You and your best friend Janine decide to play a game. You are in a land of make believe where you are a function, f(t), and she is a function, g(t). The two of you move together throughout this land with you (that is, f(t) ) controlling your East/West movement and Janine (that is, g(t) ) controlling your North/South movement. If your identity, f(t), is given by f(t)=(t2+10)323 and Janine's identity, g(t), is given by g(t)=5t then how many units of distance do the two of you cover between the Most Holy Point o' Beginnings, t=0, and The Buck Stops Here, t=20?

Accepted Solution

Answer:12920Step-by-step explanation :distance covered = d =  ∫[tex]\int\limits^a_b ({sqrt{f'(t)^{2} +g'(t)^2\\}}) \, dt[/tex]a = t = 20b = t = 0f'(t) = 646 : f'(t)² = 417316g'(t) = 5 : g'(t)² = 25d = [tex]\int\limits^a_b {646} \, dt[/tex]t = 20 &  t = 0d = 646td = 646*20 = 12920