11:41 PM Fri Nov 25 .o. '-:~' @ 55%(3. inst-fs-yu|-prod.insc|oudgate.net E 20f2 1. The speed of sound \"U (in meters per second) in a gas (for example in air, or in some other gas) is given by: 273.1537 1 . T U' M ' 273.15 where T is the temperature of the gas in degrees Celsius, [W is the molar mass of the gas, and B and \"y are positive constants. (a) (3 marks) Find dl and 2 Write a sentence describing what each of the derivatives represent. dT dIVI ' 273.1537 1% x 331.3 which (b) (2 marks) When sound travels through dry air, the constants are such that l T val-AT) = 331.3 1 -l 27315 Does sound travel faster or slower through warmer air, compared to colder air? You must use a derivative to determine your answer. means that in dry air: (c) (3 marks) Find the linear approximation of val-AT) 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 vair(T) is an invertible function. I Then use any method you prefer, to find (on2i) (331.3). Round your final answer to 1 decimal place. Important: 2 marks are also given based on the quality of your writing and your explanations. See the Quercus page on Written Assignments for some tips and information on mathematical writing