at a restaurant, 12 ounces of ground beef is used to make 4 hamburger patties. the number of hamburger patties made is directly proportional to the number of ounces of ground beef used. what is the constant of proportionality that relates the number of hamburger patties made to the number of ounces of ground beef used?

y(x)=sin^2 (x/4)+12sin(x/4)

y(x) = sin^2(x/7) +16sin(x/7)

From the Chain Rule,

y'(x) = 2sin(x/4)*(1/4)cos(x/4) + 12(1/4)cos(x/4).

At x=4pi, the slope of the tangent line is

y'(4pi) = 2sin(4pi/4)*(1/4)cos(4pi/4) + 12(1/4)cos(4pi/4).

= 2sin(pi)*(1/4)cos(pi) + 12(1/4)cos(pi)

= 2(0)(1/4)(-1) + 12(1/4)(-1)

= -3

The angle (in radians) that the tangent line makes to the positive x-axis is

pi - arctan(3)= 1.249 rad =71.565 degree