There is a pier point P in the water 3 miles away from shore

There is a pier, point P, in the water 3 miles away from shore, point A. A power plant is 10 miles from point A and Is on the shore at point B. The cost it takes to run a cable from point B to point P Is given by: C (x) = 33 squareroot 9 + (10 - x)2 18 x. x is the distance (in miles) on the shore from point B to the point where the cable goes underwater. UNITS MUST BE IN MILES ANP DOLLARS. Use interval notation to state the domain of this function. Use interval notation to state the contextual domain of this function. Use interval notation to state the range of this function. Use interval notation to state the contextual range of this function. Use your calculator to find the value of x that minimizes the cost to run cable from point B to point P. What is the minimum cost?

Solution

C(x) = 33sqrt[9 + (10 -x)^2 ]

Domain: 9+ ( 10 -x)^2 is always greater than zero

So, domain ( - inf , inf)

Range: Minima of C(x) occurs at x= 10 , C(10) = 99

Range : [ 99, inf)

C(x) is minimised when x= 10 in 33sqrt[9 + (10 -x)^2 ]

So, C(10) = 33*3 = 99 minium cost