Amountaintop is a height y above the level ground. a woman measures the angle of elevation of the mountaintop to be θ when she is a horizontal distance x from the mountaintop. after walking a distance d closer to the mountain, she measures the angle of elevation of the mountaintop to be φ. neglecting the height of the woman’s eyes above the ground, draw a well-labelled diagram representing this situation and find an expression for the height of the mountain, y, in terms of d, φ, and θ. note that your expression cannot contain x.

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.