Let ρal represent the density of aluminum and ρfe that of iron. find the radius of a solid aluminum sphere that balances a solid iron sphere of radius rfe on an equal-arm balance. (use r_f for r fe, rho_a for ρal, and rho_f for ρ as necessary.)

At time t=0, a particle is located at the point (3,6,9). it travels in a straight line to the point (5,2,7), has speed 8 at (3,6,9) and constant acceleration 2i−4j−2k. find an equation for the position vector of the particle.

Urgent pls a. coal consumption levels off and remains flat. b. petroleum, natural gas, and renewables show an increase in consumption c. more nonrenewable resources continued to be consumed than renewable. d. there is little projected increase in nuclear energy use. e. carbon dioxide emissions are projected to decline as we approach 2040. global energy consumption is defined as the total energy used by an individual or organizations from around the world. use the graph above to analyze the projected energy consumption from now until 2040. which statements in the prompt apply? a) a, b, d b) b, c, d c) a, c, d d) a, b, c, d

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)