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or Polyacrylic acid or Carbomer? I prefer purchasing from a company but not from individuals who sell them online. Thank you for your answers!

Hello, does anyone know what the letters AT stand for in AT-cut quartz crystal? I know that such crystals are cut at an angle of 35.25 degrees and that's how it's different from BT-cut ones but is AT an actual acronym, and if so, what does it mean? Thanks a lot and good day! :)

I'm stuck on this: integral of the quotient of (y^2) and (square root of (y^2 +4)). I've been doing this problem for two days but I can't find the answer. I let y = 2tan(theta) so dy = 2sec^2(theta)d(theta). The problem is that I keep on going back again and again to the previous steps whenever I continue my solution. It's like I'm in an endless loop. I know how to integrate sec^3(theta). It's by having sec^2(theta) multiplied to sec(theta) so I'll get (tan^2(theta) + 1)sec(theta). Afterwards, I can distribute sec(theta). But I keep on going back to the previous steps. Is there any way by which I can integrate this? Or is there any other possible solution. Kindly show me how. By the way, our last lesson was trigonometric substitution. Thank you so much!!!

I'm stuck on this: integral of the quotient of (y^2) and (square root of (y^2 +4)). I've been doing this problem for two days but I can't find the answer. I let y = 2tan(theta) so dy = 2sec^2(theta)d(theta). The problem is that I keep on going back again and again to the previous steps whenever I continue my solution. It's like I'm in an endless loop. I know how to integrate sec^3(theta). It's by having sec^2(theta) multiplied to sec(theta) so I'll get (tan^2(theta) + 1)sec(theta). Afterwards, I can distribute sec(theta). But I keep on going back to the previous steps. Is there any way by which I can integrate this? Or is there any other possible solution. Kindly show me how. By the way, our last lesson was trigonometric substitution. Thank you so much!!!

I'm stuck on this: integral of the quotient of (y^2) and (square root of (y^2 +4)). I've been doing this problem for two days but I can't find the answer. I let y = 2tan(theta) so dy = 2sec^2(theta)d(theta). The problem is that I keep on going back again and again to the previous steps whenever I continue my solution. It's like I'm in an endless loop. I know how to integrate sec^3(theta). It's by having sec^2(theta) multiplied to sec(theta) so I'll get (tan^2(theta) + 1)sec(theta). Afterwards, I can distribute sec(theta). But I keep on going back to the previous steps. Is there any way by which I can integrate this? Or is there any other possible solution. Kindly show me how. By the way, our last lesson was trigonometric substitution. Thank you so much!!!

There's an item in my homework that I can't figure out. I think I've already spent two hours on it. Actually, this is my first time to meet such topic. Here's the question: In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates where one of the C---H bonds is in the direction of i+j+k (these letters have caret or "hat" above them because they are unit vectors), an adjacent C---H bond is in the i-j-k (unit vectors too) direction. Calculate the angle between these two bonds.

I know from Chemistry that it's 109.5 degrees. But this subject is Physics and we need to show how we get our answer. I'm asking if you can at least teach me how to get angles using those conditions (especially if it has something to do with unit vectors). I really don't have a clue. I don't want to cheat. I just want to learn. Thank you very much!!! God bless!!! :)

There's an item in my homework that I can't figure out. I think I've already spent two hours on it. Actually, this is my first time to meet such topic. Here's the question: In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates where one of the C---H bonds is in the direction of i+j+k (these letters have caret or "hat" above them because they are unit vectors), an adjacent C---H bond is in the i-j-k (unit vectors too) direction. Calculate the angle between these two bonds.

I know from Chemistry that it's 109.5 degrees. But this subject is Physics and we need to show how we get our answer. I'm asking if you can at least teach me how to get angles using those conditions (especially if it has something to do with unit vectors). I really don't have a clue. I don't want to cheat. I just want to learn. Thank you very much!!! God bless!!! :)

i arduously searched the internet and luckily, i already found some of them. Actually, my professor is asking for 10 filipino sociologists and 10 anthropologists. I only found 3 sociologists ang 4 anthropologists. They are Walden Bello, Karina Constantino-David, Randolf “Randy” David, Alfredo Evangelista, Felipe Landa Jocano, Melba Padilla Maggay, Michael Tan. Do you know anyone else and what his/her contributions are? any relevant answer, even if it's short, would be of great help and would be greatly appreciated. thanks so much!!! God bless us!!!