Farmer bob's square plot ofland is slowly eroding away. worried about the future of his farm. farmer bob measures the rate of erosion and finds that the length of each side of his square plot is decreasing at the constant rate of 2 feet/year. if he currently owns 250,000 square feet of land, what is the current rate of change of the area of farmer bob's land?
a) farmer bob is losing 2,000 square feet of land per year
b) losing 1,000,000 square feet of land per year
c) losing 1,000 square feet of land per year
d) losing 4 square feet of land per year

Option A.

Step-by-step explanation:

Area of a square is

              .... (1)

where, x is side length.

The length of each side of his square plot is decreasing at the constant rate of 2 feet/year.

It is given that bob currently owns 250,000 square feet of land.

Fist find the length of each side.

Taking square root on both sides.

Differentiate with respect to t.

Substitute x=500 and in the above equation.

Farmer bob is losing 2,000 square feet of land per year.

Therefore, the correct option is A.

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.