Acircular jogging track forms the edge of a circular lake that has a diameter of 2 miles. johanna walked once around the track at the average speed of 3 miles per hour. if t represents the number of hours it took johanna to walk completely around the lake, which of the following is a correct statement?
a. 0.5< t < 0.75
b. 1.75< t < 2.0
c. 2.0 < t < 2.5
d. 2.5 < t < 3.0
e. 3 < t < 3.5

  C.  2.0 < t < 2.5

Step-by-step explanation:

  time = distance / speed

The circumference of the lake is given by ...

  C = πd = 2π miles ≈ 6.28 miles

Then Johanna's time is ...

  (6.28 mi)/(3 mi/h) ≈ 2.09 h

This time is in the interval (2, 2.5), so matches choice C.

___

Alternate solution

If we take pi to be 3, then this boils down to ...

  2×3/3 = 2 . . . hours

Pi is on the order of 5% more than 3, so her time will be on the order of 5% more than 2 hours, or just above 2, but not as great as 2.5 hours. This sort of estimating can get you to the correct answer without a calculator.

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)