Ime to cook a turkey model a turkey as a sphere of radius a. let t(r, t) be the temperature of the turkey at distance r from the center and time t. assume t is the (uniform) temperature of the turkey when it is put in an oven at temperature t. the heat equation says =urocre. do where k is the thermal diffusivity (a) show t r, t) t+、 a sin(n π r/a ) etn2m2 k al satisfies (1) and the boundary condition t(a, t) = t1 t > 0. 72 here the a, are constants. (b) assume the turkey is at the constant temperature to when it is put in the oven, so t(r,0) to.0s r s a. (c) the turkey is cooked when the central temperature reaches the desired value t (d) find the time to cook a turkey of radius 12 cm and temperature 40°f if it is put into a 350°f oven use the euler formula from fourier series to find a, 1,2, 2. write down this equation for t as explicitly as possible (you will need to take a limit as r →0 and is done when the central temperature reaches 185 °e. the thermal diffusivity of turkey meat is ro 10 m/s