Ali oil field contains 8 wells which produce a total of 1600 barrels of oil per day. for each additional well that is drilled, the average production per well decreases by 10 barrels per day. how many additional wells should be drilled to obtain the maximum amount of oil per day? determine whether f(x) satisfies the hypotheses of the mean value theorem; and, if so, find the point(s) c in (a, b) such that f(b) - f(a) = f'(c)(b - a), if f(x) = 1 + squareroot x^2 + 16, on [0, 3]. find the indefinite integral: integral (cube root t - cot t) dt integral (x - 1/x)^2 dx

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?