Suppose you need to minimize the cost of fencing in a rectangular region with a total area of 450 square feet. The material that will be used for three sides costs $21 per linear foot, and the material that will be used for the fourth side costs $15 per linear foot. Write a function that expresses the cost of fencing the region in terms of the length, x, of the two opposite sides of the region with material costs of $21 per linear foot.

The problem is stated as:

Min C = 15*(2*x +y) + 21*y

subject to x*y = 450

Step-by-step explanation:

Given that the region is rectangular, it has two opposite sides called x and two other opposite sides called y (both measured in feet). Then, the area (in square feet) is:

A = x*y = 450

One of the sides called y costs $21 per linear foot. The other 3 sides (two x and one y) costs $15 per linear foot. Then, the cost function is:

C = 15*(2*x +y) + 21*y

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week

192/15 = 12.8.

12.8

step-by-step explanation:

192/15 is 12.8.

however, it says to round to the nearest foot, which would equal 13.