Brody is going to invest in an account paying an interest rate of 3.7% compounded monthly. How much would Brody need to invest, to the nearest hundred dollars, for the value of the account to reach $34,000 in 13 years?

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?

Answer question above and explain each step : )

Find dy/dx using implicit differentiation ln(20+e^xy)=y