Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled by the equation a(t) =

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

a) Alice starts first, b) Briana gets the finish line first, c)

Step-by-step explanation:

a) Alice starts first, since binomial inside the squared root is equal to zero when , whereas Alice begins at .

b) The instant when each competitor reach finish line is:

Alice

Briana

Briana gets the finish line first.

c) Alice and Briana are side by side when . Then:

The roots of the second order polynomial are:

and

Just the second roots makes sense, as they must be side by side at one instant before getting the finish line.

i think it is 18

step-by-step explanation:

your answer   is c

step-by-step explanation: