Question Solved1 Answer in decibel scale. A value of 7 in linear scale corresponds to Select one: a. 3 dB b. 8.45 dB c. 10.84 dB d. 7.78 dB

This exercise studies linearity. (a) Show that the helicopter model defined in Example 2.1 is linear if and only if the initial angular velocity y(0) = 0. (b) Show that the cascade of any two linear actors is linear. (c) Augment the definition of linearity so that it applies to actors with two input signals and one output signal. Show that the adder actor is linear.

19. Which of the following is not a characteristic of the mean? (a) All the observations are used in its calculation. (b) It is influenced by extreme values. (c) The sum of the deviations from the individual observations and the mean is always greater than zero. (d) all of the above.

1. Find the pressure due to a column of mercury 80 cm high. 2. A rectangular tank 6 x 8 ft is filled with a gasoline to a depth of 80 ft. The pressure at the gasoline is 14.7 psi. Find the pressure at the bottom of the tank and force exerted on the bottom. 3. A 130 lb woman balances on the heel of her right shoe which is 1 in radius. How much pressure does she exert on the ground?4. An amount of heat equal to 2500 J is added to a system, and 1800 J of work is done on the system. What is the change in internal energy of the system? 5. Determine the change in internal energy of 1.0 L of water at 100 deg C when it is fully boiled, which results in 1671 L of steam at 100 deg C. Assume the process is done at atmospheric pressure. 

B.3. Let f: X Y and g: Y → Z be functions. For each of the following statements, decide whether it is true or false, providing either a proof or a counterexample. (a) If f is surjective and g is bijective, then go f is surjective. (b) If f is injective and g is surjective, then go f is bijective. (C) If go f is bijective, then f is injective and g is surjective. B.4. Let X and Y be sets and f: X + Y be a function. Define a relation on X by x1 ~ 2, if and only if f(x1) = f(C2). Prove that is an equivalence relation.

Tamara has 30 m of fencing which she can use to surround a rectangular garden. [5] a. What is the maximum area of the garden, assuming Tamara uses fencing for all four sides? b. How much additional area can be obtained if Tamara uses the side of her house and her neighbour’s fence as two sides of the garden? Explain and support your answer mathematically.

A walkway is illuminated by Son 230W lamps each having a luminous intensity of 4750 candela in all directions below the horizontal. Each lamp is installed at a height of 6m and the distance between them is 16 metres Calculate the illuminance contributed by each lamp: ) directly underneath. . 8 metres from the base. (1) 16 metres from the base. (iv) 32 metres from the base. (6) The total illuminance at: 0 the base of each lamp post. (ii) midway between the base of each lamp post. (c) Sketch an illuminance profile on a straight line joining the base of each lamp post.