Which statement best describes how reproduction leads to natural selection in a population?
organisms do not produce many offspring, so all of them can survive and pass on their traits.
organisms overproduce offspring; consequently, all of them are likely to survive and pass on traits.
organisms overproduce offspring, so only some survive and pass on their traits.
organisms overproduce offspring; consequently, some are likely to survive and pass on traits.

An artificial satellite circles the earth in a circular orbit at a location where the acceleration due to gravity is 6.03 m/s^2. determine the orbital period of the satellite.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

You have a resistor and a capacitor of unknown values. first, you charge the capacitor and discharge it through the resistor. by monitoring the capacitor voltage on an oscilloscope, you see that the voltage decays to half its initial value in 2.70 miss . you then use the resistor and capacitor to make a low-pass filter. what is the crossover frequency fc?