Suppose you maintain a database of cocktail recipes. You want to write a applicationthat asks a user for their favorite cocktail and returns a cocktail that they might like. To do so, you definethe distance between two cocktails to be the symmetric distance between their ingredient lists. Then, for theinput cocktail, you compute the distance to every cocktail in your database and return one of the cocktailsthat minimizes this distance.1. Prove that this distance is a metric. (Note: first, formally write out what the distance function is, including the domain and codomain)

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3.12: the speed of sound the speed of sound depends on the material the sound is passing through. below is the approximate speed of sound (in feet per second) for air, water and steel: air: 1,100 feet per second water: 4,900 feet per second steel: 16,400 feet per second write a program class the speed of sound that asks the user to enter “air”, “water”, or “steel”, and the distance that a sound wave will travel in the medium. the program should then display the amount of time it will take. you can calculate the amount of time it takes sound to travel in air with the following formula: time = distance/1,100 you can calculate the amount of time it takes sound to travel in water with the following formula: time = distance/4,900 you can calculate the amount of time it takes sound to travel in steel with the following formula: time = distance/16,400