Imagine you are a teacher of a science class. a student brings in a newspaper article that claims the world will run out of energy by the year 2050 because all the oil will be pumped out of the planet. the student is confused because she has learned in your class that energy can never be created or destroyed. how would you explain to her what "running out of energy" means in the article?

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j