thank you so much for talking slowly. thank you so much for making these videos for free. thank you for keeping it concise and uncomplicated. this channel legit is saving my grade. maybe i can do it after 17 years of just throwing in the towel bc i really thought my brain just wasn't cut out for math. seriously thank you thank you
Fin Fin you have no clue how much this comment means! I’m so thankful that you found my channel and that you’re finding the videos helpful!! I truly believe we are all cut out for math *when* we are able to connect to the material in the right way and have it explained to us in a style that best fits us! Keep up the hard work & wishing you the best!
The derivative of ax^n = a*n^(n-1). So d/dx (1/20)x = (1/20)*1x^0 = 1/20. If we were just looking at d/dx 1/20, then we are looking at the derivative of a constant = 0.
Sure, @10:40, we had 2x dx/dt + 2y dy/dt = 0. We know dx/dt = 1 since the ladder is moving away from the wall at 1 ft/s --> 2x + 2y dy/dt = 0 --> 2y dy/dt = -2x --> y dy/dt = -x --> dy/dt = -x/y
Hello, Mrs. Roshan, So for this kind of problems, when you have a triangle, you use Pythagorean theorem? But when you have like a inverted cones problems or have to many variables you have to solve for one of the variable first? Also, for exam number 4, can you use trig function to solve for it as well? Thanks!!! Your videos have been helping me for years :)
+Khoa Dang Nguyen you use the equation related to the information you have and what you are solving for. So when you have a triangle as your shape and you have info about side lengths (ie: example 4) and the rates of change those objects are moving towards/away from one another, you'll want to start with a^2 + b^2 = c^2. But if you have info about a side and an angle (ie: example 5), we use our trig to help us out since we are looking for d(theta)/dt. See - if I had started with the pythagorean identity in that one, I wouldn't have been able to find information about the angle. If I'm doing a problem involving filling/emptying a cone, I would start with the volume of a cone formula. If talking about a cylinder, I would start with it's formula (ie: material used, I'd look at surface area; filling/emptying I'd look at volume). You have to read the problem and see what information you have and what you're looking for to determine what equation to start with. Hope that helps!
For example 2, couldnt we of just used the pythagorean theorem since we knew x was 6 and z was 10 to figure out y. or did we need to show the proper steps by taking the derivative of the theorem
We do use the Pythagorean theorem to find y (at around 10:55 in the video). That is, when x is 6, y is 8. We then are able to solve for dy/dt using the steps we had taken earlier in the problem. Hope that helps clarify.
They tell us x=6... and we know z=10 since that's the height of the ladder. It's a right triangle so we know x^2 + y^2 = z^2. I recognized the 6 - y - 10 triangle as being similar to our 3-4-5 special right triangle 3x2=6 (our x), 4x2=8 (our y), 5x2=10 (our z). If you didn't recognize it as a special right triangle, you can also just use the Pythagorean Theorem... x^2 + y^2 = z^2 --> 6^2 + y^2 = 10^2 --> y^2 = 10^2 - 6^2 = 100 - 36 = 64 --> y=8
@@cassandradee4582 Let me try to break this down with a keyboard... hopefully it will make sense :) 2 = pi/12 * 3 * 3^2 dh/dt 2 = pi/12 * 3 * 9 dh/dt 2 = 9pi/4 dh/dt 4/9pi * 2 = dh/dt 8/9pi = dh/dt Hope that helps!
stephany mejia sure! You have 100 on the left side of the equation and on the right 4/3*3*(50/2)^2pi dr/dt=50^2pi dr/dt. So if we divide both sides by that 50^2 pi, that would leave us with dr/dt = 100/(50*50 pi) = 1/(25 pi)
thank you so much for talking slowly. thank you so much for making these videos for free. thank you for keeping it concise and uncomplicated. this channel legit is saving my grade. maybe i can do it after 17 years of just throwing in the towel bc i really thought my brain just wasn't cut out for math. seriously thank you thank you
Fin Fin you have no clue how much this comment means! I’m so thankful that you found my channel and that you’re finding the videos helpful!! I truly believe we are all cut out for math *when* we are able to connect to the material in the right way and have it explained to us in a style that best fits us! Keep up the hard work & wishing you the best!
When a video from 5 years ago helps you way more than the teacher I have XD Thank you!!
This seriously fills my heart!! So glad to be able to help out :) Good luck in your class!!
For the final example (5), why did u pull out 1/20? Wouldn’t it be 0 since it’s a constant? (25:45)
The derivative of ax^n = a*n^(n-1). So d/dx (1/20)x = (1/20)*1x^0 = 1/20. If we were just looking at d/dx 1/20, then we are looking at the derivative of a constant = 0.
Got it Thank you so much!!
Excellent job on this, Ms. Roshan, thank you!
Thanks for the compliment!!
Question, I don't understand how you arrived at - x/y. Could you explain??.
Sure, @10:40, we had 2x dx/dt + 2y dy/dt = 0. We know dx/dt = 1 since the ladder is moving away from the wall at 1 ft/s --> 2x + 2y dy/dt = 0 --> 2y dy/dt = -2x --> y dy/dt = -x --> dy/dt = -x/y
at 22:54 how did you get -78?
oh nvm I see haha
Hello, Mrs. Roshan,
So for this kind of problems, when you have a triangle, you use Pythagorean theorem?
But when you have like a inverted cones problems or have to many variables you have to solve for one of the variable first?
Also, for exam number 4, can you use trig function to solve for it as well?
Thanks!!! Your videos have been helping me for years :)
+Khoa Dang Nguyen you use the equation related to the information you have and what you are solving for. So when you have a triangle as your shape and you have info about side lengths (ie: example 4) and the rates of change those objects are moving towards/away from one another, you'll want to start with a^2 + b^2 = c^2. But if you have info about a side and an angle (ie: example 5), we use our trig to help us out since we are looking for d(theta)/dt. See - if I had started with the pythagorean identity in that one, I wouldn't have been able to find information about the angle. If I'm doing a problem involving filling/emptying a cone, I would start with the volume of a cone formula. If talking about a cylinder, I would start with it's formula (ie: material used, I'd look at surface area; filling/emptying I'd look at volume). You have to read the problem and see what information you have and what you're looking for to determine what equation to start with. Hope that helps!
For example 2, couldnt we of just used the pythagorean theorem since we knew x was 6 and z was 10 to figure out y. or did we need to show the proper steps by taking the derivative of the theorem
We do use the Pythagorean theorem to find y (at around 10:55 in the video). That is, when x is 6, y is 8. We then are able to solve for dy/dt using the steps we had taken earlier in the problem. Hope that helps clarify.
how did you get 8 for y in example 2?
They tell us x=6... and we know z=10 since that's the height of the ladder. It's a right triangle so we know x^2 + y^2 = z^2. I recognized the 6 - y - 10 triangle as being similar to our 3-4-5 special right triangle 3x2=6 (our x), 4x2=8 (our y), 5x2=10 (our z). If you didn't recognize it as a special right triangle, you can also just use the Pythagorean Theorem... x^2 + y^2 = z^2 --> 6^2 + y^2 = 10^2 --> y^2 = 10^2 - 6^2 = 100 - 36 = 64 --> y=8
I know this might seem like a silly question, but on example 2 you got the answer 8/9pi m/min, what is the math between 2=pi/12*3*3^2*dh/dt?
sorry it is actually example 3
@@cassandradee4582 Let me try to break this down with a keyboard... hopefully it will make sense :)
2 = pi/12 * 3 * 3^2 dh/dt
2 = pi/12 * 3 * 9 dh/dt
2 = 9pi/4 dh/dt
4/9pi * 2 = dh/dt
8/9pi = dh/dt
Hope that helps!
@@StaceyRoshan yes thank you!
hey, im struggling with where the 1/25pi came from, help please thank you so much hopefully you havent forgotten after 3 years lol
stephany mejia sure! You have 100 on the left side of the equation and on the right 4/3*3*(50/2)^2pi dr/dt=50^2pi dr/dt. So if we divide both sides by that 50^2 pi, that would leave us with dr/dt = 100/(50*50 pi) = 1/(25 pi)
poggers