Consider the paraboloid f(x, y) = 1 - (x²/25) - (y²/9) and the point P (5, 0) on the level curve f(x, y) = 0.
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.

Exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on october 4. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (d) compute the probability that a randomly selected person was not born in january. (type an integer or a decimal rounded to three decimal places as needed.)