Gfind the gradient field of the function g(x, y, z) = 8 x y + 5yz + 5xz

If the original volumes of liquid is represented by x, we have x=x for A and B. Since 120mL is poured from A to B, A loses 120 mL (x-120) and B gains 120 mL (x+120). Since we know that B contains 4 times as much liquid as A is now (x-120), we have 4*(x-120)=(x+120)=B. Using the distributive property, we get 4x-480=x+120. Adding 480 to both sides, we get 4x=x+600. After that, we can subtract both sides by x to get 3x=600. Lastly, we can divide both sides by 3 to get x=200=the original amount of liquid. Since A=x-120, we get A=200-120=80
 

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