Consider the paraboloid f(x, y) = 16 - x2/4 - y2/16 and the point p on the given level curve of f. compute the slope of the line tangent to the level curve at p and verify that the tangent line is orthogonal to the gradient at that point. f(x, y) = 0; p(0, 16)

Arectangle with an area of 47 m² is dilated by a factor of 7. what is the area of the dilated rectangle? enter your answer in the box. do not leave your answer as a fraction.

Can some one explain how to slove specifically, what is the value of x? 0.9(x+1.4)-2.3+0.1x=1.6 enter the answer as a decimal in the box. x= ?

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)