1. The speed of sound 1) (in meters per second) in a gas (for example in air, or in some other gas) is given by: v_ 273.1531 1+ T _ M 273.15 where T is the temperature of the gas in degrees Celsius, M is the molar mass of the gas, and B and '7 are positive constants. d d (a) (3 marks) Find % and i. Write a sentence describing what each of the derivatives represent. 2 .1 B (b) (2 marks) When sound travels through dry air, the constants are such that (l% w 331.3 which means that in dry air: T m-TT : 1. 1 U (l 33 3V +273.15 Does sound travel faster or slower through warmer air, compared to colder air? You must use a derivative to determine your answer. (c) (3 marks) Find the linear approximation of UMT(T) at T = 0. Does the linear approximation support your answer in part (b)? (Is the linear approximation increasing/decreasing, as needed?) (d) (2 marks) Use the derivative you found in part (b) to explain why you know val-AT) is an invertible function. 1 Then use any method you prefer, to find (om-T), (331.3). Round your final answer to 1 decimal place