Consider f and c below. f(x, y, z) = (y2z + 2xz2)i + 2xyzj + (xy2 + 2x2z)k, c. x = t , y = t + 5, z = t2, 0 ≤ t ≤ 1 (a) find a function f such that f = ∇f.

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?

Officer brimberry wrote 32 tickets for traffic violations last week, but only 4 tickets this week. what is the percent decrease? give your answer to the nearest tenth of a percent.

Einstein office equipment has a rental plan for office machines. a fax machine that lists for $722.98 can be rented for 22% of the price annually. the state imposes a usage charge of 3.2%. if stephen hawking travel decides to rent the fax machine, what will its total monthly rental charge be?