Explain why the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1.

If x varies directly as y, and x = 7.5 when y = 10, find x when y = 4

Amass weighing 16 pounds stretches a spring 8/3 feet. the mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. find the equation of motion if the mass is driven by an external force equal to f(t)=cos(2t).

Find the area of the region between a regular hexagon with sides of 6" and its inscribed circle.