1. The speed of sound in (in meters per second) in a gas (for example in air, or in some other gas) is given by: p _ l273.15 B 1: _ fl1+ T ' 'V M ll 273.15 where T is the temperature of the gas in degrees Celsius, ll! is the molar mass of the gas, and B and 1- are positive constants. (a) (3 marks) Find 3; and 51%. Write a sentence describing what each of the derivatives represent. @3155?- (b) (2 marks) When sound travels through dry air, the constants are such that V' a 331.3 which 1' means that in dry air: l T MAT} = 331.3%; 1 + 27,; 1,] 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 ism-AT) at T = 0. Does the linear approximation support your answer in part (in)? (Is the linear approximation increasingdecreasing, as needed?) (d) (2 marks} Use the derivative you found in part (b) to explain why you know 'l.-'a"r\\(T] is an invertible function. Then use any method you prefer, to find (195:), (331.3). Round your final answer to 1 decimal place