i need number 3 Determine partial differential^2 f/partial differential y partia

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

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