Drawbridges, such as this one at the tower of london, are raised and lowered by cable systems. now consider the drawbridge illustrated below wherein the nearly horizontal brown door is centered along the vertical brick wall, the door-wall angle is α = 80 o as measured relative to the black hinge axis, the tension (magnitude) in each cable is t = 600 n and the relevant dimensions are a = 330 cm, b = 110 cm, c = 600 cm and d = 390 cm. determine the resultant torque (magnitude) | ( m r ) a x i s | in nm that the two cables contribute to the moment about the hinge axis. | ( m r ) a x i s | = nm

1. the materials manager for a billiard ball maker must periodically place orders for resin, one of the raw materials used in producing billiard balls. she knows that manufacturing uses resin at a rate of 50 kilograms each day, and that it costs $.04 per day to carry a kilogram of resin in inventory. she also knows that the order costs for resin are $100 per order, and that the lead time for delivery is four (4) days.2. at what point should resin be reordered? a. 0 kilograms remainingb. 50 kilograms remainingc. 200 kilograms remainingd. 400 kilograms remaininge. 500 kilograms remaining3. if order size was 1,000 kilograms of resin, what would be the length of an order cycle? a. 0.05 daysb. 4 daysc. 16 daysd. 20 dayse. 50 days4. if the order size was 1,000 kilograms of resin, what would be the average inventory level? a. 50 kilogramsb. 200 kilogramsc. 500 kilogramsd. 800 kilogramse. 1,000 kilograms5. if the order size was 1,000 kilograms of resin, what would be the daily total inventory costs, excluding the cost of the resin? a. $5b. $10c. $20d. $25e. $40

Acarpenter builds an exterior house wall with a layer of wood 2.9 cm thick on the outside and a layer of styrofoam insulation 2.3 cm thick on the inside wall surface. the wood has k=0.080w/(m⋅k), and the styrofoam has k= 0.010 w/(m⋅k). the interior surface temperature is 19.0 ∘c , and the exterior surface temperature is -15.0 ∘c . a.)what is the temperature at the plane where the wood meets the styrofoam? celsius b.)what is the rate of heat flow per square meter through this wall? /m^2

You throw a baseball directly upward at time =0 at an initial speed of 14.9 m/s. what is the maximum height the ball reaches above where it leaves your hand? ignore air resistance and take =9.80 m/s2.