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Svetradugi [14.3K]
2 years ago
15

Farmer bob's square plot ofland is slowly eroding away. Worried about the future of his farm. Farmer Bob measures the rate of er

osion 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
Mathematics
1 answer:
kow [346]2 years ago
7 0

Answer:

Option A.

Step-by-step explanation:

Area of a square is

A=x^2               .... (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.

\dfrac{dx}{dt}=2

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

Fist find the length of each side.

A=250000

x^2=250000

Taking square root on both sides.

x=500

Differentiate with respect to t.

\dfrac{dA}{dt}=2x\dfrac{dx}{dt}

Substitute x=500 and \frac{dx}{dt}=2 in the above equation.

\dfrac{dA}{dt}=2(500)(2)

\dfrac{dA}{dt}=2000

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

Therefore, the correct option is A.

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