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MR. Organic Chemistry Tutor, thank you for an incredible video/lecture on Related Rates problems in Calculus. Related Rates problems can be highly problematic. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
For part c since the question asks "how fast is the length of the diagonal" how do we know to solve for z and not l when they are both a diagonal in the cube? Is it because z covers all the entire edge lengths?
just in case anybody else has this question in the future, you don't solve with l because that diagonal goes only across the surface of one of the cube's faces, not through the cube itself. L is used to create an upward triangle through the three-dimensional space of the cube so that z, the diagonal going through the cube, can be calculated using the pythagorean theorem :)
if you mean total surface area, then in this case there isn't any. when it says 'surface area of an object' it really means the added surface area of all the parts of an object, which is why he multiplied it by six -- there are six 'faces' (sides) of the cube. otherwise surface area refers to just one face (side), which for a cube is just a square, and total surface area talks about 3-d objects and is the added sum of all those faces. for a cube, it's all the squares added together :)
Wtf am I watching? I don't get it. You start at 5x5x5= 125m^3, you add 1000m^3/hr. What does the initial value of x in x^3 matter? What are we even looking for if the problem is saying that the rate of change is 10m/hr and the rate of volume change is 1000m^3??
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You help me not cry
bro same
Speaking for everyone, even a whole year later
“I know my drawings aren’t that great….” Proceeds to draw a badass cube 😭
MR. Organic Chemistry Tutor, thank you for an incredible video/lecture on Related Rates problems in Calculus. Related Rates problems can be highly problematic. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
This is so beautifully explained 😍 thank u!
you helped me in class :)
Can we just use the diagonal formula that is root 3 times x?
In the last problem would it be easier to relate using the formula for the diagonal of a cube D= 3^1/2(a) ? Many thanks
Its harder to take the derivative of this though, this is helpful for finding the length of the diagonal without having to do pythagorean
You are hero man
how are you supposed to just remember 9:00 where the two triangles come out of know where
How do we find each side if we only have a volume? E.g: Cube of a volume of 20cm(cubed), How long is each side of the cube
It;s very very easy, just take the cube root of the volume
For part c since the question asks "how fast is the length of the diagonal" how do we know to solve for z and not l when they are both a diagonal in the cube? Is it because z covers all the entire edge lengths?
just in case anybody else has this question in the future, you don't solve with l because that diagonal goes only across the surface of one of the cube's faces, not through the cube itself. L is used to create an upward triangle through the three-dimensional space of the cube so that z, the diagonal going through the cube, can be calculated using the pythagorean theorem :)
how do you find the rate of change of the edges given the rate of change of the volume
thanks!
Amazing
I have a question about the surface area, what is the difference of it compared to totasurface area?
if you mean total surface area, then in this case there isn't any. when it says 'surface area of an object' it really means the added surface area of all the parts of an object, which is why he multiplied it by six -- there are six 'faces' (sides) of the cube. otherwise surface area refers to just one face (side), which for a cube is just a square, and total surface area talks about 3-d objects and is the added sum of all those faces. for a cube, it's all the squares added together :)
ok but why in the part c, he didn't write z=x(root)3 instead of z^2=3x^2, wouldn't it make more sense?
I know my drawings is not that great...who cares? You literally know undergrad physics, economics, maths, chemistry and what not.
I watched this for fun.
Damn, I didn't know Stephen Hawking had a youtube account
wish i could say the same, soldier
Wtf am I watching? I don't get it. You start at 5x5x5= 125m^3, you add 1000m^3/hr. What does the initial value of x in x^3 matter? What are we even looking for if the problem is saying that the rate of change is 10m/hr and the rate of volume change is 1000m^3??
How you get 3x^2?
by driving x^3, d/dt (x^3) = 3x^2 dx/dt
watch his implisit derivation videos to understand this
Using the chain rule
👍