenge u to solve this integral.
(sin²x+sinx)/(1+sinx+cosx)
Without converting into tan(x/2) because it will become way too long and we were only given 4mins to solve it

[PugganBacklund]

I expected him to turn 5.77 minutes in to 5 minutes and 46.2 secounds. @ 5:21