Please derive the Doppler effect of light for “receding” scenario and prove it to be f = f₀ × [(√1-β)/(√1+β)]

If you have a bowl with six apples and you take away four, how many do you have? anyone take a guess and post it. lol getting rid of my account might as well do it with some fun

Three archers each fire four arrows at a target. joe’s four arrows hit at points 10 cm above, 10 cm below, 10 cm to the left, and 10 cm to the right of the center of the target. all four of moe’s arrows hit within 1 cm of a point 20 cm from the center, and flo’s four arrows hit within 1 cm of the center. the contest judge says that one of the archers is precise but not accurate, another archer is accurate but not precise, and the third archer is both accurate and precise. which description applies to which archer? explain

If you wanted to move an electron from the positive to the negative terminal of the battery, how much work w would you need to do on the electron? enter your answer numerically in joules.