In 1.logika, provide the necessary proof statements to prove the assertions for: import org. sireum. logika. val num: z = readint() val xdenom: z = readint() val ynum: z = readint() val y denom: z = readint() assume (xnum > 0 & xdenom > 0 & ynum > 0 & ydenom > 0) var r: z = 0 if (xnum *ydenom ynum * xdenom) { r= 1 { //proof here } } else { // proof here // or form of this implication assert(r > = 0 | xnum *ydenom ynum * xdenom) //r> 0 xnum *ydenom > num * xdenom assert(r ! = 0 | xnum *ydenom == ynum * xdenom) // r == 0 xnum *ydenom ==ynum * xdenom

Line joining liquid phase with liquid and solid phase mixture is known as: a) liquidus b) solidus c) tie line d) none of the mentioned

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?

The air in an automobile tire with a volume of 0.015 m3 is at 32°c and 140 kpa gage. determine the amount of air that must be added to raise the pressure to the recommended value of 206 kpa gage. assume the atmospheric pressure to be 128 kpa and the temperature and the volume to remain constant.[r-0.287 kj/kgk]