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

An engine, weighing 3000 n, is supported on a pedestal mount. it has been observed that the engine induces vibration into the surrounding area through its pedestal at the maximum operating speed. determine the stiffness of the dynamic vibration absorber spring in (n/m) that will reduce the vibration when mounted on the pedestal. the magnitude of the exciting force is 250 n, and the amplitude of motion of the auxiliary mass is to be limited to 2 mm note: in this question type-in right numbers, no decimals, no fractions, no unit. approximate to right number if needed

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w

Amass-spring-viscous damper system of mass 3 kg has a frequency of 100 rad/s and is critically damped. its initial conditions are x(0)-3 mm and (0)-2.3 m/s. does the system overshoot its equilibrium position? prove your answer