Assume that all the given functions have continuous second-order partial derivatives. if z = f(x, y), where x = 9r cos(θ) and y = 9r sin(θ), find the following: a) ∂z / ∂r b) ∂z / ∂θ c) ∂^2z / ∂r ∂θ

At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. the cyclic nature of wind and moving sand determines the shape and location of large dunes. at a test site, the prevailing direction of the wind did not change noticeably. however, the velocity did change. fifty-nine wind speed readings gave an average velocity of x = 1075 cm/sec. based on long-term experience, σ can be assumed to be 245 cm/sec. (a) find a 95% confidence interval for the population mean wind speed at this site. (round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec