Consider a particle that moves through the force field f(x, y) = (y − x)i + xyj from the point (0, 0) to the point (0, 1) along the curve x = kt(1 − t), y = t. find the value of k such that the work done by the force field is 1.

The work done by is

where is the given curve and is the given parameterization of . We have

Then the work done by is

In order for the work to be 1, we need to have .

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

d

step-by-step explanation: