(2 points) (a) Compute s4 (the 4th partial sum) of s=∑n=1[infinity]6910n5 : s4= Note: if giving a decimal approximation to this part, you may need to enter more digits than usual. (b) Estimate the error in using s4 as an approximation of the sum of the series (i. e. use ∫[infinity]4f(x)dx≥R4 ): Estimate = (c) Use n=4 and sn+∫[infinity]n+1f(x)dx≤s≤sn+ ∫[infinity]nf(x)dx to find a better estimate of the sum: ≤s≤ Note give each answer accurate to (at least) five decimal places.

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?

Find the slope of a line given the following two points

Acertain population of bacteria demonstrates exponential growth doubles in size every 4 days. how long will it take the population to triple in size?