BC: Write an ending to Luke and Leia's story | As the walls slowly closed in, Luke and Leia desperately tried to find a way out. In the zero gravity environment, Luke quickly floated to the ceiling looking for the escape hatch into empty space. There was less than a meter of room left when he looked down to see Leia's foot stuck in some wiring. He twisted open the hatch, a hissing noise was released as the oxygen escaped. Luke pushed off just in time to escape a painful death only to suffocate in the vastness of space.
FC: How Much Time is left? | By Myles Kincaid
1: Luke and Leia are trapped on a space station. The room is 20 meters long and 15 meters wide. But the length is decreasing linearly with time at a rate of 2 meters per minute, and the width is increasing linearly with time at a rate of 3 meters per minute | The Question | Let L(t) and W(t) be the length and width of the room, respectively, in meters. Let t be the number of minutes since the room was 20 by 15. Write equations for L and W. Let A(t) be the number of square meters of floor area in the room. Write the equation for A Does the area of the room reach a maximum for a positive value of t? If so, what is the value of t? If not, how do you tell? When will the area of the room be zero? What does this mean? Write an ending to Luke and Leia's story
2: Write an equation for L and W | L=20-2t W=15+3t
3: Write the equation for A | A=(20-2t)(15+3t)
4: Does the area of the room reach a maximum for a positive value of t? If so, what is the value of t? If not, how do you tell? | Yes, the room reaches a maximum area of 337 meters when the value of t is equal to 2.7 minutes.
5: When will the area of the room be zero? What does this mean? | The area of the room will equal zero after 10 minutes. This means that the length has finally decreased to zero leaving no room.