A cake has two layers. Each layer is a regular hexagonal prism. A slice removes one face of
each prism, as shown.
a. What is the volume of the slice?
b. What is the volume of the remaining cake?

Carley bought a jacket that was discounted 10% off the original price. the expression below represents the discounted price in dollars, based on x, the original price of the jacket.

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?