Grade 12 math: vectors as forces?

two tugs are towing a ship. the smaller tug is 15 degrees off the port bow, and the larger tug is 20 degrees off the starboard bow. the larger tug pulls twice as hard as the smaller tug. in what direction will the ship move?

Two resistors r1 and r2 may be connected either in series or parallel across an ideal battery with emf ε. we desire the rate of energy dissipation of the parallel combination to be 8.75 times that of the series combination. if r1 = 105 ω, what are the (a) smaller and (b) larger of the two values of r2 that result in that dissipation rate?

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. but she does have devices to measure distance and time accurately. she knows her own mass is 77.4 kg , but she is unsure of the mass of a large gas canister in the airless rocket. when this canister is approaching her at 3.50 m/s , she pushes against it, which slows it down to 1.30 m/s (but does not reverse it) and gives her a speed of 2.60 m/s . what is the mass of the canister?

During which step of the scientific method does a scientist make an educated guess about the outcome of an experiment? a. form a hypothesis b. analyze the results c. design an experiment d. collect data