Using de moivre’s theorem, express cos 6θ and sin 6θ in powers of cos θ and sin θ. do i have to use binomial expansion? ?

David is spreading mulch on a triangular area of his flower bed. the coordinates of the vertices of the area are (1, 3), (9, 3), and (4, 6). what is the area of the triangle if each square has an area of 3 square feet?

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to