In this problem, we will find the volume of a solid with circular base of radius 22, for which parallel cross-sections perpendicular to the base are squares. to do this, we will assume that the base is the circle x2+y2=4x2+y2=4, so that the solid lies between planes parallel to the xx-axis at x=2x=2 and x=−2x=−2. the cross-sections perpendicular to the xx-axis are then squares whose bases run from the semicircle y=−4−x2√y=−4−x2 to the semicircle y=4−x2√y=4−x2.

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Mariano delivers newspaper. he always puts 3/4 of his weekly earnings in his savings account and then divides the rest equally into 3 piggy banks for spending at the snack shop, the arcade and the subway

Carla is saving money for a trip this summer. she already has some money in her savings account and will add the same amount to her account each week. at the end of 2? weeks, carla has? $130. at the end of 8? weeks, she has? $280. write a linear function in the form y=mx+b to represent the amount of money m that carla has saved after w weeks.