Question
i need number 3
Determine partial differential^2 f/partial differential y partial differential x A particle is moving along a curve y = x squareroot x, x greaterthanorequalto 0. At time t its coordinates are x(t) and y(t). Find points on the curve at which both coordinates are changing at the same rates. The adiabatic law of the expansion of natural gas is PV = C At a given instant the volume is 1000 cubic feet and the pressure is 10 pounds per square inch. At what rate is the volume changing if the pressure is decreasing at a rate of .06 pounds per square inch per minute? The cost and revenue (in US $) functions for the daily production and sale of 'x' mp3 players are: C(x) = 2000 + 4x and R(x) = 28x - x^2/25 where 0 lessthanorequalto x lessthanorequalto 800 a. Estimate the break-even points b. Estimate the production level (x) that will yield the maximum profit
Explanation / Answer
Given
PV = constant
PV = C for calculating C value
P = 10 and V = 1000cubicfeet = 1.728*10^6 cubic inches
now C = 1.728*10^6 *10 = 1.728 * 107
now P = C/V
dP = C(-1/V^2).dV
0.06 = 1.728*107 (-1 / (1.728 *106)2).dV
=> dV = -10.368*10^3 = 10368cubic inches per minute
=> dV = -6cubic foot per minute
so the volume changes by 6 cubic feet per minute