You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. You will have no access to any electricity, but you must be able to illuminate the entire grounds. You know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. Suppose the intensity is 90 when the distance is 5 m. a. Write an equation to model the situation. b. Solve for the constant of variation. c. Write the equation to model the situation using the constant () of variation. d. You have been given lanterns with 40 light intensity. Use your equation to solve for the distance from the lantern. e. You need to illuminate 225 km. How many meters do you need to light? f. How many lanterns will you need?

The answer is orbit around nucleus

Sorry i don’t know what to do

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s