If f is a scalar field and f, g are vector fields, then f f, f · g, and f × g are defined by the following. (f f)(x, y, z) = f(x, y, z) f(x, y, z) (f · g)(x, y, z) = f(x, y, z) · g(x, y, z) (f × g)(x, y, z) = f(x, y, z) × g(x, y, z) find an identical expression, assuming that the appropriate partial derivatives exist and are continuous.

Aaron invested a total of $4,100, some in an account earning 8% simple interest, and the rest in an account earning 5% simple interest. how much did he invest in each account if after one year he earned $211 in interest? select one: a. $200 at 8%, $3,900 at 5% b. $3,200 at 8%, $900 at 5% c. $900 at 8%, $3,200 at 5% d. $3,900 at 8%, $200 at 5%

Tim has obtained a 3/27 balloon mortgage. after the initial period, he decided to refinance the balloon payment with a new 30-year mortgage. how many years will he be paying for his mortgage in total?

The label on a can of lemonade gives the volume as 12 fl 0z or 355ml verify that these two measurements are nearly equivalent