F(x, y, z) = yz i + xz j + (xy + 18z) k c is the line segment from (1, 0, −1) to (5, 6, 1) (a) find a function f such that f = ∇f. f(x, y, z) = (b) use part (a) to evaluate c ∇f · dr along the given curve c.

The function a represents the cost of manufacturing product a, in hundreds of dollars, and the function b represents the cost of manufacturing product b, in hundreds of dollars. a(t) = 5t + 2 b(t) = 7t - 2t +4 find the expression that describes the total cost of manufacturing both products, a(t) + b(t). a. 7t^2 - 7t + 2 b. 7t^2 + 3 +6 c. 7t^2 + 7t - 6 d. 7t^2 - 3t + 6

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (-4, 0) and (6,0). the y-intercept of thefirst parabola is (0, –12). the y-intercept of the second parabola is (0-24). what is the positive difference between the avalues for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth.

The holiday party will cost $160 if 8 people attend. if there are 40 people who attend the party, how much will the holiday party cost