QUESTION 12 Let X denote the time to failure (in years) of a certain hydraulic component. Suppose the pdf of X is f (x) = k/(x + 4)ª for x > 0. Using the value of k, calculate the probability that time to failure is between 2 and 5 years. O 0.247 0.791 0.753 O 0.209

Find the derivative of the logarithmic function. y = In Isec x + tan x| dy dx %3D

2. As ultrasound propagates into the body, absorption and scattering result in a decrease (or attenu- ation) of the intensity. This can be described by the attenuation coefficient, a. In an experiment to investigate this attenuation in the chest wall of humans, measurements were conducted in which the attenuation of ultrasound through sample human tissue was measured as a function of the ultrasound frequency, f [1]. (a) The figure below (adapted from [1]) shows a set of measurements of the attenuation coef- ficient as a function of the frequency. Fit a linear function to the data points shown. You should draw an approximate line of best fit, determine the slope and intercept of your fit, and then quote the final equation for your line. 12 10 2 1 3 4 5 Frequency (MHz) Attenuation coefficient (dB/cm)

QUESTION 2 If f(x) = - 5х -3 f(x) at x = 2. compute the instontanenus rate of change of OA -3/49 O8.7/41 Oc-7/41 O0.3/49 Oe 1/5