Andres boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 4.7 radians per minute and has a radius of 30 feet. Let t represent the number of seconds since the Ferris wheel started rotating. a. Write an expression (in terms of t) to represent the varying number of radians 8 Ryan has swept out since the ride started. Preview s height (in feet) above Preview c. Write an expression (in terms of t) to represent Ryan's height (in feet) above the ground.

Answer:a) r(t) = 0.783t radiansb) h(t) = 30cos(0.783*t) feetStep-by-step explanation:The situation is depicted in the picture attached (see picture) Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply using the fact that 1 min = 60 seconds 4.7 radians __________ 60 seconds r(t) radians ____________  t seconds [tex]\large \displaystyle\frac{4.7}{r(t)}=\displaystyle\frac{60}{t}\Rightarrow r(t)=(4.7/60)t \Rightarrow\\\\\boxed{r(t)=0.783t\;rad}[/tex] The height h(t) after t seconds is given by h(t) = 30cos(r(t)) ===> h(t) = 30cos(0.783*t) feet