Aliyah and Diego started to run in a 5 kilometer-long race at exactly the same time. By 3:00 P. M., Aliyah had completed half of the race. For the rest of the race, Aliyah ran at a constant rate of 0.25 kilometer per minute. Diego did not run the race at a constant speed. A linear function can be used to model the total distance d(t)d(t) , in kilometers, that Aliyah runs from the beginning of the race in t minutes, where t=0t=0 represents 3:00 P. M. Write an equation that defines the linear function d. Explain how you determined the equation for the function.

-2/

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

answer would be 8.64 or s = 11π/4 inches

step-by-step explanation:

s = r θ  

where s = arc length  

r = radius = 3 inches  

θ = central angle in radians = ( π /180)*165  

s = 3(π/180)*165  

= 8.64 inches