Roof Valley Problem: Figure 10-5e shows an L-shaped house that is to be built. Roof 1 and Roof 2 will have normal vectors The two roofs will meet at a valley. Point (30, 30, 10) is at the lower end of the valley. The dimensions are in feet. a. Find particular equations of the two plane roofs. b. The top end of the valley is at (15, 15, z). Use the equation of Roof 1 to calculate the value of z. Show that the point satisfies the equation of Roof 2, and give the real-world meaning of this fact. c. How high will the ridge of the roof rise above the top of the walls? d. Write the displacement vector from the bottom of the valley to the top. e. Find the obtuse angle the valley makes with the bottom edge of Roof 1. f. A piece of sheet metal flashing is to be fitted into the valley to go underneath the shingles. How long will it be? g. The two roof sections form a dihedral angle equal to the angle between the two normal vectors or to the supplement of this angle. The flashing must be bent to fit this angle. Calculate the obtuse dihedral angle between the two roof sections. h. Why do you think builders put flashing in roof valleys?

Cognitive Psychology PSYC 2 24: C hapters 4-5 Chapter 4: Working Memory ❖ Working Memory - short memory of material brain is processing in the present ➢ A few pieces are accessible so you can continue working with them ➢ (2+5)x3 → need to keep in mind what 2+5 equals...