The time t taken to buy fuel at a petrol station varies directly as the number of vehicles v on queue and jointly varies inversely as the number of pumps p available in the station. In a station station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find: i) the relationship between t, p and v; ii)the time it will take to fuel 50 vehicles in the station with 2 pumps; iii) The number of pumps required to fuel 40 vehicles in 20 minutes.​

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).