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- Write a differential formula that estimates the given change in volume or surface area. Then use the formula to estimate the change when the dependent variable changes from 10 cm to 10.05 cm. 1. The change in the surface area S=4πr2S=4πr2 of a sphere when the radius changes from atoa+draccording to the Florida agency for workplace the monthly average number of uneploment claims in a certain country is given by N (t)= 22.16t^2 - 238.5t + 2005 where t is the number of years after 1990. A) During what year did the number of claims decrease? b)Find the relative extrema and interpret it.The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of CO2 in the atmosphere from 1958 through 2010 is approximated by A(t) = 0.012313t2 + 0.7545t + 313.9 (1 ≤ t ≤ 53) where A(t) is measured in parts per million volume (ppmv) and t in years, with t = 1 corresponding to 1958.† Find the average amount of CO2 in the atmosphere from 1958 through 2010. (Round your answer to two decimal places.) ppmv
- Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, find dV dx (in mm3/mm) when x = 4 mm. V'(4) = mm3/mmWrite the differential formula that estimates the given change in volume or surface. Then, use the formula to estimate the change when the dependent variable changes from 10 cm to 10.05 cm. 14. The change in the volume V=43πr3V=43πr3 of a sphere when the radius changes from atoa+dratoa+dr 15. The change in the surface area S=4πr2S=4πr2 of a sphere when the radius changes from atoa+dratoa+drThe increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of CO2 in the atmosphere from 1958 through 2016 is approximated by A(t) = 0.012414t2 + 0.7485t + 313.9 (1 ≤ t ≤ 59) where A(t) is measured in parts per million volume (ppmv) and t in years, with t = 1 corresponding to 1958.† Find the average amount of CO2 in the atmosphere from 1958 through 2016. (Round your answer to two decimal places.) ______ ppmv/yr
- The rate of increase of the number of married couples M (in thousands) in a country from 1970 to 2005 can be modeled by dM/dt = 1.218t2 − 44.72t + 709.1 where t is the time in years, with t = 0 corresponding to 1970. The number of married couples in 2005 was 59,517 thousand. 1. Find the model for the number of married couples (in thousands) in the country. M(t) = 2. Use the model to predict the number of married couples (in thousands) in the country in 2013. (Round your answer to the nearest integer.) ___________(in thousands)According to the Florida Agency for Workforce, the monthly average number of unemployment claims in a certain county is given by N(t)= 22.16t2 - 238.5t + 2005, where t is the number of years after 1990. a) during what years did the number of claims decrease? b) Find the relative extrema and interpret it.The displacement (in meters) of a particle moving in a straight line is given by s= t2 - 5t + 16, where t is measured in seconds. Find the average velocity from 3.1 to 4 seconds. Average Velocity = ___________ meters/second. (2 decimal places)
- The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of CO2 in the atmosphere from 1958 through 2016 is approximated by A(t) = 0.012414t2 + 0.7485t + 313.9 (1 ≤ t ≤ 59) where A(t) is measured in parts per million volume (ppmv) and t in years, with t = 1 corresponding to 1958.† Find the average rate of increase of the average amount of CO2 in the atmosphere from 1958 through 2016. (Round your answer to two decimal places.)The average velocity between t=30 and t=30+h. f(t) =127850 -16t^2 for 0
