Water coming out of a fountain is modeled by the function f(x) = −x2 + 5x + 4 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 3 to x = 5 represent?

A). The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

B). The water falls down with an average speed of 5 feet per second from 3 seconds to 5 seconds.

C). The water travels an average distance of 3 feet from 3 seconds to 5 seconds.

D). The water travels an average distance of 5 feet from 3 seconds to 5 seconds.

choice A.   average rate of -3 feet/sec  from 3 sec. to 5 sec

Step-by-step explanation:

f(x) = −x2 + 5x + 4 where f(x) represents the height, in feet,  at x seconds

find average rate of change of f(x)  from x = 3  to x = 5 seconds

find f(3) =  - 3*3 + 5*3  + 4 = -9 + 15 + 4 = 10 feet.

find  f(5) = -5*5 + 5* 5 + 4 =  4 feet.

average rate of change =  (4 - 10)/(5 -3 ) =  -6/2 = -3 feet/sec.

on average  water falls  3 feet /sec  from 3 to 5 seconds   choice A.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

  answer:

  write 548 as 500 + 40 + 8. multiply each addend by 5. then add the three products to get 2,740.