Evaluate the integral i = z s f ds when f(x, y, z) = z 2 + 3xy and s is the portion of the plane x + 2y + 2z = 0 above the unit disk x 2 + y 2 ≤ 1 in the xy-plane

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. an 11-inch string has a frequency of 400 cylces per second. find the frequency of a 10-icnch string.

Solve 2 - 3 cos x = 5 + 3 cos x for 0° ≤ x ≤ 180° a. 150° b. 30° c. 60° d. 120°

The host of a game show is holding a bag with chips to see what prizes the contestants will play for. five (5) of the chips say “new car” ten (10) of the chips say “new tv” three (3) of the chips say “trip to france” contestant named “patty” reaches into the bag. a. what is the probability of choosing a tv chip? b. what is the probability of choosing a car chip next without replacing the 1st chip? c. are these dependent or independent events?