EXAMPLE 3 A wire takes the shape of a semicircle x2 + y2 = 9, y ≥ 0, and is thicker near its base than near the top. Find the center of mass of the wire if the linear density at any point is proportional to its distance from the line y = 4. SOLUTION As in this example we use the parametrization x = 3 cos(t), y = 3 sin(t), 0 ≤ t ≤ π, and find that ds = 3 dt. The linear density is rho(x, y) = k(4 − y)

What is the total surface area of this square pyramid?

In a test for esp (extrasensory perception), the experimenter looks at cards that are hidden from the subject. each card contains either a star, a circle, a wave, a cross or a square.(five shapes) as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. when the esp study described above discovers a subject whose performance appears to be better than guessing, the study continues at greater length. the experimenter looks at many cards bearing one of five shapes (star, square, circle, wave, and cross) in an order determined by random numbers. the subject cannot see the experimenter as he looks at each card in turn, in order to avoid any possible nonverbal clues. the answers of a subject who does not have esp should be independent observations, each with probability 1/5 of success. we record 1000 attempts. which of the following assumptions must be met in order to solve this problem? it's reasonable to assume normality 0.8(1000), 0.2(1000)%30 approximately normal 0.8(1000), 0.2(1000)% 10 approximately normal srs it is reasonable to assume the total number of cards is over 10,000 it is reasonable to assume the total number of cards is over 1000

  cassidy wants to cut the yellow fabric into strips that are 0.3 yards wide. how many strips of yellow fabric can cassidy make? yellow fabric 16 yards for $108.00.