Chapter 6, Problem 38RE

What is the value of the beta function, B(x, y), where x and y are positive real numbers?

Find the average value of ƒ(x, y) = x² + 4y²,x² + y² = 9. (a) 208.9 (b) 204.8 (c) 206.9 (d) 202.5

Find disjunctive normal form(DNF) and conjunctive normal form(CNF) for each problem. Show all steps that it took to convert to that form. (9) flx,y) (b) flx,y) &) Fixy) = x5 (xry) =xy +X t X.y

Let f(x, y) = xex²-y and P = (13, 169). Calculate ||Vfp|l. (Express numbers in exact form. Use symbolic notation and fractions where needed.) || Vfp|| = Find the rate of change of f in the direction Vfp. (Express numbers in exact form. Use symbolic notation and fractions where needed.) the rate of change: Find the rate of change of f in the direction of a vector making an angle of 45° with Vfp. (Express numbers in exact form. Use symbolic notation and fractions where needed.) the rate of change:

Provide the solution

Evaluate using Beta Function

Please help asap and box your final answer. Thank you.

Lake Ontario has a volume of approximately V =1600 km3. It is heavily polluted by a certain pollutant with a concentration of co = 0.1%.As a part pollution control, the pollutant concentration of the inflow is reduced to cin = 0.02%. The inflow and outflow rates Qin = Qout = Q = 500 km3 per year. Suppose that pollutant from the inflow is well mixed with the lake water before leaving the lake. How long will it take for the pollutant concentration in the lake to reduce to 0.05%?

vaim of the function find the average fcx) = x² = 5x + 6 cosx on th Interval [-1,³].