Question

A construction company has adjoined a 1100ft 2

rectangular enclosure to its office building. Three sides of the enclosure are fenced in. The side of the building adjacent to the enclosure is 110ft long and a portion of this side is used as the fourth side of the enclosure. Let x and y be the dimensions of the enclosure, where a is measured parallel to the building, and let L be the length of fencing required for those dimensions. (a) Find a formula for L in terms of x and y : L(x,y)= (b) Find a formula that expresses L as a function of z alone. L(x)= (c) What is the domain of the function in part (b)? Express as an interval. Domain =

Answer 1

Answer: the domain of the function is z > 0, expressed as an interval as (0, ∞).

Step-by-step explanation:

(a) The formula for the length of fencing required, L, can be found by adding the lengths of the three sides of the enclosure that are fenced in, which are y, x, and y. Then, we need to add the length of the side of the building adjacent to the enclosure, which is x. Thus, the formula for L in terms of x and y is:

L(x, y) = y + x + y + x

Simplifying, we get:

L(x, y) = 2x + 2y

(b) To express L as a function of z alone, we need to find the relationship between z, x, and y. We know that the side of the building adjacent to the enclosure, which is x, is also equal to z. Thus, the formula for L as a function of z alone is:

L(x) = 2z + 2y

(c) The domain of the function in part (b) depends on the possible values of z. Since z is the length of the side of the building adjacent to the enclosure, it cannot be negative or zero. Therefore, the domain of the function is z > 0, expressed as an interval as (0, ∞).