As the moon revolves around the earth, the side that faces the earth is usually just partially illuminated by the sun. the phases of the moon describe how much of the surface appears to be in sunlight. an astronomical measure of phase is given by the fraction f of the lunar disc that is lit. when the angle between the sun, earth, and moon is θ (0 ≤ θ < 360°), then the fraction f is given by the formula below. f = 1 2 (1 − cos(θ)) determine the angles θ that correspond to the following phases. (enter your answers as a comma-separated list.)

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.