The loudness level of a sound, D, in decibels, is given by the formula Upper D equals 10 log (10 Superscript 12 Baseline Upper I )D=10log1012I, where I is the intensity of the sound, in watts per metersquared2. Decibel levels range from 0, a barely audible sound, to 160, a sound resulting in a ruptured eardrum. The sound of a certain animal can be heard 500 miles away, reaching an intensity of 2.62.6times×10 Superscript 6106 watts per meter squared .meter2. Determine the decibel level of this sound. At close range, can the sound of this animal rupture the human eardrum?

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.