Radioactive decay of granite and other rocks in earth's interior provides sufficient energy to keep the interior molten, to heat lava, and to provide warmth to natural hot springs. this is due to the average release of about 0.03 j per kilogram each year.

find an increase in temperature for a thermally insulated chunk of granite that takes about 12.5 million years to change temperature. (assume that the specific heat capacity c of granite is 800 j/kg⋅c∘. use the equation q=cmδt.)

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?