The temperature in gavin's oven is a sinusoidal function of time. gavin sets his oven so that it has a maximum temperature of 270°f and a minimum temperature of 230°. once the temperature hits 270°, it takes 20 minutes before it is 270° again. gavin's cake needs to be in the oven for 30 minutes at temperatures at or above 260°. he puts the cake into the oven when it is at 250° and rising. how long will gavin need to leave the cake in the oven? (round your answer to the nearest minute.)

talk back to him about the sport and show him your expertise or leave the room

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.