Rectangle rect is rotated 360° about the y-axis. find the surface area and volume of the resulting solid of revolution. be sure to do the following: indicate the type of solid that was formed and its key dimensions. state all formulas. show all substitutions and work. use appropriate units in your answers

Given the function f(x) = 3x + 1, evaluate f(a + 1). a. 3a + 1 b. a + 2 c. 3a + 4

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?

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. identify the domain for each of the given functions.