A rectangular study area is to be enclosed by a fence and divided into two equal parts, with the fence running along the division parallel to one of the sides. If the total area is 384 square feet, find the dimensions of the study area that will minimize the total length of the fence. How much fencing will be required?

Explanation:

Let l be the length of the study area and w be the width of study area.

Area of rectangular part = l x w

A = l x w

384 = l x w

w = 384 / l .... (1)

length of the fence is equal to the perimeter.

P = 2 ( l + w)

  from equation (1)

Differentiate with respect to l

for maxima and minima, it is equal to zero

l = 19.6 ft

so w = 19.6 ft

So, the required fencing = 2 ( 19.6 + 19.6) = 78.4 ft

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.