During the battle of bunker hill, it is commonly thought that the commanders gave the order "don't shoot until you see the whites of their eyes! " to make sure the british troops were close enough that a hit was a certainty. if take your commander's instructions literally and don't fire until the whites of the enemy's eyes are just resolvable by your pupil, how far away (in meters) are they when you open fire? assume your target has an eye which is 2.9 cm across, the diameter of your pupil is 5.3 mm, and you are observing at a wavelength of 555 nm.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2