To the nearest tenth, what is the area of the shaded segment when ja=8ft ? ?
a. 27.7 ft squared
b. 33.5 ft squared
c. 5.8 ft squared
d. 13.8 ft squared

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.

Agas initially at p1 = 1 bar and occupying a volume of 0.5 liter is compressed within a piston–cylinder assembly to a final pressure p2 = 4 bar. (a) if the relationship between pressure and volume during the compression is pv = constant, determine the volume, in liters, at a pressure of 3 bar. (b) repeat for a linear pressure–volume relationship between the same end states. reference

Juan created a chart to him study for a test. which headings best complete the chart? x: transparent objects y: opaque objects x: opaque objects y: transparent objects x: high frequency waves y: low frequency waves x: low frequency waves y: high frequency waves