Find the first, second and third derivatives of the following total cost function w.r.t. Q: TC = Q3/8 -8Q2 +5Q/2 + 180

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

One action that a government could take to reduce carbon emission into the atmosphere is to place a tax on fossil fuels. This tax would be based on the amount of carbon dioxide that is emitted into the air when such a fuel is burned. The cost-benefit equation In (1-P)= -0.0036-0.0059T describes the approximate relationship between a tax of T dollars per ton of carbon dioxide and the corresponding percent reduction P (in decimals) in emissions of carbon dioxide. (a) Determine the percent reduction in carbon dioxide when the tax is $30. (b) What tax will cause a 50% reduction in carbon dioxide emissions? (a) The percent reduction in carbon dioxide when the tax is $30 is%. (Type an integer or decimal rounded to the nearest tenth as needed.) C...

Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)