Evaluate the iterated integral. 2π 0 y 0 x 9 cos (x + y + z) dz dx dy 0 Step 1 We start with the innermost integral. When integrating with respect to z, the other variables x and y are considered constants, and so x 9 cos (x + y + z) dz 0 = 9 $$sin(x+y+z) x 0 = 9 $$sin(2x+y)−sin(x+y) .

Paula makes stained-glass windows and sells them to boutique stores. if her costs total $12,000 per year plus $4 per window for the frame. how many windows must she produce to earn a profit of at least $48,000 in one year if she sells the windows for $28 each? 1. define a variable for the situation. 2. write an inequality that represents her profit. note: revenue is money coming in. cost is money going out. profit is the difference between the revenue and the cost. in other words: revenue - costs profit 3.using words, describe how many windows she must sell to have a profit of at least $48,000.