Spot builds dog houses. He needs 10 wooden boards and 15 nails to build a small dog house; and he uses 15 wooden boards and 45 nails for a large dog house. Spot makes $40 profit on every small dog house and $52 profit on every large dog house. If he has 60 wooden boards an 135 nails, how many LARGE dog houses should he make to maximize his profit?

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.