A contractor purchases gravel one cubic yard at a time.

(a) A gravel driveway L yards long and 6 yards wide is to be poured to a depth of 1 foot. Find a formula for n(L), the number of cubic yards of gravel the contractor buys, assuming that he buys 12 more cubic yards of gravel than are needed (to be sure he'll have enough).

n(L)= ________ cubic yards help

(b) Assuming no driveway is less than 5 yards long or more than 9 yards long, find the domain and range of n(L).

Domain: help (numbers)
Range:

(a) To find the formula for n(L), we need to calculate the volume of the gravel needed for the driveway.

The formula for the volume of a rectangular prism is given by V = lwh, where:
V is the volume,
l is the length,
w is the width, and
h is the height or depth.

In this case, the width (w) is given as 6 yards, and the height (h) is 1 foot. Since 1 yard is equivalent to 3 feet, the height of the driveway is (1/3) yards.

Therefore, the volume of the driveway (V) is calculated as:
V = l * 6 * (1/3)
V = 2l

Since the contractor wants to buy 12 more cubic yards than needed, the formula for n(L) is:
n(L) = 2L + 12

(b) Considering the given constraints, the domain represents the possible values for the length of the driveway (L).
It is mentioned that no driveway is less than 5 yards long or more than 9 yards long. Therefore, the domain is:
Domain: 5 ≤ L ≤ 9

The range represents the possible values for the number of cubic yards of gravel the contractor buys (n(L)).
Since the formula for n(L) is n(L) = 2L + 12, the range is determined by substituting the minimum and maximum values of L into the formula:
Range: n(L) = 2(5) + 12 to n(L) = 2(9) + 12
Range: 22 to 30

Thus, the domain is 5 ≤ L ≤ 9, and the range is 22 to 30.

(a) To find a formula for n(L), we need to determine the volume of the gravel needed for the driveway.

The volume of a rectangular prism, such as the driveway, is given by the formula: volume = length × width × depth.

In this case, the length (L) is given as "L" yards, the width is 6 yards, and the depth is 1 foot, which is equivalent to 1/3 yards.

So, the formula for the volume of gravel needed is: volume = L × 6 × 1/3 = 2L cubic yards.

Since the contractor buys 12 more cubic yards than are needed, the formula for n(L) is:
n(L) = 2L + 12 cubic yards.

(b) Assuming no driveway is less than 5 yards long or more than 9 yards long, the domain represents the possible input values for L. In this case, L can be any value between 5 and 9 inclusively. Therefore, the domain is:
Domain: [5, 9].

The range represents the possible output values for n(L). Since n(L) is given by 2L + 12, the range can be determined by substituting the minimum and maximum values of L in the formula and finding the corresponding outputs.

For L = 5, n(L) = 2(5) + 12 = 22 cubic yards.
For L = 9, n(L) = 2(9) + 12 = 30 cubic yards.

So, the range is:
Range: [22, 30] cubic yards.

L+12