Aspring with a spring constant 3 n/m is loaded with a 4 kg mass and allowed to reach equilibrium. it is then displaced 1 meter downward and released. suppose the mass experiences a damping force in newtons equal to 2 times the velocity at every point and an external force of f(t)=5sin(4t) driving the system. set up a differential equation that describes this system and find a particular solution to this non-homogeneous differential equation:

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.