Acable company wants to provide cell phone service for residents on an island. the function for the cost of laying the cable from the island to the mainland is c(x)= 6.500 square root x2+4, where x represents the length of the cable in feet. what are the domain and range of the function? a) domain: all real numbers range: all real numbers greater than or equal to 17,000 b) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 17,000 c) domain: all real numbers greater than or equal to 0 range: all real numbers greater than or equal to 13,000 d) domain: all real numbers greater than or equal to 13,000 range: all real numbers greater than or equal to 0

C

Step-by-step explanation:

E2020

C) domain: all real numbers greater than or equal to 0

range: all real numbers greater than or equal to 13,000

Step-by-step explanation:

We have, the function for the cost of laying cable is given by,

, where x is the length of the cable (in feet).

As, 'x' represents the length of the cable.

We have that, the value of x cannot be negative.

So, x ≥ 0.

Since, the domain of is the set of points where and we have that x ≥ 0.

Thus, the domain is 'Set of all real numbers greater than or equal to 0'.

Now, we substitute x= 0 in .

i.e.

i.e.

i.e.

i.e. c(0) = 13000.

So, we get that the vertex point of the function is (0,13000).

Thus, the range is 'All real numbers greater than or equal to 13,000'.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15