thank you Michel, my hero. U provided me with the best knowledge in such a short amount of time. HOW IS THAT POSSIBLE??? I don't understand how such a miracle can come into this world at the palm of my hand. Thank you for everything, and I MEAN everything. Your cool swagger and your rocking bowtie can never be replaceable. I hope you're having the best day right now. Keep up the good work. From, your biggest fan, Tarik.
an interesting result from the final answer is this: once you know "X" .. you also know d- x .. and knowing h1 and h2.. you have two side of the two Triangles... guess what?.. now you can find the value of the Angles formed by the two Ropes where they meet the ground.. Using the Tangent.... guess what again?.. lol... it turns out that those angles are always Equal!!.. amazing result!!... the same applies to the Two Light Sources in your other video... Math is SO COOL!!! thanks Michel!!
your truly a nice and wonderful guys i will recommend you in my friend that like me having hard time in this kind of problem im glad that i found your video thanks a lot you give me idea how to solve this kind of proble and again thank you
I see this video along with other videos/articles, but i have one question. This is the way to find a local extrema, and i know that. The point is, how do we confirm it's a local minimum(not maximum)? This requires the second derivative of the formula, and I found it very clumsy. However, ignoring that completely is simply not acceptable in mathematics. Math is all about complete(self-contained), precise and accurate. Honestly this type of question can be solved so easily by geometry, but i guess we want to apply AP calc here. Therefore, my question still stands, waiting for an answer.
You truly have a gift for teaching ! You make Calculus easier to understandthan anyone on the web ...Thanks for taking time to share your vast knowledge of Calculus ....and so many other subjects ...with so many many of us fortunate youtube viewers out here. CT-fred
thank you Michel, my hero. U provided me with the best knowledge in such a short amount of time. HOW IS THAT POSSIBLE??? I don't understand how such a miracle can come into this world at the palm of my hand. Thank you for everything, and I MEAN everything. Your cool swagger and your rocking bowtie can never be replaceable. I hope you're having the best day right now. Keep up the good work. From, your biggest fan, Tarik.
Tarik,
Thank you for your comment and your kind words. We are glad that our videos were helpful for you. Keep it going.
an interesting result from the final answer is this: once you know "X" .. you also know d- x .. and knowing h1 and h2.. you have two side of the two Triangles... guess what?.. now you can find the value of the Angles formed by the two Ropes where they meet the ground.. Using the Tangent.... guess what again?.. lol... it turns out that those angles are always Equal!!.. amazing result!!... the same applies to the Two Light Sources in your other video... Math is SO COOL!!! thanks Michel!!
Yes indeed.
your truly a nice and wonderful guys i will recommend you in my friend that like me having hard time in this kind of problem im glad that i found your video thanks a lot you give me idea how to solve this kind of proble and again thank you
6 / r = 8 / ( 10 - r )
60 - 6r = 8r
60 = 14r
r = 60 / 14
r = appr. 4.3
I see this video along with other videos/articles, but i have one question. This is the way to find a local extrema, and i know that. The point is, how do we confirm it's a local minimum(not maximum)? This requires the second derivative of the formula, and I found it very clumsy. However, ignoring that completely is simply not acceptable in mathematics. Math is all about complete(self-contained), precise and accurate.
Honestly this type of question can be solved so easily by geometry, but i guess we want to apply AP calc here. Therefore, my question still stands, waiting for an answer.
The maximum would require the rope to go straight down to the ground from the tall pole
Can be confirmed using the first derivative and showing that it's negative for values prior to x and positive after, which isn't too tedious
man you could just say that L1 L2 must be linear when symmetry of L1 is taken and then you will get 14-10-x triangle
You truly have a gift for teaching ! You make Calculus easier to understandthan anyone on the web ...Thanks for taking time to share your vast knowledge of Calculus ....and so many other subjects ...with so many many of us fortunate youtube viewers out here. CT-fred
Thank you for the kind words.
Thank you
thank you so much for this, this was genuinely so helpful and you explained everything very well!!
Glad it was helpful!
very educational!
Thank you very much sir. I learned a lot to your video. Godbless.
Thank you
Awesome video! Keep up the great work!
you saved my life
Well, I did it right and I throw my paper away before seeing this video. :(
thankyou
You're welcome!
Like if you see a Pikachu!