Exercise 1.4: Round the following numbers to the nearest tenth. 1. 1.3556 = 2. 21.4333 = Round the following numbers to the nearest hundredth (two decimal places). 3. 3.546 = 4. 24.9312= Round the following numbers to the nearest whole number. 5. 24.589 = 6. 12.158 =

How many state variables are needed to describe the system? O 4 O 2 O 3 1

Block A, shown in the figure below, has a weight of 60 lb and block B has a weight of 10 lb.Determine: 1. The distance sa that A must descend from rest before it obtains a speed of 2.0 ft/s when k1= 2.0 lb/ft and k2 = 3.0 lb/ft (5 points). 2. The distance sa that A descends from rest before it stops for the following combinations of k1 and k2 (10 points). 3. Draw a graph for sa as function of k2 and provide a physical explanation of the phenomenonobserved (5 points).

8-P11. These rods are welded together to form a "corner" that is supported by three eye bolts.Neglecting friction, determine the reactions at A, B and C when P = 240 lb, a = 12 in., b = 8 in.and c = 10 in.

4-P4Before the trunk of a large tree is felled,cables AB and BC are attached as shown.Knowing that the tensions in cables AB and BC are 555 N and 660 N, respectively,determine the moment about 0 of the resultant force exerted on the tree by the cables at B.

4-P5The towline exerts a force of P = 6 kN at the end of the 8-m-long crane boom. If x = 10 m, determine the position 0 of the boom so that this force creates a maximum moment about point O. What is this moment?

12-79. The particle travels along the path defined by the parabola y = 0.5x². If the component of velocity along the x axis is v, = (5t) ft/s, where t is in seconds, determine the particle's distance from the origin O and the magnitude= 0.of its acceleration when t = 1 s. When t0, x 0, y =

A train is travelling at 60 km/h. If its brakes give the train a constant deceleration of 0.5 m/s²,find the distance form the station where the brakes should be applied so that the train will come to a stop at the station. How long will it take the train to stop?

Determine the following: MATLAB or Excel output will not be accepted. Carry calculations to 4thdecimal point. a. Time for a full cycle: T= \text { b. } \omega_{\text {.a }}= C. Bi in degrees= d. B2 in degrees%3D e. Ba in degrees= f. Ba in degrees = g. Height of the cam profile at theta = 70°. h. Height of the cam profile at theta = 260°.

Find the air-fuel ratio of a 4-stroke, 1 cylinder, air cooled engine with fuel consumption time for 10 cc as 20.0 sec. and air consumption time for 0.1 m³ as 16.3 sec. The load is 16 kg at speed of 3000 rpm. Also find brake specific fuel consumption in g/kWh and thermal brake efficiency. Assume the density of air as 1.175 kg/m³ and specific gravity of fuel to be 0.7. The lower heating value of fuel is 44 MJ/kg and the dynamometer constant is 5000.