Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 4, x = 0, y = 4, y = 6

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.

Michael and imani go out to eat for lunch if their food and beverages cost 25.30 and there is an 8% meals tax how much is the bill

Renee hiked for 6 3/4 miles. after resting, renee hiked back along the same route for 5 1/4 miles. how many more miles does renee need to hike to return to the place where she started? represent your answer as a simplified mixed number, if necessary.