Driving , Patrick made the trip to his grandmother’s house in 4 hours and 30 minutes. A week later, driving at a constant rate of speed, he returned home in 4 hours and 15 minutes. If Patrick took the same route home, what
was his average rate of speed for his return trip?
A. 50 mph
B. 52 mph
C. 53 mph
D. 54 mph

Alake near the arctic circle is covered by a 222-meter-thick sheet of ice during the cold winter months. when spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. after 333 weeks, the sheet is only 1.251.251, point, 25 meters thick. let s(t)s(t)s, left parenthesis, t, right parenthesis denote the ice sheet's thickness sss (measured in meters) as a function of time ttt (measured in weeks).

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?

Write the expression as a single natural logarithm. 2 in a - 4 in y