Question Find a unique (numerical) solution for the system of linear equations (x, y, z are unknowns, assume that the determinant of the coe¢ cient matrix is non-zero) ax + dy + gz = a + 2d + 3g bx + ey + hz = b + 2e + 3h cx + fy + iz = c + 2f

Consider a thin rod oriented on the x-axis over the interval [π/2, π]. If the density of the rod is given by ρ(x) = sin x, what is the mass of the rod?

roblem 6 A reinforced concrete footing supports a \( 450 \mathrm{~mm} \) square column. GIVEN : Thickness of the footing \( =645 \mathrm{~mm} \) Effective depth of the flexural reinforcement \( =545 \mathrm{~mm} \) Column axial loads: \( \mathrm{DL}=800 \mathrm{KN} \) \( \mathrm{LL}=800 \mathrm{KN} \) \( \mathrm{U}=1.2 \mathrm{DL}+1.6 \mathrm{LL} \) roblem 6 A reinforced concrete footing supports a \( 450 \mathrm{~mm} \) square column. GIVEN : Thickness of the footing \( =645 \mathrm{~mm} \) Effective depth of the flexural reinforcement \( =545 \mathrm{~mm} \) Column axial loads: \( \mathrm{DL}=800 \mathrm{KN} \) \( \mathrm{LL}=800 \mathrm{KN} \) \( \mathrm{U}=1.2 \mathrm{DL}+1.6 \mathrm{LL} \) Materials : Concrete, \( \mathrm{f}_{\mathrm{c}}{ }^{\prime}=24 \mathrm{MPa} \) Steel, \( \mathrm{f}_{\mathrm{y}}=280 \mathrm{MPa} \) Allowable effective soil bearing capacity \( =219.38 \mathrm{kPa} \) Strength reduction factors: \( \quad 0.75 \) for shear \( 0.90 \) for bending 1. Determine the length required for the footing \( (\mathrm{m}) \) if site conditions limits the width of the footing to \( 2.0 \mathrm{~m} \). A. \( 3.65 \) B. \( 2.45 \) C. \( 4.25 \) D. \( 5.20 \) 2. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) flexural reinforcements along the long dimension of the footing. A. 8 B. 10 C. 12 D. 14 3. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) reinforcements along the short dimension of the footing over a bandwidth (centered on centerline of the column), the bandwidth having a width equal to the length of the short side of the footing. A. 6 B. 9 C. 11 D. 13 4. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) reinforcements (per side) along the short dimension of the footing outside the center bandwidth of the footing. A. 2 B. 3 C. 4 D. 5

simplify the answer 12.5-4. Concentration of NaOH Solution in a Triple-Effect Evaporator. A forced-circulation triple-effect evaporator using forward feed is to be used to concentrate a 10 wt% NaOH solution entering at 37.8°C to 50%. The steam used enters at 58.6 kPa gage. The absolute pressure in the vapor space of the third effect is 6.76 kPa. The feed rate is 13 608 kg/h. The heat-transfer coefficients are U1 = 6246, U2 = 3407, and U3 = 2271 W/m2.K. All effects have the same area. Calculate the surface area and steam consumption. Ans. A = 97.3 m². S=5284 kg steam/h 410

Coursework 3.3 Write the state-space representation for the following systems: Yilt 7. 421t) К. M2 KI m W fit) bi yait) be -Ma RA 2. 20 + yilt) Ta í It) = Uzlt) Milt=VLE R2 R2

Consider the following diagram: Internet Modem Wireless AP Switch Wireless AP DO Wireless AP Server 2.1 Using a table, compare 4 types of area networks. Consider the size of the network and the transmission media that is most likely to be found in each type of network. (8) 2.2 Based on the information given in 2.1, which type if network is shown in the Consider the following diagram: Internet Modem Wireless AP Switch Wireless AP DO Wireless AP Server 2.1 Using a table, compare 4 types of area networks. Consider the size of the network and the transmission media that is most likely to be found in each type of network. (8) 2.2 Based on the information given in 2.1, which type if network is shown in the diagram? Motivate your (2) answer. 2.3 This network has wireless access points. Compare three modulation techniques, using sketches, that could be used by these access points to transmit data. Use the bit-stream 10000101111. (6)

P3.5 The sales revenue, food cost of sales, and guests served for a small fast- food carryout division of a restaurant for the past six months are given below. Sales Month Cost of Revenue Guests Served Sales, Food 1 2. 4 $258,200 274,800 285,600 289,400 298,300 304,600 $ 96,200 104,300 110,500 113,100 118,900 123,700 10,200 10,400 10,300 10,100 10,400 10,500 6 For each of the six months calculate average check and average costs of sales food. Using these averages, calculate an index number. Set the in- dex for month 1 at 100 and complete index numbers for the remaining five months. With the index numbers identified, convert sales revenue and cost of sales food from historic to current dollars.