Scientists found a fossilized bone from an organism at an excavation site in North Dakota. When they took the bone back to the lab, they realized that the bone had only 12.5% of the total carbon-14 left. Based on the amount of carbon-14 left in the bone how old is the bone if the half-life of carbon-14 is 5730 years? A) 5730 years old B) 17,190 years old C) 71,625 years old D) Cannot determine answer based on information given.

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