Explain how we know dark matter exists if we cannot see it

Atown is considering building a biodiesel power plant that would burn biomass to generate electricity. which of the following correctly lists an advantage and a disadvantage of this project?

In a vernier instrument the main scale is in 1/2 mm divisions .vernier is made by redividing 19 such divisions into 20 equal parts. calculate the least count of the instrument.

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.