Written(Submit as an pdf file, or hand-in in class.)1. Order following function by growth rate: N, √N, N1.5, Nlog(N), log (log (N)), log (N)log (N), N2, 2N, 200, NN2. Give a useful Θ(big Theta) estimation for each of following functiont(n). a. t(n) = 122*212
b. t(n) = 2log2(n2) + log4(n)+(log2n)2+ (log2(202))2
c. t(n) = 3t(n/2) + n
d. t(n) = 3t(n/2) + (n+1)(n-1)
e. t(n) = 4t(n/2) + (n2+ n-1)
f. t(n)is the runtime of following function, public static int f1(int n){intmid = n/2;for (int i = mid; i >= 0; i--) System. out. println(i);for (int i = mid + 1; i <= n; i++) System. out. println(i);return mid;}
g. t(n)is the runtime of following function, public static int f2(int n){if (n < 1) return 1; //update from originalintmid = n/2;mid = f2(mid);for (int i = 30; i >0; i /=3){System. out. println(i );}return mid;}

City a and city b had two different temperatures on a particular day. on that day, four times the temperature of city a was 8â° c more than 3 times the temperature of city b. the temperature of city a minus twice the temperature of city b was â’3â° c. what was the temperature of city a and city b on that day? city a was 5â° c, and city b was 4â° c. city a was 3â° c, and city b was â’1â° c. city a was 8â° c, and city b was â’3â° c. city a was 5â° c, and city b was â’5â° c.

Actual ingredients of lab (the cookies i am actually making) 1/2 cup sugar 1/2 cup brown sugar 1 1/3 stick margarine 1 egg 1/2 tsp salt 1 tsp vanilla 1/2 tsp baking soda 1 1/2 cup flour 1 1/3 cup chocolate chip can you answer the questions below ? discussion 1. suppose you are given the following amounts of ingredients: 1 dozen eggs 24 tsp. of vanilla 1 lb. (82 tsp.) of salt 1 lb. (84 tsp.) of baking soda 3 cups of chocolate chips 5 lb. (11 cups) of sugar 2 lb. (4 cups) of brown sugar 1 lb. (4 sticks) of margarine a. for each ingredient, calculate how many cookies could be prepared if all of that ingredient were consumed. (for example, the recipe shows that using 1 egg- with the right amounts of the other ingredients- yields 24 cookies. how many cookies can you make if the recipe is increased proportionately for 12 eggs? ) b. to determine the limiting reactant for the new ingredients list, identify which ingredient will result in the fewest number of cookies. c. what is the maximum number of cookies that can be produced from the new amounts of ingredients?

What happens to the average kinetic energy of a gas when the particles of the gas collide against each other at a constant temperature and volume? explain your answer.