Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

  sales are increasing at the rate of 6000 units per week

Step-by-step explanation:

Your demand equation appears to be ...

  4p³ +x² =38400

Then differentiation gives ...

  12p²·p' +2x·x' = 0

Solving for x', we get ...

  x' = -6p²·p'/x

Filling in the given values, we find the rate of change of sales to be ...

  x' = -6(20²)(-0.20/wk)/80 = 6/wk . . . . . in thousands of units/wk

Sales are increasing at the rate of 6000 units per week.

i am thinking c. sorry if im wrong .

step-by-step explanation:

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.