1 A farmer wants to build a fence along a river He has 800 f

1. A farmer wants to build a fence along a river. He has 800 feet of fencing and wants to enclose a rectangular pen on three sides (with the river providing the fourth side). If x is the length of the side perpendicular to the river, determine the area A of the pen as a function of x.

Solution

1)   x is the length of the side perpendicular to the river

800 feet fencing is to be done on 3 three sides

length of the side of pen = x , x , 800 - 2x

therefore,

area of the pen = x ( 800 - 2x) = 800x - 2x^2

2) g(t) = sqrt ( 3- t ) - sqrt ( 2+ t)

since , square root cannot have a negative number

setting parentheses = zero and solving for t to find the domain

( 3 - t ) >= 0

t <= 3

(2+t) >= 0

t >= -2

therefore domain is

-2 <= t <= 3

interval notation

[ -2,3 ]