Find f. (x, y, z), f,(x, y, z) and f-(x, Y, z) for f(x, y, z) = e® - 6z – 4 ln(xyz). fr(x, Y, z) = Preview f,(x, y, z) = Preview f.(x, y, z) Preview
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture. Turbulence makes it difficult to directly measure the thickness of the slick at the source where x=0, but for x >0, it is found that y=0.5(x^2 + 3x)/x^3 + x^2 + 4x. Assuming the oil slick is continuously distributed how thick would you expect it to be the source?A ruptured pipe produces a circular oil slick that is y meters thick at a distance x meters from the rupture. It is difficult to directly measure the thickness of the slick at the source (where x=0), but for x>0, it is found that y=0.5(x2+3x)/x3+x2+4x. assuming that the oil slick is continuously distributed, how thick would you expect it to be at the source?
- Also the 7th integration of x,y,z,wAt time 0, M is deposited into Fund X, which accumulates at a force of interest δt =0.006t2. At time m, 2M is deposited into Fund Y, which accumulates at an annual effective rate of 10%. At time n, where m > m, the accumulated value of each fund is 4M. Determine m.From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)
- Let f (x, y, z) = ln(x2 + z) + y2 exz. Find fzyxAn insulated cylinder of solid gold (K = 310 kW/m-k) of radius ,./2 m and height 5 m is heated at one end until the temperature at each point in the cylinder is given by w(x, y, z) = (30 - z2)(2 - (x2 + y2)). Determine the rate of heat flow across each horizontal disk given by z = 1, z = 2, and z = 3, identifying which has the greatest rate of heat flow across it.Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and the value of the maximum rate of decrease.